10mat41- engineering mathematics-iv
TRANSCRIPT
10MAT41- ENGINEERING MATHEMATICS-IV
SYLLABUS
Sub Code: 10MAT41 IA Marks: 25
Hours/week: 04 Exam Hours: 03
Total Hours: 52 Exam Marks: 100
PART – A UNIT 1:
NUMERICAL METHODS Numerical solutions of first order and first degree ordinary differential equations – Taylor’s
series method, Modified Euler’s method, Runge – Kutta method of fourth order, Milne’s and
Adams-Bashforth predictor and corrector methods (All formulae without
Proof). 6 Hours
UNIT 2:
COMPLEX VARIABLES Function of a complex variable, Limit, Continuity Differentiability – Definitions. Analytic
functions, Cauchy – Riemann equations in cartesian and polar forms, Properties of analytic
functions. Conformal Transformation – Definition. Discussion of transformations: W = z2, W =
ez, W = z + (I/z), z ≠ 0 Bilinear transformations.
7 Hours
UNIT 3:
COMPLEX INTEGRATION Complex line integrals, Cauchy’s theorem, Cauchy’s integral formula. Taylor’s and Laurent’s
series (Statements only) Singularities, Poles, Residues, Cauchy’s residue theorem (statement
only). 6
Hours
UNIT 4:
SERIES SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS AND SPECIAL
FUNCTIONS Series solution – Frobenius method, Series solution of Bessel’s D.E. leading to Bessel function
of fist kind. Equations reducible to Bessel’s D.E., Series solution of Legendre’s D.E. leading to
Legendre Polynomials. Rodirgue’s formula. 7
Hours
PART – B UNIT 5:
STATISTICAL METHODS Curve fitting by the method of least squares: y = a + bx, y = a + bx + cx
2, y = ax
b y = ab
x, y
= aebx, Correlation and Regression.
Probability: Addition rule, Conditional probability, Multiplication rule, Baye’s theorem.
6 Hours
UNIT 6: Random Variables (Discrete and Continuous) p.d.f., c.d.f. Binomial, Poisson, Normal and
Exponential distributions.
7 Hours
UNIT 7: Sampling, Sampling distribution, Standard error. Testing of hypothesis for means. Confidence
limits for means, Student’s t distribution, Chi-square distribution as a test of goodness of fit.
7 Hours
UNIT 8: Concept of joint probability – Joint probability distribution, Discrete and Independent random
variables. Expectation, Covariance, Correlation coefficient.
Probability vectors, Stochastic matrices, Fixed points, Regular stochastic matrices. Markov
chains, Higher transition probabilities. Stationary distribution of regular Markov chains and
absorbing states.
6 Hours
Text Book:
Higher Engineering Mathematics by Dr. B.S. Grewal (36th
Edition – Khanna Publishers)
Unit – VIII: Text book: Probability by Seymour Lipschutz (Schaum’s series) Chapters 5 & 7
Reference Books: 1. Higher Engineering Mathematics by B.V. Ramana (Tata-Macgraw Hill).
2. Advanced Modern Engineering Mathematics by Glyn James – Pearson Education.
Note: 1. One question is to be set from each unit.
2. To answer Five questions choosing atleast Two questions from each part.
LESSON PLAN
Sub Code: 10MAT41 Hours/week: 04
Sub: Engineering Mathematics-IV Total Hours: 52
Period
No. TOPIC TO BE COVERED (IN DETAIL)
NUMERICAL METHODS
1 Numerical solutions of first order first degree O.D.E: Taylor’s series method-
problems
2 Euler’s methods - problems
3 Modified Euler’s method - problems
4 Runge-Kutta method of fourth order – problems
5 Milne’s predictor and corrector method -problems
6 Adam’s-Bashforth predictor and corrector method- problems
COMPLEX VARIABLES
7 Function of complex variables, limits, continuity, and differentiability.
8 Analytic functions, Cauchy-Riemann equations in Cartesian form.
9 Analytic functions, Cauchy-Riemann equations in Polar form and
Consequences.
10 Construction of analytic function in Cartesian form
11 Construction of analytic function in Polar form
12 Definition of Conformal transformation: z2
13 Transformation : ez
14 Transformation: +Z
Z
a2
15 Bilinear transformations.
COMPLEX INTEGRATION
16 Line integral – Problems.
17 Cauchy’s theorem, Corollaries-problems
18 Cauchy’s integral formula - problems.
19 Cauchy’s integral formula for derivatives - problems
20 Taylor’s series.- Problems.
21 Laurent’s series.- Problems
22 Singularities, Poles, residues – Problems
23 Residue theorem – Problems
SERIES SOLUTION OF O.D.E AND SPECIAL FUNCTIONS
24 Series solution- Frobenius method
25 Series Solution of Bessel’s Differential Equation
26 Equations reducible to Bessel’s D E
27 Recurrence relations
28 Series Solution of Legendre’s Diff equation
29 Recurrence relations
30 Rodrigue’s formulae
STATISTICAL METHODS
31 Curve fitting by the method of Least Squares: y= a+bx- problems.
32 y = a.bx , y = ax - problems,
33 y=a+bx+cx2 - problems
34 Correlation – problems
35 Regression - problems
36 Addition rule, Conditional probability, Multiplication rule-Examples
37 Baye’ Theorem-Examples
RANDOM VARIABLES
38 Discrete Random Variables-PDF-CDF and examples
39 Continuous Random Variables-PDF-CDF and examples
40 Binomial Distributions Examples
41 Poisson’s Distributions – Examples
42 Normal Distribution-Properties & Examples
43 Exponential Distribution & Examples
SAMPLING DISTRIBUTION
44 Sampling, Sampling Distribution, Standard error.
45 Testing of Hypothesis for Means,.
46 Confidence limits for Means
47 Student’s t-distribution
48 Chi- square distribution as a test of goodness of fit
JOINT PROBABILITY DISTRIBUTION AND MARKOV CHAINS
49 Concept of joint probability, joint distribution-discrete random variables
50 Independent random variables, Problems on Expectation and Variance
51 Markov chains-Introduction, probability vectors
52 Stochastic matrices, Fixed points and Regular Stochastic matrices
Staff HOD-IEM
QUESTION BANK
SEMESTER: IV Subject : ENGG. MATHEMATICS
Subject Code: 10MAT41
NUMERICAL METHODS 1) Using the Taylor’s series method,find the solution at the point 0.1 of the intial value problem
1)0(,2 =−= yyxdx
dy
2) Using the Taylor’s series method, find the solution at the point 2.01.0 == xandx of the
initial value problem 1)0(,22 =+= yyxdx
dy.
3) Use modified Euler method to find y (1.2) and y (1.4) given that y
1 = x
2 + y,
y (1) = 2 taking h =0.2
4) Using modified Euler’s method obtain the solution of )1(' yxy += with 1)1( =y at 1.1=x
with step length 2.0=h
5) Find y (0.2) and y (0.4) using R-K IV order method given y1 + 2xy
2 = 0 Y (0) = 1
6)Using the fourth order Runge Kutta method, solve the problem
1.02.01)0(,2' ofstepsinxatyyxy ==+= .
7) By using the Milne’s Predictor-corrector method, find an approximate solution of the
equation int0,2
potheatxx
y
dx
dy≠=
13.6)75.1(5.4)5.1(,13.3)25.1(,2)1(2 ===== yandyyythatgivenx
8) By using the Milne’s Predictor-corrector method, find an approximate solution ofy
at 17.0)6.0(07.0)4.0(,02.0)2.0(,0)0(,8.0 2 ====−== yandyyyyxdx
dythatgivenx
9)By using the Adam Bashforth Predictor-corrector method, find an approximate solution of the
equation int,22 potheatyxdx
dy+=
18.6)75.0(6.4)5.0(,5.3)25.0(,2)0(1 ===== yandyyythatgivenx
10) By using the Adam Bashforth Predictor-corrector method, find an approximate solution ofy
at 18.0)3.0(05.0)2.0(,03.0)1.0(,0)0(,24.0 2 ====== yandyyyxydx
dythatgivenx
COMPLEX ANALYSIS
1.Show that following functions f(z) are analytic and hence find their derivatives
i. ez ii. Cosz iii. Sin2z
2.Construct the analytic function f(z) = u + i v as a function z using the following data
i.u = ex( x cos y – y sin y ) ii) v = e
–x ( x cos y + y sin y )
3.Show that the following functions are harmonic and find their harmonic conjugates. Also find the
corresponding analytic function
i) u= (x-1)3 – 3xy
2 +3y
2 ii) v = e
-2y sin2x
4.Show that f(z) = x- iy / x2+ y
2 is holomorphic except at the origin.
5.Show that f(z) = 2z +3z is not analytic. 6.Show that an analytic function with constant modulus is itself a constant.
7.Determine which of the following function is harmonic and hence find its harmonic
conjugate. Also determine the corresponding analytic function.
i)u= e2x(xcos2y –ysin2y )
8.Find the bilinear transformation which maps the points as below
1. z= 2,i,-2 to w= 1,I,-1.
2. z=1,i ,-1 to w=i,0,-1.
3.z=2,1,0 to w=1,0,i.
9. Show that there are two points which are left invariant by the general bilinear
transformation. What is the condition that
1. these two points coincide?
2. these are two finite fixed points
3. one finite and another infinite fixed point
4. only one infinite fixed point.
10. Prove that w=z/1-z maps the upper half of the z plane onto the upper half of the w-plane.
11. Show that the transformation w=z-i/1-iz maps the unit circle width center origin in the z-plane
onto the real axis in the w-plane.
12. Given w=z-i/iz-1 show that the unit circle with center origin in the w-plane is mapped on to the
imaginary axis in the z-plane.
13.Obtain the image of the region bounded by the lines x=1,x=2,y=1,y=2 under the transformation
w=ez & sketch the region.
14. If w=x+i( by/a), 0<a<b,prove that the inside of the circle x2 +y
2=a
2corresponds, to the inside of
an ellipse in the w-plane.
15. Given w=cosz show that the straight lines parallel to the co-ordinate axes in the z-plane maps on
to ellipse and hyperbola in the w-plane with the same foci.
16.Evaluate,
( ) dzz
i
∫+2
0
2
along
i ) the line y =x\2
ii) the real axis to 2 and then to the point 2+ i
17. Verify Cauchy`s theorem for the function f(z) = 3z2 + iz - 4
where C is the square having vertices as 1± I, -1± i
18. Verify Cauchy`s theorem for the function f(z) =z2 over the curve C formed by the line segment
joining the points O(0,0), P(2,0), Q(1,I) and O(0,0).
19. Evaluate ∫ −cz
dz
94 2
where C is the circle 2=z
20. ∫ −+c
zz
zdzEvaluate
)9)(1( 22
where C is the circle
I) 2=z ii)
22 =−z
21.The necessary condition that a single valued function w= f(z)=u(x,y)+iv(x,y) may be analytic at
any point z=x+iy is that, there exists four continuous first order partial derivatives
y
v
x
v
y
u
x
u
∂∂
∂∂
∂∂
∂∂
,,,
and satisfy the equations
y
u
x
v
y
v
x
u
∂∂
−=∂∂
∂∂
=∂∂
,
These are known as cauchysriemann equations. Prove the above equations in Cartesian form.
22. State and prove cauchy Reimann equation in the polar form.
23.State and prove the cauchy integral theorm.
24. If f(z) is analytic inside and on a siple closed curve C and if ‘a’ is a point within C then show
that
∫ +−=
c
n
n dzaz
zf
i
naf
1
)(
)(
)(
2
!)(
π.
25 If f(z) is analytic at all points inside the circle C:!z-a!=r then for all z inside C
.......)(''
!2
)()(')()()(
2
+−
+−+= afaz
afazafzf
26.State and prove Laurent’s. theorm.
27. Expand the following functions in a taylor’s series about the indicated point:
izzb
zz
a
π=
=+
,sinh)
1,1
1)
28. Expand f(z) in a laurent’s series valid for regions as indicated:
21
1!:!)2)(1(
32)(
3!!1;)3)(1(
)(
2
<<
<−+
+=
<<++
=
zand
zzz
zzf
and
zzz
zzf
29.If z=a is a pole of order m of f(z) then the residue of f(z) at z=a is denoted by R[m,a] and
show that
)}(){()!1(
1],[
1
1
lim zfazdz
d
mamR m
m
m
az
−−
=−
−
→ 30. State cauchy’s residue theorem.
31.Find the residue at each pole for the following functions:
22
2
)4(
1)
)1)(1()
+
−
+−
z
zb
zz
za
32. Evaluate the following integrals by using Cauchy’s residue theorm.
4:,)2/(
sin)
1::41(
1)
3
6
)22
=−
=−
+
∫
∫
C
C
zCdzz
zb
zCdzzz
za
π
1. Obtain the solution of the Bessel’s differential equation x
2y′′ +xy′ + (x2-n2)y =0
leading to Jn(x).
or.
Obtain the series solution to the Bessel’s differential equation leading to Jn(x).
2. Prove the following:
xx
xJ
xx
xJ
xxJxxJdx
d
xJxJdx
d
cos2
)(.4
sin2
)(.3
)()]([.2
)()(.1
2
1
2
1
01
10
π
π
=
=
=
−=
−
3. When n is an non negative integer, show that y = A Jn(x) +Byn(x)
where A & B are arbitarary constants &
∫=2)]([
)()(xJx
dxxJxY
n
nn
is a solution of Bessel’s differential equation
4. Show that x-n Jn(x) is a solution of the differential equation xy′′ + (1+2n)y′ + xy = 0.
5. Show the following
∫ −=
+=
=+
=
→
−
−
x
o
nnnx
xxJxxJxxdxxJ
nxJ
x
xxJxJ
xxJ
xJ
0
10
0
2
2/1
2
2/1
2/1
2/1
]cos)(sin)([sin)(.4
)1(2
1)(
1.3
2)}({)}(.{2
tan)(
)(.1
lim γ
π
6. Prove the following reccurence relations.
)()()('.6
)()()('.5
)()}({.4
)()}({.3
)}()({2
1)('.2
)}()({)(2.1
1
1
1
1
11
1!
xxJxnJxxJ
xnJxxJxxJ
xJxxJxdx
d
xJxxJxdx
d
xJxJxJ
xJxJxxnJ
nnn
nnn
n
n
n
n
n
n
n
n
nnn
nnn
+
−
+−−
−
+−
−+
−=
−=
−=
=
−=
+=
7. Show that
]cos3
sin3
[2
)(.2
2
cos)(sin)(.1
2
2
2/5
2/32/33
xx
xx
x
xxJ
xxxJxxJ
−−
=
=− −
π
π
8. Prove the following .
∫ −−= )(2
)()(.1 123 xJx
xJcdxxJ
where c is an arbitrary constant.
9. Ifα and β are the roots of the equation Jn(x)=0. Show that
∫
=
≠=
+
1
0
2
1 )]([2
1
0
)()(βα
βαβα
ifxJ
if
dxxJxxJn
nn
10. Prove that (Generating function of Jn(x))
∑∞
−∞=
− =n
n
n
ttx txJe )()/1)(2/(
11.Prove the following
1.J0(x)+2J2(x)+2J4(x)+--------=1
2.J1(x)-J3(x)+J5(x)-+-----------=sinx
12.Prove the following
2/30
0
0
2
1
12
2
1
2
2
)22()(.4
)sin(02cos)1(
)(.3
)()12()1(2cos.2
)()2()1(2sin.1 1
ba
adxbxJxe
dxscnxJ
xJnxx
xJnxx
ax
n
n
n
n
n
n
nn
+=
−=
+−=
−=
∫
∫
∑
∑
∞−
∞
=+
∞
=
+
π
θθθπ
13. If n is an integer,prove that
∫ −=π
θθθπ
0
)sincos(1
Jn(x) dnx
LEGENDRE’S DIFFERENTIAL EQUATION
1. Obtain the series solution of Legendre’s Differential equation leading to
Legendre polynomial.
2. Express the polynomial in terms of legendre polynomial.
a. 2x3-x
2-3x+2
b. x4+3x
3-x
2+5x-2
c. x3-3x
2+5x+1
3. Prove the following:
a. )(3
2)()(
3
21 210
2 xPxPxPxx −+=−+
b.3
22)(
5
3)(
3
4)(
5
88324 123
23 +−−=+−− xPxPxPxxx
4. Show that :
)()1()(.
)cos5cos3(8
1)(cos.
)cos31(4
1)(cos.
3
2
xPxPc
Pb
Pa
n
n
n −=−
+=
+=
θθθ
θθ
5. Generating Function for Pn(x)
Prove that (1-2xz+z2)-1/2
=∑∞
=0
)(n
xPn
5. Prove the following Recurrence relations:
a. (2n+1)xPn(x) = (n+1) Pn+1(x) +nPn-1(x)
b.nPn(x) = xPn’(x)-Pn-1
c. (2n+1)Pn(x) = P′n+1(x)-P′n-1(x) d. (1-x
2)P′n(x)=n{Pn-1(x)-xPn(x)}
e. (2n+1)(x2-1)P′n(x)= n(n+1){Pn+1(x)-Pn-1(x)}
f. (1-x2)Pn′(x) = (n+1) {xPn(x)-Pn+1(x)}
6. Rodrigue’s Formula for Pn(x)
i.e. Pn(x) = })12{()!(2
1 n
n
n
nx
dx
d
n−
7. Evaluate Po(x),P1(x), P2(x),P3(x), and P4(x) by using the Rodrigue’s formula.
8. Show that Pn(x) =
−
−−−
n
n
n
nn xx
dx
d
n 2
11)1(
!
)1(
9. Orthogonolity of Legendre Polynomials
i.e. ∫−
=+
≠=
1
1 12
2;0
)()(nm
n
nmdxxPnxPm
10. Prove the following :
[ ]
∫
∫
∫ ∫
−
−
− −
=+
+<
=
+=−+−
−−
=
1
1
1
1
1
1
1
1
)!12(
)!(12
0
)(.
.12
22/1)221)((.
)12()()!(2
)1()()(.
nifmn
nn
nifm
dxxxmPnc
n
hndxhxhxPnb
dxnxxfnnn
ndxxPnxfa
STATISTICS AND PROBABILITY
1. Fit a straight line by the method of least squares to each of the following data.
X: 0 1 3 6 8
Y: 1 3 2 5 4
2. Fit an equation of the form y=abx to the given data
x: 2 3 4 5 6
y: 8.3 15.3 33.1 65.2 127.4
3. Fit a parabola each of the following data.
X: -1 0 0 1
Y: 2 0 1 2
4 .For the data in the following table compute (a) standard deviation of x (b)standard
deviation of y (c) covariance of x and y, and (d)the coefficient of correlation between x and
y.
5. The standard deviation of x and y are 2 and 3 respectively. If the coefficient of the
correlation between x and y is 0.4, find the standard deviation of x+y and x-y,
6. Find the coefficient of correlation and the regression lines for the following data
x : 1 2 3 4 5 6 7 8 9 10
y : 10 12 16 28 25 36 41 49 40 50
7. The correlation coefficient between two variables x and y is r = 0.6. If σx =1.5
σy = 2.00, x = 10 and y = 20 , find the regression of y on x and of x on y.
8. For the data given in the following table, compute (a) standard deviation of X,
(b) standard deviation of Y , (c) Co-variation of X and Y , and (d) the
coefficient of correlation between X and Y.
X 1 3 4 6 8 9 11 14
Y 1 2 4 4 5 7 8 9
9.Psychological tests of intelligence and computational ability were applied to
ten children. Following is the record showing intelligence ratio (I.R) and
ability ratio (A.R) . Calculate the coefficient of correlation
10.Find the coefficient of correlation and regression lines for the following data.
X 1 2 3 4 5 6 7 8 9 10
Y 10 12 16 28 25 36 41 49 40 50
11. The following table indicates the test scores of ten sales person in an
intelligence test and their weekly sales (in hundred units)
Find the regression line of the sales on test scores and estimate the most probable
weekly sale of the sales person whose test score is 85.
I.R.(x) 105 104 102 101 100 99 98 96 95 94
A.R.(y) 101 103 100 98 95 96 104 97 97 96
Test scores 40 70 50 60 80 50 90 40 60 60
Sales 2.5 6.0 4.5 5.0 4.5 2.0 5.5 3.0 4.5 3.0
12. In a partially destroyed laboratory data, only the following regression
equations were available: 7X-16Y+9=0,5Y-4X-3=0.Find the coefficient of
correlation between X and Y.
13.A correlation coefficient based on a sample of size 27 was computed to be
0.40. can we conclude at a significance level of 0.01 that the corresponding
population correlation coefficient differs from 0?
14.A correlation coefficient based on a sample of space 35 was computed to be
0.50. Can we reject the hypothesis that the population correlation coefficient is
ρ=0.70 at 0.05 significance level? 28. A correlation coefficient of 0.5 is found from a sample of size 19 . Can we say
that the population correlation coefficient is closed to 0.3 at 5% level of
significance?
15. Find 99% confidence limits for correlation coefficient which is computed to
be 0.60 from a sample of size 28.
16.A student’s study habits are as follows: If he studies one night he is 70% sure
not to study next night; on the other hand if he does not study one night, he is
60% sure not to study the next night as well. Supposing that he studies on
Monday night, find the probability that he does not study on Friday night. In
the long run, how often does he study.
17.A house wife buys 3 brands of soaps : A, B, C. She never buys the same brand on
successive weeks. If she buys brand A in a week she buys brand B in next week. If she buys
brand other than A in a week, then in the next week she is three times as likely to buy brand A as
the other brand. Supposing that she has brought brand B in
the first week, find the probability of her buying each of the three brands in the fourth week.
29. A barber takes 25 minutes to complete one hair cut on the average. If the customers
arrive at an average interval of 40 minutes, how long on the average must a customer wait
for service?
A company wants to employ an additional assistant. The arrival rate of jobs is found to be 3
per hour and the present service rate is 4 jobs per hour and the cost of present service is Rs.
7.00 per hour. Each delayed job incurs an opportunity cost of Rs. 10.00 per hour. Should the
extra assistant be employed?
30. A normal population has a mean 0.1 and a standard deviation 2.1. Find the
probability that the mean of a sample of 900 members will be negative.
31. Find the probability that in 120 tosses of a fair coin i ) between 40% and 60% will be
heads, ii) 5/8 or more will be heads.
32. It has been found that 2% of the items produced by a certain machine are defective.
What is the probability that in a sample of 400 items, i ) 3% or more, ii) 2% or less
will be defective?
33. A certain machine part manufactured by a company has a weight of 0.5 gm on the
average with a standard deviation of 0.02gm. What is the probability that the mean
weight in two lots, of 1000 such parts each, will differ by more than 0.02 gm.
34. An urn contains 60 red marbles and 40 white marbles. Two sets of 30 marbles each
are drawn with replacement from the urn and their colors are noted. What is the
probability that the two sets differ by 8 or more red marbles.
35. A sample of 5 measurements of the diameter of a sphere were recorded as 6.33,
6.37,6.36,6.32,6.37 mm. Determine unbiased and efficient estimate of i ) the true
mean, and ii) the true variance.
36. For the frequency distribution given below, find the unbiased and efficient estimate
for the mean and variance.
xi 60 61 62 63 64 65 66 67 68
fi 2 0 15 29 25 12 10 4 3
37. Suppose that 10, 12, 15, 16, 19 is a sample taken from a normal population with
variance σ2 = 6.25, find the 95% of confidence interval for the mean µ.
38. If the measurement of a sample mean is recorded as 216.48 with a probable error of
0.272, find the 95% confidence limits for the measurement.
39. Suppose that the CPU service time of a job is normal variate with standard deviation
1.5 sec. Find the how large a sample is to be taken in order to assert with 99%
confidence that the estimated mean service time is less than half a second of the true
mean time.
40. In a sample of 200 items produced by a machine, 15 were found defective, while in a
sample of 100 items produced by another machine, 12 were found defective. Find
99% and 99.74% confidence limits for the difference in proportions of defective
items produced by the two machines.
41. In a hospital, 230 females and 270 males were born in a year. On the basis of this
information, can the hypothesis that sexes are born in equal proportions be rejected.
42. The mean life time of sample of 150 bulbs produced by a company is computed to be
1570 hours with a standard deviation of 120 hours. Test the hypothesis that the mean
life time of all bulbs produced by the company is 1590 hours at 0.01 and 0.05 levels
of significance.
43. A sample of 100 electric bulbs produced by manufacturer A showed a mean life time
of 1190 hours and a standard deviation of 90 hours. A sample of 75 bulbs produced
by manufacturer B showed a mean life time of 1230 hours with a standard deviation
of 120 hours. Is there a difference between the mean life time of the two brands at a
significance level of 0.05.
44. The mean life time of electric bulbs manufactured by a company has in the past been
1120 hours with a standard deviation of 125 hours. A sample of 8 bulbs chosen from
supply of newly produced bulbs showed a mean life time of 1070 hours. Test the
hypothesis that the mean life time has not changed, using a level of significance of
0.01.
45. The following table gives the marks of 10 students in two tests
Test 1 67 24 57 55 63 54 56 68 33 43
Test 2 70 38 58 58 56 67 68 75 42 38
Can we conclude that there is a difference in the performance in the two tests at 0.5
level of significance?
46. For the data given in the following table, compute (a) standard deviation of X,
(b) standard deviation of Y , (c) Co-variation of X and Y , and (d) the
coefficient of correlation between X and Y.
X 1 3 4 6 8 9 11 14
Y 1 2 4 4 5 7 8 9
47. Psychological tests of intelligence and computational ability were applied to ten
children. Following is the record showing intelligence ratio (I.R) and ability ratio
(A.R) . Calculate the coefficient of correlation
I.R.(x) 105 104 102 101 100 99 98 96 95 94
A.R.(y) 101 103 100 98 95 96 104 97 97 96
48. Find the coefficient of correlation and regression lines for the following data.
X 1 2 3 4 5 6 7 8 9 10
Y 10 12 16 28 25 36 41 49 40 50
49. The following table indicates the test scores of ten sales person in an
intelligence test and their weekly sales (in hundred units)
Test scores 40 70 50 60 80 50 90 40 60 60
Sales 2.5 6.0 4.5 5.0 4.5 2.0 5.5 3.0 4.5 3.0
Find the regression line of the sales on test scores and estimate the most probable
weekly sale of the sales person whose test score is 85.
50. In a partially destroyed laboratory data, only the following regression
equations were available: 7X-16Y+9=0,5Y-4X-3=0.Find the coefficient of
correlation between X and Y.
51A correlation coefficient based on a sample of size 27 was computed to be 0.40. can
we conclude at a significance level of 0.01 that the corresponding population correlation
coefficient differs from 0?
52A correlation coefficient based on a sample of space 35 was computed to be 0.50. Can
we reject the hypothesis that the population correlation coefficient is ρ=0.70 at 0.05 significance level?
1. Define Random experiment, Sample space, Event and classical definition of
probability with example each.
2. State axioms of Probability and prove the following
B)P(A-P(B)P(A)B)P(A iii)
0 )P( )
)(1A)P( )
∩+=∪
=Φ
−=
ii
APi
3.A box contains 75 good IC chips and 25 defective IC chips. If 12 IC chips are
selected at random, what is the probability at least one chip is defective.
4. A tea set has 4 sets of cups and saucers. Two of these sets are one color and the other
two sets are of different color. If the cups are placed at random on the saucers, what
is the probability that the no cup is on a saucer of the same color.
5. A class consists of 6 girls and 10 boys. If a committee of 3 is chosen at random from
the class, find the probability that
i ) 3- boys are selected
ii) exactly 2 boys are selected
iii) atleast one boy is selected
iv) exactly 2 girls are selected
6. A five digit number is formed by the digits 0,1,2,3,4 without repetition. Find the
probability that number formed is divisible by 4.
7. If A and B are independent events, prove that
)()(1)( BPAPBAP −=∪
B)AP( and P(A) Find
5/8,)BP(A1/4,B)P(A7/8,B)P(A with events are B andA If 8.
∩
=∩=∩=∪
9. In a housing colony,70% of the houses are well planned and 60% of the houses
are well planned and well built. Find the probability that a house that is well
planned is also well built.
10. A bag contains 2 white marbles and 4 red marbles and another bag contains 2
red marbles and 4 white marbles. If a marble is selected at random from one of
the two bags, what is the probability that it is a white marble.
11. Two different digits are selected at random from the digits 1 to 9.
i ) If the sum is odd, what is the probability that 2 is one of the digit
selected
ii) If 2 is one of the digit selected, what is probability that the sum is odd.
12. State and prove Bayes’ theorem.
13. A picnic is arranged to be held on a particular day. The weather forecast says
that there is 80% chance of rain on that day. If it rains the probability of good
picnic is 0.3 and f it does not the probability is 0.9. What is the probability of good
picnic.
14. The chances that doctor A will diagnose a disease X correctly is 60%. The
chances that a patient will die by his treatment after correct diagnose is 40%
and the chance of death by wrong diagnose is 70%. A patient of doctor A,
who had disease X died, what is the chance that his disease was diagnosed
correctly.
15. A binary communication channel carries data as one of two types of signals
denoted by 0 and 1. Due to noise, a transmitted 0 is received as 1with the
probability 0.06 and a transmitted 1 is received as 0 with probability 0.09. The
probability of transmitting 0 is 0.45. If a signal is sent find
i ) the probability that a 0 is received
ii) the probability that a 1 was transmitted, given that 1 was received.
16. A ball is drawn from an Urn containing 3 white and 3 black balls. After the
ball is drawn it is placed and another ball is drawn. This goes indefinitely,
what is probability that of the first four balls drawn exactly 2 are white.
17.Define discrete and continues random variables with an example.
18. Define Probability mass function and density function.
19. Find the mean , variance and standard deviation for the following distribution
Xi -5 -4 1 2
P(xi) ¼ 1/8 ½ 1/8
20. The probability distribution of a random variable X is given by the following table.
Find k and evaluate mean and standard deviation.
Xi 0 1 2 3 4 5
P(xi) K 5k 10 10k 5k k
21. If a random variable X has the probability density function
≤
>=
−
00
02)(
2
x
xexf
x
Evaluate P(1<X<3) and P(X>0.5)
22. The length of time (in min.) that a certain lady speaks on the telephone is found to be
a random variable with density function
≥
=−
whereelse0
0 x)(
5/ forAexp
x
i) Find the value of A
ii) Find the probability that the number of minutes that she will speak on the
phone
a) more than 10 minutes
b) less than 5 minutes
c) between 5 and 10 minutes.
23. The probability density function p(x) of a continues random variable is given by
p(x) = y0e-|x| , -∞<x<∞ . Prove that y0=1/2 and hence find mean and variance of the
distribution.
24. Obtain the mean and variance of the binomial distribution.
25. Let X be binomially distributed random variable based on 6 repetitions of an
experiment. If p = 0.3, evaluate the following probabilities
4)p(X and 4)ii)p(X 3)p(X ) >=≤i
26. The probability that a pen manufactured by a company will be defective is
0.1. If 12 such pens are selected at random find the probability that i )
exactly 2 will be defective ii) at least 2 will be defective iii) none will be
defective.
27.Obtain the mean and variance of Poisson distribution.
28. Suppose 2% of the items produced by a machine are defective. Find the probability
that there are 3 defective items in a sample of 100 items.
29. The number of accidents in a year to auto-drivers in a city is a poisson variate with
mean 3. Out of 1000 such drivers find approximate number of drivers with a) no
accidents b) more than 3 accidents in a year.
30. Obtain the mean and variance of a Geometric distribution.
31. In a certain city the probability that rain occurs on a day during June is 5/8. Find the
probability that there is a rain on June 5th and not earlier.
32. The probability that the prediction of a sooth sayer will come true is 0.01. What is
the probability that his 13th prediction is the first one to be true.
33. A random variable X has a uniform distribution over (-α α) where α>0, Determine
α in the following cases i ) P(X>1) ii) P(X<1/2) iii) p(|X|<1)=p(|X|>1). 34. Find the cdf for a uniform distribution in the interval (a b ).
35. On a certain city transport rute, buses ply every 30 min. between 6am and 10pm. If a
person reaches a bus stop on this rute at a random time during this period, what is the
probability that he will have to wait for at least 20 minutes.
36. If X is uniformly distributed over the interval (-1 1 ), find the density function of
Y=CosπX. 37. Find the mean and standard deviation of exponential distribution.
38. Find the cdf of an exponential distribution.
39. The duration of a telephone conversation has been found to have exponential
distribution with mean 3 min. Find the probability that the conversation may last i )
more than 1 min. ii) less than 3 min.
40. In a certain town the duration of a shower is exponentially distributed with mean
equal to 5 min. What is the probability that i ) a shower will last for at least 2 min.
more given that it has already lasted for 5 min. ii) a shower will last for not more than
6 min. if it has already lasted for 3 min.
41. For the following joint probability distribution of two random variables X and Y,
find i ) marginal distribution of X and Y ii)Cov(X,Y) iii) ρ(X,Y)
X,Y -4 2
7
1
1/8
1/4
1/8
5
¼
1/8
½
42. The following table gives the joint distribution of two random variables X and Y.
Find the probability of X given Y=0
X,Y -1 0
1
-1 0 0.2 0
0
0.1 0.2 0.1
1 0.1 0.2 0.1
43. For the distribution with the density function
<<<<−−
=wiseother
yxyxyxp
0
42,20)6)(8/1(),(
evaluate i ) p(x<1,y<3) ii) p(x+y<3) iii)p(x<1| y<3)
44. For the distribution defined by the density function
≥≥
=+−
wise0
0,0),(
)1(
other
yxxeyxp
yx
evaluate E(y | x) and E(x | y).
45. The joint probability density function for a distribution is
≥≥
=−−
wise0
0,06),(
32
other
yxeyxp
yx
Verify that x and y are independent.
SAMPLING DISTRIBUTION
1. Given below are the marks of 12 students in an examination, find the mean marks
68,82,94,105,120,122,127,130,133,140,141,145.
2. A firm purchased a certain type of items from four different manufactures.
Manufacturer A supplied 50% of the items at a price of Rs 1.35 per item, B supplied 35% at
a price of Rs 1.40, C’, 10%at Rs1.42 and D, 5%at Rs1.47. Find the mean price of the
items.
3. The mean wage of 1oo labourers in a factory, running two shifts of 60 and40 workers
respectively, is Rs.38. the mean wage of 60 labourers working in one shifts isRs.40. Find the
mean wage of 40, labourers working in the other shifts
4. If x is the mean of n items x1, x2, ……..xn of an observation, prove that
−∑
−
xxi =0.
5. If x1 and x2
are the means of two samples of sizes n1 and n2, prove that the mean x−
of
the combined sample of size n1+n2 is given by
x−
= nnxnxn
21
2211
+
+
6. Prove that the arithmetic progression is equal to the mean of its first and last terms.
7. Calculate the mean for the following data
x: 0 1 2 3 4 5 6 7 8
f: 1 9 26 59 72 52 29 7 1
8. Find the mean for the following data
In a
test
carry
ing 100 marks given to 88 students, 77 students get above 10 marks, 72 get
above20, 65 get above 30, 55 get above 40, 43 get above 50, 28 get above 60,
16 get above70, 10 get above 80 and 8 get above 90. Find the mean marks.
9. Calculate the standard deviation for the following
X 6 12 18 24 30 36 42
F 4 7 9 18 15 10 5
10. Calculate the standard deviation for the following distribution.
Class 0-5 0-10 0-15 0-20 0-25
Frequency 6 16 28 38 46
11. The following are the runs scored by two batsman x and y in ten test matches
X 30 44 66 62 60 34 80 46 20 38
Y 34 46 70 38 55 48 60 34 45 30
Who of this is (i) a better scorer (ii) more consistent?
Class 0-10 10-
30 30-50
50-
60 60-90
90-
100
Frequency 2 5 17 22 20 9
12. The items of an observation are in the A.P. a, a+d, a+2d…a+2nd. Find the
standard deviation.
13. A student computed the mean and standard deviation for 100 items of an
observation as 40 and 5.1 respectively. It was later discovered that he had
wrongly copied down an item as 50 instead of 40. Calculate the correct mean and
correct standard deviation.
14. Define raw moments and central moments. Derive the relation between the central
moments and raw moments.
15. Find the first four moments about the mean for the distribution given by the
following table.
X 12 14 16 18 20 22
F 1 4 6 10 7 2
Also find the coefficients of skewness and kurtosis.
16. Calculate the coefficient of kurtosis for the following distribution.
Class 0-10 10-20 20-30 30-40
Frequency 1 3 4 2
JOINT PROBABILITY DISTRIBUTION AND MARKOV CHAINS
17.Amarkov chain with three states α ,β,γ is defined by the transition matrix
3
1
2
1
6
13
20
3
1
02
1
2
1
Taking the initial state to be α ,Determine nth step transition probability )(n
ixP
and absolute probability )(
.
n
jP
18.Determine if the following transition matrix is ergodic Markov chain
32
31
41
21
41
41
41
21
31
31
31
00
0
0
0
4
3
2
1
Pr
4321
statesFuture
statesesent
19.Suppose there are two market products of brad A and B ,respectively.Let each of these
two brands have exactly 50% of the total market in the same period and let the market be of
a fixed size . The transition matrix is given below
5.05.0
1.09.0
TO
B
AFROM
BA
If the initial market share breakdown is 50% for each brand,then determine there market
shares in the steady states.
10ME42B - MECHANICAL MEASUREMENTS AND METROLOGY
MECHANICAL MEASUREMENTS AND METROLOGY
Sub Code: 10ME42B IA Marks: 25
Hrs/week: 04 Exam Hours:
03
Total Lecture Hrs: 52 Exam Marks:
100
PART – A
UNIT 1:
Standards of measurement: Definition and Objectives of metrology, Standards of length -
International prototype meter, Imperial standard yard, Wave length standard, subdivision of
standards, line and end standard, comparison, transfer from line standard to end standard,
calibration of end bars (Numerical), Slip gauges, Wringing phenomena, Indian Standards (M-
81, M-112), Numerical problems on building of slip gauges.
6 Hours
UNIT 2:
System of limits, Fits, Tolerances and gauging: Definition of tolerance, Specification in
assembly, Principle of inter changeability and selective assembly limits of size, Indian standards,
concept of limits of size and tolerances, compound tolerances, accumulation of tolerances,
definition of fits, types of fits and their designation (IS 919 -1963), geometrical tolerance,
positional - tolerances, hole basis system, shaft basis of system, classification of gauges, brief
concept of design of gauges (Taylor's principles), Wear allowance on gauges, Types of gauges -
plain plug gauge, ring Gauge, snap
gauge, limit gauge and gauge materials. 7
Hours
Comparators and Angular measurement: Introduction to Comparator, Characteristics,
classification of comparators, mechanical comparators - Johnson Mikrokator, Sigma
Comparators, dial indicator, Optical Comparators -principles, Zeiss ultra optimeter, Electric and
Electronic Comparators -principles, LVDT, Pneumatic Comparators, back pressure
gauges, Solex Comparators. Angular measurements, Bevel Protractor, Sine Principle and. use of
Sine bars, Sine center, use of angle gauges, (numericals on building of angles) Clinometers.
7 Hours
UNIT 3:
Interferometer and Screw thread gear measurement : Interferometer Principle of
interferometery, autocollimator. Optical flats. Terminology of screw threads, measurement of
major diameter, minor diameter pitch, angle and effective diameter of screw threads by 2-wire
and 3-wire methods, Best size wire. Toolmakers microscope, gear terminology, use of gear tooth
Vernier caliper and gear tooth micrometer
6 Hours
PART – B
UNIT 4:
Measurements and Measurement systems: Definition, Significance of measurement,
generalized measurement system, definitions and concept of accuracy, precision, calibration,
threshold, sensitivity, hystersis, repeatability,
linearity, loading effect, system response-times delay. Errors in Measurements, Classification of
Errors. Transducers, Transfer efficiency, Primary and Secondary transducers, electrical,
Mechanical, electronic transducers, advantages of each type transducers.
7 Hours
UNIT 5:
Intermediate modifying and terminating devices: Mechanical systems, inherent problems,
Electrical intermediate modifying devices, input circuitry, ballast, ballast circuit, electronic
amplifiers and telemetry. Terminating devices, Mechanical, Cathode Ray Oscilloscope,
Oscillographs, X-Y Plotters. 6
Hours
UNIT 6:
Measurement of Force and Torque, pressure: Principle, analytical balance, platform balance,
proving ring, Torque measurement, Prony brake, hydraulic dynamometer. Pressure
Measurements, Principle, use of elastic members, Bridgeman gauge, Mcloed gauge, Pirani
Gauge.
6 Hours
UNIT 7:
Temperature and strain measurement: Resistance thermometers, thermocouple, law of
thermocouple, materials used for construction, pyrometer, Optical Pyrometer. Strain
Measurements, Strain gauge, preparation and mounting of strain gauges, gauge factor, methods
of strain measurement
7 Hours
Text Books:
1. “Mechanical measurements” by Beckwith Marangoni and Lienhard, Pearson Education, 6th
Ed., 2006
2. “Engineering Metrology” by R.K.Jain, Khanna Publishers, 1994.
Reference Books:
1. “Engineering Metrology” by I.C.Gupta, Dhanpat Rai Publications, Delhi
2. “Mechanical measurements” by R.K.Jain
3. “Industrial Instrumentation” Alsutko, Jerry. D.Faulk, Thompson Asia Pvt. Ltd.2002
4. “Measurement Systems Applications and Design” by Ernest O, Doblin, McGRAW Hill
Book Co.
Scheme of Examination:
One Question to be set from each chapter. Students have to answer any FIVE
full questions out of EIGHT questions, choosing at least 2 questions from
part A and 2 questions from part B.
LESSON PLAN
Sub Code: 10 ME 42B Hrs/week: 04
Total Lecture Hrs: 52 Exam Marks: 100
Subject: Mechanical Measurements And Metrology Sem: IV
Hour.
No TOPICS TO BE COVERED
1. Standards of measurement: Definition and Objectives of metrology,
2. Standards of length - International prototype meter, Imperial standard yard
3. Wave length standard, subdivision of standards
4. Line and end standard, comparison, transfer from line standard to end standard
5. calibration of end
bars (Numerical), Slip gauges, Wringing phenomena
6. Indian Standards (M- 81, M-112), Numerical problems on building of slip
gauges.
7. System of limits, Fits, Tolerances and gauging: Definition of tolerance,
Specification in assembly,
8. Principle of inter changeability and selective assembly limits of size, Indian
standards
9. Concept of limits of size and tolerances, compound tolerances, accumulation
of tolerances
10. Definition of fits, types of fits and their designation (IS 919 -1963),
geometrical tolerance
11. Positional - tolerances, hole basis system, shaft basis of system
12. Classification of gauges, brief concept of design of gauges (Taylor's
principles), Wear
allowance on gauges
13. Types of gauges -plain plug gauge, ring Gauge, snap gauge, limit gauge and
gauge materials.
14. Comparators and Angular measurement: Introduction to Comparator,
Characteristics,
15. Classification of comparators, mechanical comparators -Johnson Mikrokator,
Sigma Comparators
16. Sigma Comparators, dial indicator, Optical Comparators -principles
17. Zeiss ultra optimeter, Electric and Electronic Comparators -principles,
18. LVDT, Pneumatic Comparators, back pressure gauges, Solex Comparators
19. Angular measurements, Bevel Protractor, Sine Principle and. use of Sine bars,
Sine center
20. use of angle gauges, (numericals on building of angles) Clinometers.
21. Interferometer and Screw thread gear measurement : Interferometer
Principle of interferometery, autocollimator
22. Principle of interferometery, autocollimator
23. Optical flats. Terminology of screw threads
24. Measurement of major diameter, minor diameter pitch, angle
25. Effective diameter of screw threads by 2-wire and 3-wire methods Best size
wire
26. Toolmakers microscope, gear terminology
27. Use of gear tooth Vernier caliper and gear tooth micrometer
28. Measurements and Measurement systems: Definition, Significance of
measurement
29. Generalized measurement system, definitions and concept of accuracy,
precision,
30. Calibration, threshold, sensitivity, hystersis, repeatability
31. Linearity, loading effect, system response-times delay
32. Errors in Measurements, Classification of Errors.
33. Transducers, Transfer efficiency, Primary and Secondary transducers,
electrical,
34. Mechanical, electronic transducers, advantages of each type transducers
35. Intermediate modifying and terminating devices: Mechanical systems,
inherent problems
36. Electrical intermediate modifying devices
37. Input circuitry, ballast, ballast circuit,
38. Electronic amplifiers and telemetry
39. Terminating devices, Mechanical, Cathode Ray Oscilloscope
40. Oscillographs, X-Y Plotters
41. Measurement of Force and Torque, pressure: Principle, analytical balance,
42. Platform balance, proving ring
43. Torque measurement, Prony brake,
44. Hydraulic dynamometer. Pressure Measurements
45. Principle, use of elastic members, Bridgeman gauge
46. Mcloed gauge, Pirani Gauge.
47. Temperature and strain measurement: Resistance thermometers,
thermocouple,
48. Law of thermocouple materials used for construction,pyrometer
49. Optical Pyrometer
50. Strain Measurements, Strain gauge,
51. Preparation and mounting of strain gauges
52. Gauge factor, methods of strain measurement
STAFF HOD - IEM
QUESTION BANK
Unit-1
1. Describe with neat sketch 1) imperial standard yard 2) international prototype meter.
2. Describe with neat wavelength standard.
3. Describe with neat sketch line and end standards.
4. What is metrology? State and explain the objectives of metrology.
5. Explain the following terms 1) primary standard 2) secondary standard.
6. Describe the procedure for ringing of slip gauges. Using a slip gauge set m-87, build
up the following dimensions.29.758 mm and 2) 46.635 mm.
Unit-2
1. Illustrate the principle of go and no go gauges.
2. Differentiate between the following 1) hole basis system 2) interchangeability and
selective assembly.
3. Write in brief about BIS classes of fits
4. Write in brief about clearance fit, interference fit and transition fit.
5. Explain gauge tolerance Taylor’s theory.
6. Write in brief about limit gauges.
7. Write in brief about plug gauges.
8. Write in brief about selection of fits.
9. Write in brief about gap gauges.
10. Write in brief about system of limits and fits.
11. Describe with neat sketch the construction and working of mechanical optical
comparator.
12. Describe with neat sketch the construction and working of pneumatic comparators.
13. Describe with neat sketch the construction and working of any one electrical
comparators.
14. Describe with neat sketch the construction and working of any one electronic
comparators
15. Describe with neat sketch the construction and working of johnson’s microkrator.
16. Describe with neat sketch the construction and working of brook – level
comparator.
17. Describe with neat sketch the construction and working of sigma comparator
18. Describe with neat sketch the construction and working of brook – level comparator
19. Explain the method of measuring angles using clinometers
20. Explain the method of measuring angles using a bevel protractor.
21. Explain the method of measuring angles using a universal protractor.
22. Explain the method of measuring angles using a sine bar.
23. Explain the method of measuring angles using angle gauges..
24. Explain the method of measuring angles using taper gauges.
25. Explain the terms 1) wear allowance 2) gauge makers allowance
26. Give the combination of angle gauges to obtain the following angles, also sketch the
arrangement of gauges (1)34° 23′ 43′′ (2)15° 51′ 24′′
Unit-3
1. Describe with neat sketch the construction and working of autocollimator
2. Describe with neat sketch the construction and working of toolmakers
microscope.
3. How pitch of a screw thread is is measured and what are the different types of
pitch errors?
4. Explain the there wire method of measuring the effective diameter of a metric
thread. Derive an expression for the best size used in the above method.
5. Write short notes on terminology of screw threads.
6. How pitch of a screw thread is is measured and what are the different types of
pitch errors.
7. Explain the method of measuring 1) major dia 2) pitch dia using 2 – wire
method
8. Explain the method of measuring 1) major dia 2) pitch dia using 3 – wire
method
9. Describe with neat sketch the construction and working of gear tooth vernier.
10. Describe with neat sketch the construction and working of gear tooth
micrometer.
11. Write in brief terminology of a gear tooth vernier.
12. Write in brief terminology of a gear tooth micrometer.
13. List out the uses of 1) gear tooth micrometer. 2) gear tooth micrometer.
Unit-4
1. Explain with example the three stages of a generalized measurement system.
2. Write in brief 1) accuracy 2) precision 3) sensitivity with respect to measurements.
3. Write in brief 1) threshold 2) resolution hysterisis 3) repeatability
4. Write in brief 1) loading effect 2) input impedance 3) system response
5. Write in brief about time delay in a measurement.
6. What are errors in measurements?
7. How the errors in the measurements are classified.
8. List out the importance of measurement and measurement systems
9. What are transducers? List out advantages and disadvantages of a mechanical
transducer.
10. Describe with neat sketch the construction and working of an electronic
transducer.
11. Describe with neat sketch the construction and working of an electrical
transducer
12. What are the advantages and disadvantages of an electronic transducer?
13. What are the advantages and disadvantages of an electrical transducer?
14. What is a pneumatic load cell? Explain.
15. Describe with neat sketch the construction and working of various mechanical
transducer elements.
Unit-5
1. Explain about the mechanical systems used as the intermediate modifying
stages.
2. Write short notes on Inherent problems.
3. Write short notes on Electronic amplifiers.
4. Write short notes on telemetry.
5. Write short notes on mechanical terminating devices.
6. Explain with neat diagram the working of hode ray oscilloscope.
7. Write short notes on Oscillograph.
8. Write short notes on X – Y Plotters.
Unit -6
1. Describe with neat sketch the construction and working of electrical
dynamometer
2. Describe with neat sketch the construction and working of proving ring.
3. Describe with neat sketch the construction and working of prony brake
dynamometer.
4. Describe with neat sketch the construction and working of hydraulic
dynamometer.
5. Write a short note on analytical balance.
6. Write a short note on platform balance.
7. Write a short note on hydraulic dynamometer.
8. Describe with neat sketch the construction and working of Bridgman gauge
9. Describe with neat sketch the construction and working of McLeod gauge
10. Describe with neat sketch the construction and working of pirani gauge.
11. Explain how pressure can be measured with elastic transducer.
12. Write short notes on the elastic members used in the measurement of pressure.
Unit-7
1. Describe with neat sketch the construction and working of resistance thermometer
2. List the thermocouple laws.
3. Describe with neat sketch the construction and working of radiation pyrometer.
4. Describe with neat sketch the construction and working of pressure thermometer.
5. Explain the principles of thermocouples and illustrate the applications of
thermocouples.
6. Describe with neat sketch the construction and working of vapour, pressure
thermometer with a neat sketch.
7. Write short notes on Optical Pyrometer.
8. Explain the null balance and deflection methods of strain measurements.
9. Write in brief about treatment regarding preparation & mounting of strain gauges.
10. Explain a) calibration of strain gauges b) temperature compensation
11. Write a note on strain gauge material its alloys.
12. Write short notes on Gauge Factor.
10ME43 – APPLIED THERMODYNAMICS
APPLIED THERMODYNAMICS
Sub Code: 06ME43 IA Marks: 25
Hours / Week: 04 Total Hours: 3
Total Hours: 52 Exam Marks: 100
1. Combustion thermodynamics: Theoretical (Stoichiometric) air for combustion of fuels.
Excess air, mass balance, actual combustion. Exhaust gas analysis, A/F ratio. Energy balance
for a chemical reaction, enthalpy of formation, enthalpy and internal energy of combustion.
Combustion efficiency 7 hrs
2. Gas power Cycles: Air standard cycles; Carnot, Otto, Diesel, Dual & stirling cycles, P-V &
T-S diagrams, description, efficiencies and mean effective pressures. Comparison of Otto and
Diesel cycles. Gas turbine (Brayton) cycle; description and analysis. Regenerative gas turbine
cycle. Inter-cooling and reheating. 8 hrs
3. Gas Turbines and Jet Propulsion: Classification of gas turbines, analysis of open cycle gas
turbine cycle .advantages and disadvantages of closed cycle .methods to improve thermal
efficiency. Jet propulsion and rocket propulsion. 6 hrs
4. Vapour power cycles: Carnot vapour power cycle, drawbacks as reference cycle. Simple
rankine cycle; description, T-S diagram, analysis for performance. Comparison of Carnot &
rankine cycles. Effect of pressure and temperature on rankine cycle performance. Actual
vapour power cycles. Ideal and practical regenerative rankine cycles open and closed feed
water heaters. Reheat Ranking cycles. 8 hrs
5. Reciprocating compressors: operation of single stage reciprocating compressors, Work
input through P-V diagram and steady state flow analysis, Effect of clearance and volumetric
efficiency .Adiabatic ,isothermal and mechanical efficiencies ,Multi stage compressor, saving
in work, optimum intermediate pressure, inter cooling, minimum work for compression.
6 hrs 6. Refrigeration: vapour compression refrigeration system; description, analysis, refrigerating
effect, capacity, power required, units of refrigeration, COP, refrigerants and their desirable
properties, Air cycle refrigeration; reversed carnot cycle, reversed bryton cycle, vapour
absorption refrigeration system. Steam jet refrigeration. 6 hrs
7. Psychometrics: Atmospheric air & psychrometric properties; Dry bulb temperature, wet bulb
temperature, dew point temperature; partial pressures, specific & relative humidity, and the
relation between the two. Enthalpy and adiabatic saturation temperature. Construction 7 use
of psychrometric chart, Analysis of various processes, heating, cooling dehumidifying and
humidifying. Adiabatic mixing of stream of moist air. Summer and winter air conditioning.
6 hrs 8. I C Engines: testing of Two stroke and four stroke SI and CI engines for performance, related
numerical problems, heat balance, Mores test. 5 hrs
TEXTBOOKS:
1. Basic and applied thermodynamics by P.K Nag, Tata McGraw Hill pub, 2002
2. Thermodynamics- An Engineering Approach by Yunus.A.Cenegal and Michael A Boles,
Tata McGraw hill pub co, 2002
REFERENCE BOOKS:
1. Engineering thermodynamics by J.B Jones and G A Hawkins, john Wiley and sons Co
2. Fundamentals of classical thermodynamics by GJ Van Wylen and R E Sonnatag, Wiley
eastern
3. Thermodynamics by CP Arora, Tata McGraw Hill Internal combustion engines ML Mathur
and R.P Sharma
LESSON PLAN
Sub Code: 10ME43 I A Marks: 25
Hours / Week: 04 Total Hours: 52
Subject: Applied Thermodynamics Sem:IV
Hour. No Topics to be covered
1. Combustion thermodynamics: Interconversion of mole & mass fractions,
combustion process
2. Combustion stoichiometry, theoretical Air required for combustion & actual
combustion processes
3. Exhaust gas analysis, determination of the actual air-fuel ratio
4. Calculation of equilibrium composition, Heat generated by combustion, energy
balance
5. Heat of reaction, kirchoff’s equation, calorific value
6. Adiabatic flame temperature, enthalpy & internal energy of combustion, HCV &
LCV
7. Combustion efficiency, Numericals on determination of calorific value, A/F ratio
8. Numericals on determination of adiabatic flame temperature
9. Gas power cycles: Air standard cycles: Assumptions, working of carnot cycle,
expression for work done by engine running on carnot engine, efficiencies of actual
engines
10. Expression for work done & efficiencies by engine by Otto cycle, T-S & P-v
diagram
11. Expression for mean effective pressure by Otto cycle
12. Expression for work done by engine by diesel cycle, T-S & P-v diagram, efficiency
13. Expression for mean effective pressure by diesel cycle
14. Dual cycles & stirling cycle efficiency, expression for Mep
15. Comparison of air cycles on the basis of efficiency, feasibility, mep, temperature
limits
16. Gas turbines and propulsion: Classification of gas turbines
17. Analysis of open cycle gas turbine cycle
18. Advantages and disadvantages of closed cycle
19. Methods to improve thermal efficiency
20. Jet propulsion and rocket propulsion
21. Exercise problems
22. Exercise problems
23. Vapour power cycles: Carnot vapour power cycle, drawbacks a reference cycle
24. Rankine cycle, T-s diagram, comparison of carnot & Rankine cycles,
25. Effects of pressure & temperature on Rankine cycle performance
26. Actual vapour power cycles, Regenerative cycles
27. Ideal and practical regenerative Rankine cycles
28. Open & closed feed water heaters, reheat Rankine cycle
29. Numericals on determining work done, quality of steam at the exhaust
30. Numericals on determining work done, quality of steam at the exhaust, SSC, power
ratio
31. Reciprocating compressors: Operation of single stage reciprocating compressors
32. Work input, steady state flow analysis
33. Effect of clearance & volumetric efficiency
34. Adiabatic, isothermal & mechanical efficiencies.
35. Multi stage compressor
36. Work saving by inter cooling, optimum intermediate pressure
37. Minimum work of compression
38. Refrigeration: Vapour compression refrigeration system,
39. Description, analysis
40. Reversed Bryton cycle, Refrigerating effect, power required, Units of refrigeration
41. Expression for COP, Refrigerants & Desirable properties of refrigerants
42. Vapour absorption refrigeration system,
43. Steam jet refrigeration, Numericals
44. Psychrometry: Atmospheric air and psychometric properties
45. DBT, WBT, DPT, expressions for specific humidity, RH
46. Enthalpy & adiabatic saturation temperature, Numericals
47. Use of psychrometric charts for various processes, Numericals
48. Analysis of various processes, heating, cooling, dehumidifying and humidifying
49. Adiabatic mixing of air stream, Summer & winter air conditioning
50. IC Engines: Testing of Two stroke, four stroke SI and CI engines for Performance
51. Morse test & Heat balance
52. Numericals
STAFF HOD - IEM
QUESTION BANK
1. Combustion Thermodynamics:
1. What is combustion?
2. Define the terms – heat of formation and heat of reaction. How are they related
3. Define adiabatic flame temperature
4. Calculate the composition when 1 [Kmol H2] reacts with 1 [kmol O2] and reaches
equilibrium at 1 atm & 1500 K
5. Aniline is a popular rocket propellant. It has the benzene structure with one of H atoms
replaced with N-H2. The resonance energy for aniline is 291.4 [ MJ/kmol] what will the
standard heat of formation
6. Calculate the calorific value of ethane
7. Calculate the calorific value of a coal with composition of C= 51.3%, H2= 3.5 %, N2= 1.8
%, O2= 7.3 % , S= 0.7 % and rest being ash & moisture
8. A sample of gobar gas contains 55% methane and the rest is CO2. What will be its calorific
value
9. Compute the enthalpy of an exhaust gas at 1000 K with composition of CO2=12.3%, CO=
1.74 %, O2= 3%, N2= 76.4% and H20 = 6.6 %
2. Gas Power cycles:
1. Show the efficiencies of the air standard Brayton cycle is a function of isentropic pressure
ratio.
2. cycle on p-V and T-s diagrams.
3. Sketch Otto, Diesel and Dual cycle for the (a) same maximum pressure and heat input (b)
same maximum pressure and temperature (c) same maximum pressure and output and
compare the efficiency of the same.
4. Prove that for the same compression ratio and heat input, Otto cycle efficiency is more than
Diesel cycle efficiency.
5. Derive an expression for air standard efficiency if dual combustion cycle in terms of
compression ratio, explosion ratio and cut of ratio.
6. Mention the advantages and disadvantages of closed cycle gas turbine over open cycle
turbine power plant. Show the processes of T-s diagram.
7. Draw the simple Gas Turbine flow diagram. Derive the thermal efficiency equation in terms
of pressure ratio of the cycle. Show the cycle both on p-V and T-s diagrams.
8. Write short notes on the following a) Ram-Jet b) Turbo Jet c) Rocket propulsion d) Joule’s
cycle e) Turbo prop propulsion systems.
9. Obtain an expression for increase in efficiency of Gas turbine with intercooling.
10. Obtain an expression for optimum pressure in the inter cooler
11. The air enters the compressor of an open cycle constant pressure gas turbine at a pressure of
1 bar and temperature of 200C.The pressure of the air after compression is 4 bar. The
isentropic efficiency of compressor and turbine are 80% and 85% respectively. The air-fuel
ratio is 90%, flow rate of air is 3 Kg /sec. Find a) power developed b) thermal efficiency of
the cycle Take γ = 1.4 Cp = 1kj/kg and CV= 41720kJ/kg.
12. An industrial gas turbine takes air at 1 bar and 27 0C and compresses it to 5.5 times the
original pressure. The temperature at the salient points are, compressor outlet 251 0C,
turbine inlet 7600C and turbine outlet 447
0C calculate the compressor and turbine efficiency.
Compare for the ideal cycle and cycle considering component efficiency. Determine a)
thermal efficiency b) work ratio c) optimum pressure ratio for maximum out put and d)
optimum pressure ratio for maximum efficiency.
13. A gas turbine plant consists of 1 turbine as a compressor drive and other to drive a
generator. Each turbine has its own combustion chamber and supplied air directly from the
compressor. Air enters the compressor at 1 bar and 150C and compressed with isentropic
efficiency of 76% . The gas inlet pressure and temperature in both the turbines are 5 bar and
6800C respectively. The isentropic efficiency of both turbines is 86%. The mass flow rate of
air entering the compressor is 23 kg./ S. The calorific value of the fuel is 42000kJ/kg.
Calculate the power output of the plant and its thermal efficiency. Take Cp for air as 1.005
kJ/Kg K and γ = 1.4, Cp for gas as 1.128kJ/kg K and γ = 1.34. 14. Explain the working of Striling engine and discuss its practical applications
15. Expalin the carnotization of Stirling engine
3.Gas Turbines And Jet Propulsion
1.What do you mean by the term gas turbine ? How are gas turbines classified?
2.Enumarate the various uses of gas turbines
3.Explain the working difference between propeller – jet, turbo jet and turbo prop
4.State the fundamental differences between the jet propulsion and rocket propulsion
5.In an air standard gas turbine, air at a temperature of 150C and a pressure of
1.01 bar enters the compressor, where its compressed through a pressure ratio of 5.
1.02 Air enters the turbine at a temperature of 8150C and expands to original pressure
of 1.01 bar. Determine the ratio of turbine work to compressor work and the
thermal efficiency when the engine operates on ideal Brayton cycle.
Take γ = 1.4 Cp =1.005 KJ/Kg K. 6.A Turbo Jet has a speed of 750 Km/h while flying at altitude of 10000 m .the propulsive
efficiency of the jet is 50 % and overall efficiency of the turbine plant is 16% .the density of the air
at 10000 m altitude is 0.173 Kg/m3 .the drag of plant is 6250 N .The caloric value of the fuel is
48000 KJ/Kg. Calculate
i. Absolute velocity of the jet
ii. Volume of air compressed per minute
iii. Diameter of the jet
iv. Power output of the unit in KW
v. Air fuel ratio
4. Vapour power cycles:
1. Explain the need for vapour cycles
2. With a neat sketch explain the working of Rankine cycle in steam power plant
3. What is the need for Regeneration and reheat in case of Rankine engines
4. A steam turbine receives steam at 15 bar and 3000C and leaves the turbine at 0.1 bar and 4%
moisture. Determine, a) Rankine cycle b) steam consumption per kW per hr, if the efficiency
ratio is 0.70 c) Carnot cycle efficiency for the given temperature limits. D) Changing the
Rankine efficiency and specific consumption if the condenser pressure is reduced to 0.04
bar.
5. An ideal reheat cycle has pressure at HP turbine inlet equal to 9 Mpa, reheat pressure equal
to 1.6 Mpa and exhaust pressure equal to 7kPa. The useful work developed by the turbine is
1400 kJ/kg. Determine the temperature of steam leaving the reheater, if thermal efficiency of
the cycle is 38%. Temperature at turbine inlet is 5000C and steam expands to dry saturated
state before entering the reheater at 1.6Mpa.
6. A regenerative cycle has turbine inlet pressure of 40 bar and dry saturated. Steam expands in
the condenser to a pressure of 0.04 bar. Steam is bled at optimum pressure from the turbine
to heat the condensate water in the feed water heater. Neglecting pump work, determine the
cycle efficiency.
7. Steam at 500°C enters from super heater into HP turbine at pressure of 150 bars. It is
expanded in the HPT to a pressure of 10 bars. Calculate the work done by the turbine per kg
if steam if the dryness fraction is 0.8.
5. Reciprocating compressors:
1. Explain the working principal of reciprocating compressors?
2. What are the advantages of multi-staging
3. What do your understand by intercooling? Explain its benefits
4. Write a short notes on the working principles of the following. A) Rotary compressor b)
Fans c) Blowers d) Turbo-compressors and Turbo-blowers
5. A single stage reciprocating compressors takes 1 m3 of air per minute at 1.013 bar and 150C
and delivers it at 800 kPa. Assuming that the law of compression is pV1.35 = constant, and
that clearance is negligible, calculate the indicated power. A) IF the compressor is to be
driven at 360 rpm and is single acting, single cylinder machine, Calculate the cylinder bore
required assuming a stroke t bore ratio of 1.5:1. Calculate the power of the motor required to
drive the compressor if the mechanical efficiency of the compressor is 90% and that of the
motor transmission is 90%
6. A small single acting compressor has a bore and stroke both of 10 cm and is driven at
350rpm. The clearance volume is 75 cm3 and the index of compression and expansion is
1.23. The suction pressure is 0.95 bar and delivery is 7 bar. Calculate (i) the volume of free
air at 1 bar and 20 0C dealt with per minute, if the temperature at the start of compression is
30 0C and (ii) mean effective pressure of the indicator diagram, assuming constant section
and delivery pressure.
7. The LP cylinder of a compound air compressor draws 0.1m3 of air at a temperature of 15
0C
and pressure 1 bar. It compresses the air adiabatically to 2 bar and then delivers in to a
receiver where the air is cooled to 250C. This air is drawn in to the HP cylinder and
compressed adiabatically, 5 bar and delivered into the receiver. Find the power required
when the compressor makes 100 rpm. What pressure in the receiver would give the best
efficiency assuming the other data as above?
8. The following particulars apply to a two-stage single acting air compressor. Stroke =
28.5cm; pressure cylinder diameter =23cm; Final pressure = 24 bar; intermediate pressure
=5 bar; temperature of air leaving the intercooler = 340C. If the air drawn in the compressor
is at 1 bar and 140C, find the power required in compressing air when running at 350 rpm.
Assuming law of compression pV1.3= constant
6. Refrigeration:
1. Define the following terms a) Coefficient of performance b) one ton of refrigeration
2. With the help of p-V and T-s diagrams analyze the following cycles a) Carnot refrigerator
cycle b) Bell-Coleman cycle
3. What are the advantage of vapour absorption system over vapour compression system
4. Briefly discuss the applications of Cryogenics
5. A reversed Carnot cycle Refrigerator is used to manufacture ice at 00C from water at 25
0C.
Assume brine temperature used for this purpose is at-80C. Find the ice formed per kW-hr.
6. A refrigerator works on Bell-Coleman cycle between the pressure limits of 100kPa and
400kPa. Air leaves the refrigerator at 60C and the cooler at 32
0C. The compression and
expansion follow the law pV1.3=constant. Assume Cp = 1.005kJ/kg K and γ = 1.4 for air.
Determine COP of the cycle.
7. A CO2 refrigerator is working under the temperature limits 20°C and -5°C. If the refrigerant is superheated by 5°C calculate the work done per kg flow of refrigerant
8. A refrigerator using Freon –12 has an evaporator saturation temperature of 248 K and a
condenser saturation temperature of 308 K. The vapour is dry saturated before the beginning
of compression and has a temperature of 338 K after compression to the condenser pressure
Calculate, a) work done per kW refrigeration b) COP of the refrigerator c) compare this
result when compression is isentropic.
9. Explain the Aqua-Ammonia absorption system
10. Explain steam jet refrigeration system
7. Psychrometrics:
1. Define the following terms a) dry air b) Moist air c) superheated vapour d) saturated vapour
e) dry-bulb temperature f) wet-bulb temperature g) specific humidity h) relative humidity I)
saturation ratio
2. Write a brief note on the following a) Comfort air conditioning b) summer and winter air
conditioning system
3. Atmospheric air at 750mm Hg has a DBT of 340C and WBT of 24
0C compute a) relative
humidity b) humidity ratio c) dew point temperature, d) enthalpy of atmospheric air and e)
density of moist
4. As a result of adiabatic saturation in a steady state steady flow device at a constant pressure
of 96kN/m2, the temperature of an air-water vapour mixture is reduced from 32
0C to 22
0C.
What is the relative humidity of the mixture at inlet?
5. Air at 200C, 40% RH is mixed adiabatically with air at 40
0C, 40% RH in the ratio of 2 kg of
the former with 3 kg of the latter. Find the final condition of air.
8. I C engines
1. Define the following a) Mechanical efficiency b) Brake thermal efficiency c) indicated
thermal efficiency d) relative efficiency e) volumetric efficiency f) Air standard efficiency
g) compression ratio h) break power I) specific fuel consumption
2. Sketch the Heat balanced curves for an SI engine at constant speed and discuss the nature of
curves compare the both.
3. What is an indicator? What is an advantage of indicator diagram?
4. Define Knocking in SI engines and discuss the factors affecting knocking in SI engines
5. With the help of p-θ diagram explain the phenomenon of combustion is SI engines and CI
engines.
6. Discuss the effect of the following engine variables on flame propagation. A) Compression
ratio b) Engine load c) Size of engine d) Engine speed e) Turbulence
7. The following data refers to a four stroke diesel engine Cylinder diameter = 200mm, stroke
= 300mm, Speed = 300rpm Effective brake load = 500Kg, Mean circumference of the brake
drum = 400mm, Mean effective pressure = 6bar, Diesel oil consumption = 0.1m3 /mini,
Specific gravity of diesel = 43900 Kj/Kg. Find a) Break power b) indicated power, c)
frictional power d) Mechanical efficiency e) Break thermal and indicated thermal efficiency.
8. A 6-cylinder four stroke Diesel engine of 34 cm bore and 38 cm stroke gave the following
results during testing. BP = 142 kW; N = 350rpm; Pm =3.7bar, mf = 44kg/hr; (CV)f =
44,800 kJ /Kg; ma =38Kg /min, Piston cooling oil = 35 Kg/min, Cp of oil =- 2.1lJ/Kg K, Rise
in cooling oil temperature = 280C, Exhaust gas temperature = 190
0C, Ambient temperature =
200C, Fuel contains 14% H2by mass and Cpg = 1.05kJ/Kg K, Partial pressure of water
vapour carried in exhaust gases = 0.06 bar. Draw the heat balance sheet on minute basis and
percentage basis. Find the specific fuel consumption at full load assuming mechanical
efficiency as 0.6.
9. A 4-stroke cycle, four cylinder petrol was tested at full throttle at constant speed. The
cylinders have dia 80mm and stroke 100mm. Fuel was supplied at the rate of 5.44 Kg/hr and
the plugs of four cylinders were successively short circuited without the change of speed.
The power measured was as follows. With all cylinders working = 14.7 kW, With cylinder 1
cut off = 10.1kW, With cylinder 2 cut off = 10.3kW, With cylinder 3 cut off = 10. 4kW,
Calorific value of petrol used was 41900kJ/kg. The clearance volume of each cylinder is
100cc. Determine a) the mechanical efficiency b) indicated thermal efficiency c) the air
standard efficiency d) the relative efficiency. Take γ = 1.4
10ME44 – KINEMATICS OF MACHINES
KINEMATICS OF MACHINES
Sub Code: 10ME44 IA Marks : 25
Hrs/week: 04 Exam Hours : 03
Total Lecture Hrs: 52 Exam Marks : 100
PART – A
UNIT 1:
INTRODUCTION: DEFINITIONS: Link or element, kinematic pairs, degrees of freedom,
Grubler’s criterion (without derivation), Kinematic chain, Mechanism, structure, Mobility of
Mechanism, Inversion, Machine.
KINEMATIC CHAINS AND INVERSIONS: Inversions of Four bar chain; Single slider crank
chain and Double slider crank chain.
7 Hours
UNIT 2:
MECHANISMS: Quick return motion mechanisms -Drag link mechanism, Whitworth mechanism
and Crank and slotted lever Mechanism. Straight line motion mechanisms –Peaucellier’s
mechanism and Robert’s mechanism. Intermittent Motion mechanisms –Geneva mechanism and
Ratchet and Pawl mechanism. Toggle mechanism, Pantograph, Ackerman steering gear mechanism.
7 Hours
UNIT 3:
VELOCITY AND ACCELERATION ANALYSIS OF MECHANISMS
(GRAPHICAL METHODS)
Velocity and acceleration analysis of Four Bar mechanism, slider crank mechanism and Simple
Mechanisms by vector polygons: Relative velocity and acceleration of particles in a common link,
relative velocity and accelerations of coincident Particles on separate links- Coriolis component of
acceleration. Angular velocity and angular acceleration of links, velocity of rubbing. 7 Hours
UNIT 4:
VELOCITY ANALYSIS BY INSTANTANEOUS CENTER METHOD:
Definition, Kennedy’s Theorem, Determination of linear and angular velocity using instantaneous
center method
KLEIN’S CONSTRUCTION: Analysis of velocity and acceleration of single slider crank
mechanism.
6 Hours
PART – B
UNIT 5:
VELOCITY AND ACCELERATION ANALYSIS OF MECHANISMS (ANALYTICAL
METHODS): Analysis of four bar chain and slider crank chain using analytical expressions. (use
of complex algebra and vector algebra) 6 Hours
UNIT 6:
SPUR GEARS: Gear terminology, law of gearing, Characteristics of involute action, Path of
contact, Arc of contact, Contact ratio, Interference in involute gears, Methods of avoiding
interference, Back lash, Comparison of involute and cycloidal teeth. 6 Hours
UNIT 7:
GEAR TRAINS: Simple gear trains, Compound gear trains for large speed reduction, Epicyclic
gear trains, Algebraic and tabular methods of finding velocity ratio of epicyclic gear trains. Tooth
load and torque calculations in epicyclic gear trains.
7 Hours
UNIT 8:
CAMS: Types of cams, Types of followers, Displacement, Velocity and Acceleration time curves
for cam profiles. Disc cam with reciprocating follower having knife -edge, roller and flat-faced
follower, Disc cam with oscillating roller follower, Follower motions including SHM, Uniform
velocity, uniform accele ration and retardation and Cycloidal motion. 7 Hours
Text Books:
1. “Theory of Machines”, Rattan S.S, Tata McGraw-Hill Publishing Company Ltd., New Delhi,
and 2nd edition -2005.
2. “Theory of Machines”, Sadhu Singh, Pearson Education (Singapore) Pvt. Ltd., Indian Branch,
New Delhi, 2ND Edi. 2006.
Reference books:
1. “Theory of Machines & Mechanisms ” , Shigley. J. V. and Uickers, J.J., OXFORD University
press.2004
2. “Theory of Machines -I”, by A.S.Ravindra, Sudha Publications, Revised 5th Edi. 2004.
Scheme of Examination:
One Question to be set from each chapter. Students have to answer any FIVE full questions out of
EIGHT questions, choosing at least 2 questions from part A and 2 question from part B.
Graphical Solutions may be obtained either on the Graph Sheets or on the Answer Book itself.
LESSON PLAN
Sub Code : 10ME44 Hours / Week: 04
I.A. Marks: 25 Total Hours: 52
Subject: Kinematics Of Machines Sem:IV
Hour. No Topics to be covered
1. Definitions of link or element, type of links, constraints motions, kinametic
pair, types of kinametic pair
2. Explanation of kinametic pairs classified and different factor with examples.
Kinametic chain and definition of mechanism and inversion machine
3. Definition of degrees of freedom and mobility of mechanism. Kutzbach and
grubles’s criterion, problems to find mobility of mechanism
4. Classification of kinametic chain: four bar chain mechanism and its
inversions
5. Single slider crank chain and Inversion of single slider crank chain
6. Double slider crank chain and its inversion
7. Quick return motion mechanism: drag link mechanism, and crank and slotted
lever mechanism
8. Whit worth mechanism– sketches & explanations.
9. Straight-line motion mechanism: peacellier’s mechanism and Robert’s
mechanism – sketches & explanations
10. Intermittent motion mechanism: Geneva mechanism and ratchet and pawl
mechanism – sketches & explanations.
11. Toggle mechanism, Pantograph,
12. Hook’s joint and Ackerman steering gear mechanism
13. Gears: definition & different types of gears. Law of gearing. Nomenclature
14. Involutemetry, characterization of involute action
15. Involutes, path of contact, arc of contact, contact ratio etc.
16. Interference in involute gear, methods to avoiding interference.
Determination of backlash
17. Deference between cycloidal and involute teeth
18. Problems on Gears
19. Gear trains: types of gear trains: explanation of sample and compound gear
trains, teeth ratio. Epicyclic gear train
20. Algebraic method to find velocity ratio of sample gear train & compound
gear trains & some problems to be solved
21. Tabular method: to find velocity ratio of epicyclic train
22. Problems to find velocity ratio & speed of the particular gear
23. Problems on epicyclic gear trains
24. Tooth load & torque calculation in epicyclic gear train & some problems
25. Sun and planet gear system
26. Spider gear systems and problems.
27. Differential mechanism of all automobile & some more problems in gear
drive
28. Types of cams & follower with sketches
29. Displacement diagram of different types of motions of follower
30. Cam profiles: drawing cam profile for the reciprocating follower having
knife edge
31. Cam profiles: drawing cam profile for the reciprocating follower having
Roller follower.
32. To draw the cam profile for a cam with roller follower with & without offset
with SHM
33. To draw cam profile for a cam with knife edge and roller with uniform
velocity motion
34. To draw profile of cam of follower with uniform velocity with offset
problem with combine motion of uniform
35. To draw cam profile when follower has URAM with & without offset of cam
axis follower axis
36. To draw cam profile when follower has cycloidal motion
37. Offset Cam
38. Problem to draw profile with combined motions i.e. SHM & UARM during
return stroke & forward stroke
39. Problem to draw the cam profile with reciprocating flat faced follower
40. To draw cam profile of disk cam with oscillating follower
41. Motion & type of motion. Explanation of relative velocity. Ratio between
linear & angular velocity
42. Determination of velocity in mechanism by relative velocity methods with an
examples
43. Problems to find velocity in mechanism
44. Definition of instantaneous center. Three center in line theorem and its
application to locate the no. Of instantaneous center
45. Problem to determine velocity in mechanism by instantaneous center method
46. Relation of linear acceleration with angular acceleration of acceleration with
relative velocity methods
47. Some more problems on to find acceleration of point in the simple
mechanism
48. Problems to determine relative acceleration point on a command line and no
separate line
49. Coniolies component and klein’s contraction for slider arm mechanism
50. Velocity analysis using complex algebra for four bar chain mechanism
51. Acceleration analysis using complex algebra for Four bar chain mechanism
52. Velocity & Acceleration analysis using complex algebra for Slider crank
chain mechanism
STAFF : HOD - IEM
QUESTION BANK
SIMPLE MECHANISMS
1. Explain the term kinematic link? Give the classification of kinematic link.
2. Define the fallowing:-
i) Link. ii) kinematic pair. iii) kinematic chain.
iv) Inversion v) degrees of freedom
3. What is a machine ? giving example, differentiate between a machine and a structure.
4. Write notes on complete and incomplete constraints in lower and higher pairs, illustrating
your answer with neat sketches.
5. Explain different kinds of kinematic pairs giving example for each one of them.
6. Explain the terms: lower pair, higher pair, kinematic chain, and inversion.
7. Sketch and explain the various inversions of a slider crank chain.
8. Sketch and describe the four bar chain mechanism. Why it is considered to be the basic
chain.
9. Sketch and describe the working of two different types of quick-return mechanisms.
10 Sketch a pantograph, explain its working and show that it can be used to reproduce to an
enlarged scale a given figure.
11. What are straight line mechanisms? Describe one type of exact straight line motion
mechanism with help of a sketch.
12. Describe the Watt’s parallel mechanism for straight line motion and derive the condition
under which the straight line is traced.
13. Sketch an intermittent motion mechanism and explain its practical applications.
14. What is the condition for correct steering? Sketch and show the main types of steering gears
and discuss their relative advantages.
15. Explain why two hooke’s joints are used to transmit motion from the engine to the
differential of an automobile.
16. Sketch and explain
a. Approximate straight line motion mechanism
b. Ackerman’s steering gear mechanism.
VELOCITY IN MECHANISMS
1. Explain how the velocities of a slider and the connecting rod are obtained in a slider crank
mechanism?
2. In a slider crank mechanism, the length of crank OB and connecting rod AB are 125 mm
and 500 mm respectively, the center of gravity G of the connecting rod is 275 mm from the
slider A. the crank speed is 600 r.p.m. clockwise. When the crank has turned 45° from the
inner dead position, determine: 1. velocity of the slider A, 2. velocity of the point G, and 3.
angular velocity of the connecting rod AB.
a. in a Whitworth quick return notion mechanism.
ACCELERATION IN MECHANISMS
1. Draw the acceleration diagram of a slider crank mechanism.
2. Explain how the coriolis component of acceleration arises when a point is rotating about
some other fixed point and at the same time its distance from the fixed point varies.
3. Derive an expression for the magnitude of coriolis component of acceleration.
4. State and prove Kennedy’s theorem for three instantaneous center method.
5. Using complex algebra, derive expressions for velocity and acceleration of the piston in a
reciprocating engine mechanism.
6. What do you mean by an instantaneous center? Locate all the instantaneous centers for a 4-
bar chain mechanism.
7. In a reciprocating engine, the length of the crank is 250mm and the length of the connecting
rod is 1000 mm. The crank rotates at an uniform speed of 300 rpm. By Klein’s construction
determine the velocity and acceleration of the piston when the crank is at 30 degrees from
IDC.
8. Using Raven’s approach, derive expressions for angular velocity and angular acceleration (ω and α1) pf the 4-bar linkage shown in figure. Hence obtain ω4 and α4 for the following date.
r1=210mm, r2=60mm, r3=80mm, r4=80mm, θ2=60 degrees, n2=10 rpm cw, α2=0 rad/sq.sec.
GEARS & GEAR TRAINS
1. Explain the terms: Module, Pressure angle, and Addendum.
2. State and prove the law of gearing. Show that involute profile satisfies the conditions for
correct gearing.
3. Derive an expression for the velocity of sliding between a pair of involute teeth. State the
advantages of involute profile as a gear tooth profile.
4. Derive an expression for the length of the arc of contact in a pair of meshed spur gears.
5. Derive an expression for the minimum number teeth required on the pinion in order to
avoid interference in involute gear teeth.
6. Define interference, normal pitch, and axial pitch in gears. How do you reduce the
Interference.
7. Two parallel shafts are connected by spur gearing. The approximate distance between the
shafts is 600 mm. If one shaft runs at 120 r.p.m and the other at 360 r.p.m, find the number of
teeth on each wheel, if the module is 8 mm. Also determine the exact distance apart of the
shafts.
8. The pitch circle diameter of the smaller of the two spur wheels which mesh externally and
have involute teeth is 100 mm. The number of teeth are 16 and 32. the pressure angle is 20° and the addendum is 0.32 of the circular pitch. Find the length of the path of contact of the
pair of teeth.
9. Two gears of 4 module have 24 and 33 teeth. The pressure angle is 20° and each has a stadard addendum of one module. Find the length of the arc of contact and the maximum
velocity of sliding if the pinion rotates at 120 r.p.m.
10. Two mating gears have 20 and 40 involute teeth of module 10 mm and 20° pressure angle. If the addendum on each wheel is such that the path of contact is maximum and interference is
just avoided, find the addendum for each gear wheel, path of contact, arc of contact and
contact ratio.
11. Two shafts inclined at an angle of 65° and with a least distance between them of 175 mm
are to be connected by a spiral gears of normal pitch 15 mm to give a reduction ratio 3:1. find
suitable diameters and numbers of teeth . determine also the efficiency if the spiral angles are
determined by the condition of maximum efficiency. The friction angle is 7°. 12. What do you understand by ‘gear train’? discuss the various types of gear trains.
13. Explain the difference between simple, compound and epicyclic gear trains. What are the
special advantages of epicyclic gear trains.
14. How the velocity ratio is of epicyclic gear train is obtained by tabular method.
15. Explain with a neat sketch the ‘sun and planet wheel’.
16. A compound train consists of six gears. The number of teeth on the gears are as follows:
Gear: A B C D E F
No.of teeth 60 40 50 25 30 24
The gears B and c are on one shaft while the gears D and E are on another shaft . The A drive
gear B, gear C drives D and E drives F. if the gear A transmits 1.5 kW at 100 r.p.m. and the
gear train has an efficiency of 80%, find the torque on gear F.
17. Two involute gears of 200 pressure angle are in mesh. The number of teeth on pinion is 20 and
the gear ratio is 2. If the pitch expressed in module is 5mm and the pitch line speed is 1.2m/s,
assuming addendum as standard and equal to one module, find:
a. The angle turned through by pinion when one pair of teeth is in mesh; and
b. The maximum velocity of sliding.
19. In an epicyclic gear train, an arm carries two gears A and B having 36 and 45 teeth
respectively. If the arm rotates at 150 rpm in the anticlockwise direction about the centre of
the gear A which is fixed, determine the speed of gear B. If the gear A instead of being fixed
, makes 300rpm in the clockwise direction, what will be the speed of gear B?
20. An epicyclic train of gears is arranged as shown in fig. How many revolutions does the arm,
to which the pinions B and C are attached, make:
When A makes one revolution clockwise and D makes half a revolution anticlockwise, and
When A makes one revolution clockwise and D is stationary? The number of teeth on the
gears A and D are 40 and 90 respectively.
21. In an epicyclic gear of the ‘sun and planet’ type shown in fig. The pitch circle diameter of
the internally toothed ring is to be 224mm and the module 4mm. When the ring D is
stationary, the spider A, which carries three planet wheels C of equal size, is to make one
revolution in the same sense as the sun wheel B for every five revolutions of the driving
spindle carrying the sun wheel B. determine suitable numbers of teeth for all the wheels.
22. An internal wheel B with 80 teeth is keyed to a shaft F. A fixed internal wheel C with 80
teeth is concentric with B. A compound wheel D-E gears with the two internal wheels; D has
28 teeth and gears with C while E gears with B. The compound wheels revolve freely on a pin
which projects from a disc keyed to a shaft A co-axial with F. If the wheels have the same
pitch and the shaft A makes 800rpm, what is the speed of shaft F ? sketch the arrangement.
CAMS AND FOLLOWERS:
1. Write short notes on the cams and followers.
2. Explain with sketches the different types of cams and followers.
3. What are the different types of motion with which a follower can move.
4. Define the following terms as applied to cam with a neat sketch:
a) Base circle, b)Pitch circle, c) Pressure angle, and
d) Stroke of the follower
5. Give the expressions for velocity and acceleration during outstroke and return stroke of the
follower.
a) When it moves with SHM
b) When it moves with Uniform acceleration and retardation
6. A cam is to be designed for a knife edge follower with the following data:
Cam lift = 40 mm during 900 of cam rotation with simple harmonic motion.
a. Dwell for the next 300.
b. During the next 600 of cam rotation, the follower returns to its original position with
simple harmonic motion.
c. Well during the remaining 1800.
Draw the profile of the cam when the line of stroke of the follower passes through the axis of
the cam shaft, and he line of stroke is offset 20mm from the axis of the shaft. The radius of the
base circle of the cam is 40mm. Determine the maximum velocity and acceleration of the
follower during its ascent and descent, if the cam rotates at 240 r.p.m.
7. A cam rotating clockwise with a uniform speed is to give the roler follower of 20mm
diameter with the following motion:
a) Follower to move outwards through a distance of 30mm during 1200 of cam
rotation:
b) Follower to dwell for 600 of cam rotation;
c) Follower to return to its initial position during 900 of cam rotation; and
d) Follower to dwell for the remaining 900 of cam rotation.
The minimum radius of the cam is 45 mm and the line of stroke of the follower is offset
15mm from the axis of the cam and displacement of the follower is to take place with simple
harmonic motion on both the outward and return stroke. Draw the cam profile.
8. A flat faced reciprocating follower has the motion:
i) The follower moves out for 800 of cam rotation with uniform acceleration and
retardation, the acceleration being twice the retardation.
ii) The follower dwells for the next 800 of cam rotation.
iii) It moves in for the next 120 of cam rotation with uniform acceleration and
retardation, the retardation being twice the acceleration.
iv) The follower dwells for the remaining period.
The base circle diameter of the cam is 60 mm and the stroke of the follower is 20mm. The
line movement of the follower passes through the cam centre.
Draw the displacement diagram and the profile of the cam very neatly showing all
constructional details.
9. Draw the profile of the cam when the roller follwer moves with Cycloidal motion as given
below:
a) Outstroke with maximum displacement of 44 mm during 1800 of cam
rotation.
b) Return stroke for the next 1500 of cam rotation.
c) Dwell for the remaining 300 of cam rotation.
The minimum radius of cam is 20 mm and the diameter of the roller is 10 mm. The axis of
the roller follower passes through the cam shaft axis.
06ME 45 – MANUFACTURING PROCESS – II
MANUFACTURING PROCESS – II
Subject code: 06ME45 I A Marks: 25
Hours / Week: 05 Exam Hours: 3
Total Lecture Hours: 52 Exam Marks: 100
PART A
1. UNIT 1: Theory of metal cutting: Single point cutting tool nomenclature, geometry of
single point cutting tool. Merchant’s circle diagram and analysis, Ernst-Merchant’s solution,
Shear angle relationship, Problems on Merchant’s analysis, Tool wear & tool failure, Tool
life, Effects of cutting parameters on tool life, Tool’s failure criteria, Taylor’s tool life
equation, Problems on tool life evaluation.
7 Hrs 2. UNIT 2: Cutting tool materials: Desired properties, types of cutting tool materials- HSS
carbides, coated carbides, ceramics, cutting fluids, desired properties, types and selection,
Heat generation in metal cutting, factors affecting heat generation. Heat distribution in tool
and w/p. Measurements of tool tip temperature.
7 Hrs 3. UNIT 3: Turning (Lathe), Shaping and Planning Machines: Classification,
Constructional features, tool layout, driving mechanisms and operations of Capstan and
turret lathes, shaping m/c and planning m/c.
6 Hrs 4. UNIT 4: Drilling machines: Classification, constructional features, drilling and related
operations, Types of drill and drill-bit nomenclature, Drill materials.
6 Hrs
PART B
5. UNIT 5: Milling machines: Classification, constructional features, milling cutters
nomenclatures, milling operations, Up milling down milling concepts.
Indexing: Simple, compound, differential &angular indexing calculations. Simple problems
on simple and compound indexing. 7 Hrs
6. UNIT 6: Grinding machines: Types of abrasives, bonding process, classification,
constructional features (cylindrical and surface grinding), Selection of grinding wheel. 6 Hrs
7. UNIT 7: Lapping and Honing Machines: Principle of operation, Construction and
applications. 7 Hrs
8. UNIT 8: Non-Traditional Machining Process: Principle, need, equipment, operation and
applications of LBM, Plasma Arc Machining, Electro chemical machining, Ultrasonic
Machining, Abrasive jet machining, Water jet machining. 7 Hrs
Text Books:
1. ‘Workshop Technology’, Hajra Choudhry Vol-II, Media Promoters and Publishers Pvt. Ltd.,
2004.
2. ‘Production Technology’, R.K. Jain, Khanna Publications, 2003.
3. ‘Production Technology’, HMT, Tata McGraw Hill, 2001.
Reference Books:
1. ‘Manufacturing Science’, Amitabha Ghosh and Mallik, Affiliated East-West Press, 2003.
2. ‘Fundamentals of Metal Machining and Machine Tools’, G. Boothroyd, McGraw Hill, 2000.
LESSON PLAN
Sub Code: 06ME45 Hours/Week:05
I A Marks: 25 25Total Lecture Hours: 52
Subject: Manufacturing Process-II Sem: IV
Hour. No Topics to be covered
PART A
01 Unit 1: Theory Of Metal Cutting:- Single Point Cutting Tool Nomenclature,
Geometry,
02 Merchant’s Analysis.
03 Ernst-Merchant’s Solution, Shear Angle Relationship.
04 Problems On Merchant’s Analysis
05 Tool Wear And Tool Failure, Effects Of Cutting Parameters.
06 Tools Life Criteria, Taylor’s Tool Life Equation
07 Problems On Tool Evaluation,
08 Unit 2: Heat Generation In Metal Cutting,
09 Factors Affecting Heat Generation
10 Measurement Of Tool Tip Temperature.
11 Cutting Tool Materials: - Desired Properties,
12 Types Of Tool Cutting Materials-
13 HSS, Carbides, and Coated Carbides.
14 Ceramics Cutting Fluids, Desired Properties
15 UNIT 3: Capstan And Turret Lathe Constructional Features
16 Tool Layout In Capstan And Turret Lathe
17 Shaping And Planning Machine:- Classifications
18 Constructional Features Of Shaping and Planning Machine
19 Driving Mechanisms In Planning And Shaping Machines
20 Shaping Machine, Planning Machine Operations
21 UNIT 4: Classification Of Drilling Machines
22 Constructional Features Of Drilling Machines
23 Drill Bit Nomenclature
24 Types Of Drill
25 Drill Materials
26 Drilling And Related Operations
PART B
27 UNIT 5: Milling Machines: Classification, Constructional Features
28 Milling Cutters Nomenclature, Operation Of Milling Machine
29 Up milling And Down Milling Concepts, Indexing
30 Simple And Compound Indexing
31 Differential And Angular Indexing
32 Calculations In Simple And Compound Indexing
33 Calculations In Differential And Angular Indexing
34 UNIT 6: Grinding Machines: Types Of Abrasives
35 Bonding Processes
36 Classification Of Grinding Machines
37 Constructional Features Of cylindrical Grinding Machine.
38 Constructional Features Of surface Grinding Machine
39 Designation And Selection Of Grinding Wheel
40 U NIT 7:Lapping: Principles of operation
41 Lapping m/c construction
42 Lapping applications
43 Honing: Principles of operation
44 Honing m/c construction
45 Honing applications
46 UNIT 8: Non Traditional Machining Processes: - Principle, Need, Equipment
47 Operations And Applications Of Laser Beam Machining
48 Operations And Applications Of Electro-Chemical Machining
49 Operations And Applications Of Ultrasonic Machining
50 Operations And Applications Of Plasma Arc Machining
51 Operations And Applications Of Abrasive Jet Machining
52 Operations And Applications Of Water Jet Machining
STAFF: HOD - IEM
DEPT OF IEM IV SEMESTER 65
QUESTION BANK
01 Briefly explain about the single point cutting tool nomenclature.
02 What is Orthogonal And Oblique Cutting?
03 State the differences between orthogonal and oblique cutting.
04 Explain the Mechanism Of Chip Formation with a neat sketch.
05 What are the types Of Chips? Explain in detail.
06 What is the concept of Merchant’s Analysis?
07 Draw the merchant circle diagram and derive the equation for the co-efficient of friction.
08 Describe the shear angle relationship.
09 In orthogonal cutting of a mild steel bar of 60 mm dia. on a lathe, a feed of 0.8mm was
used; a continuous chip of 1.4 mm thickness was removed at a rotational speed of 80 rpm.
Calculate the chip thickness ratio, chip reduction ratio and the total length of the chip
removed in one minute.
10 In orthogonal turning of a 50mm dia mild steel bar on a lathe the following data were
obtained rake angle =150 , cutting speed =100m/min, feed=0.2mm/rev., cutting force
=180kg,feed force=60kg.Calculate the shear angle, coefficient of friction, cutting force,
chip flow velocity & shear force, if the chip thickness =0.3mm.
11 Carbide tipped tool of designation 0-10-5-5-8-90-1mm(ORS) is used to turn a steel work
piece of 50mm dia. with abutting speed of 240m/min and feed of 0.25 mm/rev. The data
obtained shows the cutting force=180kg,feed force=100kg and chip
thickness=0.32mm.calculate the shear angle, shear force, friction force, coefficient of
friction and velocity of chip flow.
12 Write a brief note on Tool Wear And Tool Failure
13 Enumerate the Effects Of Cutting Parameters and elaborate.
14 Explain the tools Life Criteria in detail.
15 Give the Taylor’s Tool Life Equation and elaborate.
16 What are the factors that lead to the Heat Generation In Metal Cutting? Explain.
17 List the properties of Cutting Tool Materials and explain.
18 What are the Types Of Tool Cutting Materials? Give a brief explanation.
19 What is Machinability? Explain in detail the Factors Affecting Machinability.
20 Draw a neat sketch of an engine lathe and explain briefly.
21 Explain about the Capstan And Turret Lathe Constructional Features.
22 Explain the Capstan And Turret Lathe Functional Features.
23 Explain the differences between capstan lathe and turret lathe
24 Explain about the tool holding devices used in Capstan And Turret Lathe.
25 Explain about the work holding devices used in Capstan And Turret Lathe.
26 Describe the Tool Layout In Capstan And Turret Lathe.
27 Give the Classification Of Drilling Machines and explain briefly with neat sketches.
28 Explain about the Drill Bit Nomenclature.
29 What are the tools holding devices used in drilling machines? Explain with neat sketches.
30 Give the classification of shaping machines with brief explanation.
31 Explain about the Constructional and operational Features Of Shaping Machine.
32 What are the Driving Mechanisms In Shaping Machines? Explain briefly with sketches.
33 Explain the Tool And Work Holding Devices Used In Shaping Machine.
34 Explain crank and slotted link mechanism in a shaper.
35 Explain whit worth quick return mechanism in a shaper.
36 Explain hydraulic shaper with a neat sketch.
DEPT OF IEM IV SEMESTER 66
37 Mention work-holding devices in a shaper and explain any two.
38 Explain with neat sketch a planer.
39 Explain briefly different types of planning machines.
40 Explain the drive mechanisms of a planer.
41 Mention different types of milling machines and explain briefly.
42 Explain about the column & knee type-milling machine.
43 Explain the nomenclature of milling cutter.
44 Mention various milling operations and explain each one of them briefly.
45 Mention differences between up milling and down milling.
46 What does indexing mean? Explain simple & compound indexing.
47 Explain universal dividing head with neat sketch.
48 Explain the mechanism of indexing in universal dividing head.
49 It is required to divide the periphery of a job in to 87 divisions. Find the crank movement
by compound indexing.
50 Explain differential indexing with an example.
51 Index for 73 divisions by differential indexing.
52 Index for 140 40’ by angular indexing.
53 What is grinding. Mention different types of grinding.
54 Give the classification of grinding machines.
55 Explain horizontal spindle reciprocating table-grinding machine.
56 Explain vertical spindle rotary table surface grinding machine.
57 Explain center type cylindrical grinding machine.
58 Explain center less grinding with neat sketch. Mention advantages and disadvantages.
59 Mention different types of grinding wheels with their applications.
60 Explain how you select a grinding wheel.
61 Explain the terms loading and glazing in grinding wheels.
62 Explain truing and dressing in grinding wheels.
63 Explain how balancing of grinding wheel is done.
64 What is hobbing? Mention various gear-cutting operations.
65 Explain a gear hobbing machine with a neat sketch.
66 Mention different broaching machines. Explain them briefly.
67 Explain the principle of broaching. Mention various broaching operations.
68 What is honing and lapping. Explain honing machine.
69 Explain the terms polishing, buffing, and super finishing
70 Write a brief note on non-traditional machining processes.
71 Describe the Operations And Applications Of Electric Discharge Machining.
72 Describe the Operations And Applications Of Electro-Chemical Machining.
73 Describe the Operations And Applications Of Ultrasonic Machining.
74 Describe the Operations And Applications Of Laser Beam Machining.
75 Describe the Operations And Applications Of Abrasive Jet Machining.
76 Describe the Operations And Applications Of Water Jet Machining.
77 Describe the Operations And Applications Of Electron Beam Machining
DEPT OF IEM IV SEMESTER 67
DEPT OF IEM IV SEMESTER 68
DEPT OF IEM IV SEMESTER 69
DEPT OF IEM IV SEMESTER 70
DEPT OF IEM IV SEMESTER 71
DEPT OF IEM IV SEMESTER 72
DEPT OF IEM IV SEMESTER 73
06ME 46B – FLUID MECHANICS
DEPT OF IEM IV SEMESTER 74
FLUID MECHANICS
Sub Code: 06ME46B IA Marks: 25
Hrs/week: 04 Exam Hours: 03
Total Lecture Hrs: 52 Exam Marks: 100
PART – A
UNIT 1:
Properties of Fluids: Introduction, properties of fluids, viscosity, thermodynamic properties,
Surface tension and Capillarity, Vapour pressure and Cavitation.
6 Hours
UNIT 2:
Fluid Statics: Fluid pressure at a point, Pascal’s law, pressure variation in a static fluid, Absolute,
gauge, atmospheric and vacuum pressures, simp le manometers, differential manometers, total
pressure and center of pressure,
vertical plane surface submerged in liquid, horizontal plane surface submerged in liquid, inclined
plane surface submerged in liquid, curved surface submerged in liquid. Buoyancy, center of
buoyancy, metacenter and metacentric height, conditio ns of equilibrium of floating and submerged
bodies. 7 Hours
Fluid Kinematics: Types of fluid flow, Introduction, continuity equation,continuity equation in
three dimensions (Cartesian co-ordinate system only),velocity and acceleration, velocity potential
function and stream function. 7 Hours
UNIT 3:
Dimensional Analysis: Introduction, derived quantities, dimensions of physical quantities,
dimensional homogeneity, Buckingham’s p theorem, Raleigh’s method, dimensionless numbers,
similitude, types of similitudes. 6 Hours
PART – B
UNIT 4:
Fluid Dynamics: Introduction, equations of motion, Euler’s equation of motion, Bernoulli’s
equation from Euler’s equation, Bernoulli’s equation for real fluids.
6 Hours
UNIT 5:
Fluid flow measurements: Introduction, venturimeter, orifice meter, Pitot tube.
Flow through pipes: Frictional loss in pipe flow, Darcy- Equation for loss of head due to friction in
pipes, Chezy’s equation for loss of head due to friction in pipes, hydraulic gradient and total energy
line. 7 Hours
UNIT 6:
Laminar flow and viscous effects: Reynold’s number, critical Reynold’s number, Laminar flow
through circular pipe-Hagen poiseulle’s equation, Laminar flow between parallel and stationery
plates. 6 Hours
UNIT 7:
Flow past immersed bodies: Drag, Lift, expression for lift and drag, pressure drag and friction
drag, boundary layer concept, displacement thickness, momentum thickness and energy thickness.
DEPT OF IEM IV SEMESTER 75
Introduction to compressible flow: Velocity of sound in a fluid, Mach number, Propagation of
pressure waves in a compressible fluid. 7 Hours
Text Books:
1. Fluid Mechanics by Oijush K.Kundu, IRAM COCHEN, EL SEVIER 3rd Ed. 2005.
2. Fluid Mechanics by Dr. Bansal.R.K, Lakshmi Publications, 2004.
3. Fluid Mechanics and hydraulics, Dr. Jagadishlal: Metropolitan Book Co-Ltd., 1997.
4. Fluid Mechanics (SI Units), Yunus A. Cingel John M. Oimbala. Tata MaGrawHill,2006.
Reference books:
1. Fluid Mechanics, Fundamental & applications, by Yunus A, Cenegel, John M,Cimbala, Tata
MacGraw Hill, 2006.
2. Fluid Mechanics by John F.Douglas, Janul and M.Gasiosek and john A.Swaffield, Pearson
Education Asia, 5th ed., 2006
3. Fluid Mechanics and Fluid Power Engineering,” Kumar.D.S, Kataria and Sons.,2004.
4. Fluid Mechanics R.K.Hegde, Niranjana Murthy Spana Book House, 2005.
Scheme of examination:
One Question to be set from each chapter. Students have to answer any FIVE full questions out of
EIGHT questions, choosing at least 2 questions from part A and 2 questions from part B.
DEPT OF IEM IV SEMESTER 76
LESSON PLAN
Sub Code: 06ME46B Hours / Week: 04
I A Marks: 25 Total Lecture Hours: 52
Subject: Fluid Mechanics Sem: IV
Hour.
No TOPICS TO BE COVERED
1 Properties of Fluids: Introduction, properties of fluids
2 viscosity and kinematic viscosity and its principles
3 Thermodynamic properties
4 Surface tension and Capillarity
5 Vapour pressure
6 Cavitation.
7 Fluid Statics: Fluid pressure at a point, Pascal’s law
8 pressure variation in a static fluid, Absolute, gauge,
9 atmospheric and vacuum pressures, simple manometers, differential
manometers
10 total pressure and center of pressure, vertical plane surface submerged in
liquid, horizontal plane surface submerged in liquid
11 Curved surface submerged in liquid. Buoyancy, center of buoyancy,
12 metacenter and metacentric height
13 conditions of equilibrium of floating and submerged bodies.
14 Fluid Kinematics: Types of fluid flow, Introduction, continuity equation,
continuity equation in three dimensions (Cartesian co-ordinate system only),
velocity and acceleration, velocity potential function and stream function
15 Introduction, continuity equation
16 continuity equation in three dimensions(Cartesian co-ordinate system only),
17 velocity and acceleration
19 velocity potential function
20 stream function
21 Dimensional Analysis: Introduction, derived quantities, dimensions of
physical quantities, dimensional homogeneity, Buckingham’s p theorem,
Raleigh’s method, dimensionless numbers, similitude, types of similitudes.
22 dimensions of physical quantities
23 dimensional homogeneity, Buckingham’s p theorem
24 Buckingham’s p theorem
25 Raleigh’s method, dimensionless numbers
26 similitude, types of similitudes
27 Fluid Dynamics: Introduction,
28 equations of motion
29 , Euler’s equation of motion
30 Bernoulli’s equation from Euler’s equation
31 Bernoulli’s equation for real fluids.
32 Fluid flow measurements: Introduction,
DEPT OF IEM IV SEMESTER 77
33 venturimeter, orifice meter
34 Pitot tube and Pitot tube
35 Flow through pipes: Frictional loss in pipe flow
36 Darcy- Equation for loss of head due to friction in pipes
37 Chezy’s equation for loss of head due to friction in pipes
38 hydraulic gradient and total energy line.
39 Laminar flow and viscous effects:
40 Reynold’s number
41 critical Reynold’s number
42 Laminar flow through circular pipe-Hagen poiseulle’s equation
43 Laminar flow between parallel and stationery plates.
44 Flow past immersed bodies: Drag, Lift,
45 expression for lift and drag,
46 pressure drag and friction drag
47 boundary layer concept
48 Displacement thickness, momentum thickness
49 energy thickness.
50 Mach number
51 Propagation of pressure waves in a compressible fluid.
52 Revision & numerical practice
STAFF: HOD - IEM
DEPT OF IEM IV SEMESTER 78
QUESTION BANK
Unit-1
1. Differentiates between Real fluids and ideal fluids
2. Explain the following
a. Concept of continuity
b. Vapour pressure
c. Surface tension
d. Viscosity
e. Compressibility
f. Newtonian fluid &non-Newtonian fluid
3. Explain the phenomenon of capillarity. Obtain an expression for capillary rise of a liquid
4. A liquid bubble of 2cm in radius has an internal pressure of 12.95 pascals.Calculate the
Surface tension of the liquid film
5. The surface tension of H2O in contact with air at 200C is 0.072N/M. If the diameter of the
droplet is 0.04mm, calculate the pressure with in the droplet.
6. A plate having an area of 0.6m2 is sliding down the inclined plane at 30
0to the horizontal
with a velocity of 0.36m/s, there is a cushion of fluid 1.8mm thick between the plane and the
plate. Find the viscosity of the fluid if the weight of the plate is 280 N
7. The capillary rise in the glass tube is not to exceed 0.2mm of H20, Determine its minimum
size, given that surface tension for H20 in contact with air is 0.0725N/M
8. Calculate the capillary effect in a glass tube of 3mm diameter when immersed in mercury of
specific gravity 13.6 of contact angle 1300 and surface tension 0.51N/M
9. Explain vapour pressure & its effect on cavitation
Unit-2
1. Show that the pressure in a static fluid is same in all directions
2. Explain with a neat sketch how a differential manometer is used to find the pressure
difference between two points in a fluid
3. With a neat sketch explain any two mechanical gauges
4. Define the following terms: a) Total pressure b) center of pressure
5. Derive expression for total pressure and center of pressure for a vertically immersed surface
6. Derive an expression for the depth of center of pressure from free surface of liquid of an
inclined plane surface submerged in the liquid.
7. A manometer containing mercury is connected to two points 15m apart on a pipeline
conveying water. The pipeline is straight & slopes at an angle of 15° with the horizontal. The monometer gives a reading of 150 mm. determine the difference between the two points
of pipeline. take specific gravity of mercury as 13.6 & that of H2O as 1.0.
DEPT OF IEM IV SEMESTER 79
8. A circular plate of 2m diameter is immersed in an oil of specific gravity of 0.8 such that its
surface is 30° to the free surface. Its top edge is 2.5 m below the free surface. Find the force
and center of pressure.
9. Find the total pressure & position of center of pressure on a triangular plate of base 2m &
height 3m which is immersed in H2O in such a way that the plan of the plate mates an angle
of 600 with the free surface of the H2O. The base of the plate is parallel to H2O surface & at
a depth of 2.5 m from H2O surface.
10. Define metacentre & metacentric height Derive an expression analytical method for meta
center height
11. Derive on expression for calculating time of rolling of a floating body
12. A solid cylinder of diameter 4m has a height of 3 mts. Find the meta centric height of the
cylinder when it is floating in H2O with its axis vertical. the specific gravity of the cylinder
is 0.6
13. A ship of weight 32000KN is floating in sea H2O. The center of buoyancy is 1.6 m below
its center of gravity. The moment of inertia of the ship area at the H2O level is 8320m4 If the
radius of gyration of the ship is 3.2m Find its period of rolling .Take specific weight of sea
H2O = 10.1kN/m3
14. A circular plat 3m diameter is immersed in H2O in such a way that its greatest & least depth
below the free surface are 4m & 1.5m respectively. Determine the total pressure on one face
of the plate & position of the center of pressure.
15. A wooden cylinder of specific gravity 0.6 and diameter D and length L is required to float in
oil of specific gravity 0.9. Find the L/D ratio for the cylinder to float with its axis vertical
16. Explain different types if fluid flows
17. Explain the following a)path line b) stream line c) streak line
18. Derive the continuity equation for a 3 dimensional steady incompressible flow
19. Define a) velocity potential b) stream function
20. Show that the stream function ψ=x2-y2 represents a case of two dimensional flow. Find its
velocity potential
21. A stream function is given by the expression ψ=2x2-y3.Find components of the velocity ,as
well as the resultant velocity at a point (3,1)
22. Define Flow net. mention uses & limitation of flow nets
23. Differentiate between forced vortex flow and free vortex flow
24. Derive an equation of motion for forced vortex flow and free vortex flow
25. The velocity potential function for a two dimensional flow is φ=x(2y-1) at a point p(4,5) determine a) The velocity & b) the value of stream function
Unit-3
1. Define dimensional analysis? Mention advantages and uses of dimensional analysis.
2. What do you mean by fundamental units & derived units? Give examples
3. Define the following 1) Reynolds number 2) frond’s number 3) Euler number 4) mach
number 5) Weber number
4. Write a brief note on model studies
DEPT OF IEM IV SEMESTER 80
5. Explain similitude& types of similitude’s
6. Describe the Rayleigh’s method for dimensional analysis.
7. State Bucking ∏ theorem. Write the step by step procedure followed in dimensional analysis
using Bucking ∏ theorem
8. The pressure drop ∆p in a pipe of diameter D and length l depends on the density ρ and viscosity µ of fluid flowing, mean velocity v of flow and average height of protuberance t
show that the pressure drop can be impressed in the form
∆p = ρv2 φ [l/d, µ/vDρ ,t/D ]
9. Using Bucking ∏ theorem, show that the velocity through a circular orifice is given by
V=√2gH φ[D/H, µ/vHρ ] Where.
H=heading causing flow, D=diameter of the orifice, µ=co-efficient of viscocity , g=acceleration due to gravity, ρ=mass density
10. The pressure drop ∆p between two points in pipe due to turbulent flow depends on velocity v, diameter D, dynamic viscocity µ , density ρ, Roughness K and distance between points L ,using dimensional analysis show that ∆p/ρ v2= φ [L/D, VDρ/M ,K/D ]
11. The frictional torque T of a disc of diameter D rotating at a speed N in a fluid of viscosity µ and density ρ in a turbulent flow is given by T=D5
N2 ρ φ [ µ/D2ρN] , Prove this by
dimensional analysis
Unit-4
1. Derive the Euler’s equation of motions along a streamlines and reduce it to Bernoulli’s
equation
2. Name 3 application of Bernoulli’s theorem and mention the use of each
3. Derive Bernoulli’s equation for real fluids.
4. water is flowing through a pipe having diameters 600mm & 400 mm at the bottom & upper
end respectively ,then intensity of pressure at the bottom end is 350 k/m2 and the pressure at
the upper end is 100 KN/m2 .Determine the difference in datum head if the rate of flow
through the pipe is 60 lit /sec
5. A 6m long pipe is inclined at an angle of 20 degree with the horizontal. The smaller section
of the pipe which is at lower level is of 100mm diameter and the larger section of the pipe is
of 300m diameter. If the pipe is uniformly tapering and the velocity of water the smaller
section is 1.8 m/s. determine the difference of pressure between the two sections.
6. An oil of specific gravity 0.8 is flowing through a taper pipe of length 50m having a
diameter of 40 cm at the upper end and 20 cm at the lower end at a rate of 60 l/s. The pipe
has a slope of 1 in 50.Find the pressure at the lower end if the pressure at the higher end is
2.5 bar. Indicate the direction of fluid flow. Neglect the losses.
Unit-5
1. Derive the expression of discharge through a V- notch
2. Define venturimeter ? Derive the expression for rate of flow through venturimeter
3. Derive the expression for coefficient of discharge through orifice
DEPT OF IEM IV SEMESTER 81
4. An oil of specific gravity 0.9 flows through a venturimeter having inlet diameter 200mm and
throat diameter 100mm. The mercury manometer reads 200mm, if cd=0.98, Find the
discharge
5. An orificemeter with orifice diameter 10cm is inserted in a pipe of 20cm diameter. The
pressure gauges fitted upstream & downstream of the orificemeter give reading of 19.62
N/cm2 & 9.81 N/cm
2 respectively. co-eff of discharge for the meter is given as 0.6 Find the
discharge of water through pipe.
6. A horizontal venturimenter with inlet & throat diameters 300mm and 100mm respectively is
used to measure the flow of water, the pressure intensity at inlet is 130 KN/m2 while the
vacuum head at the throat is 350 mm of mercury. Assuming that 3% of head is lost in
between the inlet & throat find
(a)The value of cd for the venturimeter (b) Rate of flow
7. A 200mmx100mm venturimeter is provided in a vertical pipe carrying water flowing in
the upward direction. A differential mercury manometer connected to the inlet & throat
gives a reading of 220 mm Find the rate of flow assume cd=0.98
8. Determine the rate of flow of water though a pipe 300mm dia placed in an inclined position
where a venturimeter is inserted having a throat dia 150 mm. The difference of pressure
between the main & throat is measured by a liquid of specific gravity 0.7 in an inverted U-
tube which gives a reading of 260mm. The loss of head between the main & throat is 0.3
times the kinetic head of the pipe.
9. A pitot state is used to measure the velocity of an aeroplane. If a U tube differential
monometer is connected between stagnation & Static pressures and shows 100mm of H2O
find the speed of the plane in km/hr, take co-efficient of the tube as 0.98 & density of air
0.125Kg/m3 Neglect other losses.
10. Derive darcy-weisbach formula for calculating loss of head due to friction in a pipe.
11. Derive chezy’s formula for loss of head due to friction in a pipe
12. Explain with the help of a neat skeatches (a) Hydraulic gradient (b)Total Energy line
13. A pipe 60mm diameter & 9m long in which water is flow at the rate of 3m/s. If the central
pipe 3m length is replaced by a 90mm diameter pipe, determine the loss of head saved. f
=0.01
14. A reservoir has been built 4 km, away from a college campus having 5000 inhabitants.
Water is to be supplied from the reservoir to the campus. It is estimated that each inhabitant
will consume 200lts of water per day, and that half of the daily supply is pumped within 10
hours, calculate the size of the supply main, if the loss of head due to friction in pipeline is
20m, Assume the co-efficient of friction for the pipeline as 0.008
15. Petrol of specific gravity 0.716 is flowing through a pipe of 200mm diamter at a rate of 600
litres/sec. The length of the pipe is 1 Km. The friction factor is f=0.052 in the equation hf
=4flv2/2gD , determine the head lost due to friction & power required to maintain the flow,
kinematic viscosity of petrol is 4 x 10-5 m
2/s
16. A town having a population of 1 lakh is to be supplied with water from a reservoir Km
distant. Half the daily supply os 150 lit/head is supplied in 8 hours. If the head available is
15m find the size of the pipe.By Darcy’s formula f=0.005,By Chezy’s formula c=45
DEPT OF IEM IV SEMESTER 82
17. A pipe of uniform diameter connects two reservoirs at different elevations. What would be
the percentage increase in discharge if another pipe of same diameter is added from the
middle length parallel to it ? neglect minor losses and assume equal values of Darcy’s co-
efficient of friction f for both pipes.
Unit-6
1. Write a short note on Reynold’s number
2. Derive Hagen-poiseuille equation & state the assumptions made.
3. A fluid of viscosity 8 poise and specific gravity 1.2 is flowing through a circular pipe of
diameter 100mm. The maximum shear stress at the pipe wall is 210 N/m2 Find (a)The
pressure gradient (b) Reynolds number of flow (c)The average velocity
4. The fluid of viscosity 0.7 N.S/m2 and specific gravity 1.3 is flowing through a circular pipe
of diameter 10cm.the maximum shear stress at the pipe wall is 196.2 N/m2.Find the pressure
gradient , the average velocity and Reynolds number
Unit-7
1. Explain the terms (a)friction drag (b) lift (c) flow pas cylinder (d) pressure drag (e)model
studies (f) Form drag
2. what is meant by boundary layer ?Explain
3. Explain mach number and with sketch explain waveforms for different values of mach
number corresponding to subsonic, sonic and supersonic conditions
4. Calculate the mach number at a point on a jet propelled air craft, which is flying at 1100
km/hr at sea- level where air temp is 20 degree C. Take γ=1.4 and R=287 J/kg.k.
5. A rocket travels in air at an altitude of about 18 km. where the temp is approximately -60
degree C. If the speed of the rocket is 2000 km/hr, find the mach number & mach angle
Take γ=1.4 and R=287 J/kg.k for air
6. Find the velocity of bullet fired in standard air if the mach angle is 30 degree.
7. Take R= 287.14 J/Kg.0 k and K=1.4 for air. Assume temperature of air as 15 degree C.
8. Derive the continuity equation for a 2-D compressible flow in differential form
9. Show that the velocity of propagation of elastic wave in an adiabatic medium is given by
C=√KRT starting from fundamentals.
A jet fighter flying at Mach number 2.0 is observed directly over head at a height of 10
km .How much distance it would cover before the sonic boom is heard on the ground?
DEPT OF IEM IV SEMESTER 83
DEPT OF IEM IV SEMESTER 84
DEPT OF IEM IV SEMESTER 85
DEPT OF IEM IV SEMESTER 86
DEPT OF IEM IV SEMESTER 87
ME
DEPT OF IEM IV SEMESTER 88
DEPT OF IEM IV SEMESTER 89
MECHANICAL MEASUREMENT & METROLOGY LAB
Subject code: 06MEL47B I A Marks: 25
Hours / Week: 04 Exam Hours: 3
Total Practical Hours: 52 Exam Marks: 100
PART-A: MECHANICAL MEASUREMENTS
1. Calibration of Pressure Gauge
2. Calibration of Thermocouple
3. Calibration of LVDT
4. Calibration of Load cell
5. Determination of modulus of elasticity of a mild steel specimen using strain gauges.
6. Optical Projector / Toolmaker Microscope.
7. Measurements of angle using Sine Center / Sine bar / bevel protractor
8. Measurements of alignment using Autocollimator / roller set
9. Measurements of cutting tool forces using
a) Lathe tool Dynamometer
b) Drill tool Dynamometer.
10. Measurements of Screw thread Parameters using two wire or three-wire
method.
11. Measurements of Surface roughness. Using Tally surf/mechanical
Comparator.
12. Measurements of gear tooth profile using gear tooth vernier /gear
tooth micrometer.
13. Calibration of micrometer using slip gauges
14. Measurement using Optical Flats
Scheme of Examination:
ONE question from Metrology (part -A) 20 Marks
ONE question from Instrumentation (part -B) 20 Marks
Viva –Voce 10 Marks
Sl.
No Date Name of the Experiment
Page
No.
Mark
s
Initial
of
Staff
PART – A (MECHANICAL MEASUREMENTS)
1. Calibration Pressure Transducer 3-4
2.
Calibration Of Thermocouple 5-7
3. Calibration Of LVDT 8-11
4.
Calibration Of Load Cell 12-13
5.
Young’s Modulus2 14-17
DEPT OF IEM IV SEMESTER 90
PART – B (METROLOGY)
6. Tool Maker’s Microscope 18-19
7. Thread Terminology – Optical Profile
Projector 20-21
8.
Measurement Of Angle
(I)Using Sine – Bar
(Ii) Using Bevel Protractor 22-26
9. Measurement Of Cutting Forces Using
Lathe Tool Dynamometer 27
10
.
Measurement Of Effective Diameter
Using Three-Wire Method 28-29
11
. Gear Tooth Vernier Caliper 30-31
12
. Calibration Of Micrometer 32-33
13
. Flatness Test 34
14
.
Measurement of forces in Lathe l by
Lathe Tool Dynamometer
15
.
Measurement of forces in drilling
machine by Drill Tool Dynamometer
DEPT OF IEM IV SEMESTER 91
MACHINE SHOP – II
Subject code: 06MEL48B I A Marks: 25
Hours / Week: 03 Exam Hours: 3
Total Practical Hours: 52 Exam Marks: 50
PART A
Preparation of three models on lathe involving plain turning, taper turning, step turning,
thread cutting. Facing, knurling, drilling, boring, internal thread cutting and eccentric
turning.
PART B
Cutting of ‘V’ Groove dovetail / Rectangular groove using shaping and cutting of gear
teeth using milling machine.
Scheme of examination:
One model from Part-A 30 Marks
One model from Part-B 10 Marks
Viva Voce: 10 Marks
Total Marks 50 Marks