how to use virtual calculator
TRANSCRIPT
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 1/44
Virtual Calculator
Excellent use of Virtual calculator for GATE-2016
It is an interactive PDF file just click on the content and you will be directed to the required page
For all Branch of Engineering For Mechanical Engineering
General Instructions
Some functions
1. Exp
2. ln
3. log
4. log yx
5. ex
6. 10x
7. x y
8.
9.
10. √
11.1/x
12.sin cos tan sinh cosh tanh
13. sin -1 cos -1 tan -1 sinh -1 cosh -
1 tanh -1
14. Factorial n (n!)
15. Linear Interpolation
16. Linear regression
Production Engineering
Theory of Metal Cutting
Shear angle
Shear strain
Velocity relations
Merchant Circle
Force Relations
Turning
Specific Energy
Linear Interpolation
Tool life equation
Linear regression
Economics
Metrology
Rolling
Forging
Extrusion
Wire Drawing
Sheet Metal Operation
Casting
Welding
Machine Tools
ECM Calculation
Strength of Materials
Elongation
Thermal Stress
Principal stresses
Deflection of Beams
Bending stresses
Torsion
Spring
Theories of column
Theories of Failure
Theory of Machines
Frequency
Transmissibility ratio
Thermodynamics
SFEE
Entropy Change
Available Energy
Heat and Mass Transfer
Conduction
Unsteady Conduction
Heat Exchanger
Radiation
Industrial Engineering
Forecasting
Regression Analysis
Optimum run size
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 2/44
2 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
General Instructions
Operation procedures and sequence of operations are totally different in Virtual
calculator. Hence all students are requested to practice the following procedures.
It is very weak calculator, can’t handle large equation at a time, we have to
calculate part by part.
Use more and more bracket for calculations
BODMAS rule should be followed
B → Bracket O → Order (Power and roots) D → Division
M → Multiplication A → Addition
S → Subtraction
For answer must click on = [= means you have to click on this = button]
In the starting of any calculation you must click on C
[ C means you have to click on this C button]
For writing sin30 first write 30 and then click on sin (same procedure should be
follow for all trigonometric calculations)
[ sin means you have to click on this sin button]
Here mod button is simply a showpiece never press mod button. It is indicating
calculator is in deg mode or in rad mode. For changing degree mode to radian
mode you have to press radio ⊙ button.
Some functions
1. Exp
It is actually power of 10
102 1 Exp 2 = 100
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 3/44
3 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
200 GPa 200 Exp 9 = 2e+11 means 2 x 1011
Note: Instead of Exp we will use 10X button of ten.
2. ln
ln2 2 ln = 0.6931472
Note: you have to first type value then ln button.
2ln2 2 * 2 ln = 1.386294
3ln5 3 * 5 ln = 4.828314
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 4/44
4 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
3. log
log100 100 log = 2
Note: you have to first type value then log button.
5 log50 5 * 50 log = 8.494850
4. logyx
log10100 100 logy
x 10 = 2
Note: you have to first type value of x then logyx button then value of y. Logically
value of x should be given first then value of y.
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 5/44
5 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
log550 50 logy
x 5 = 2.430677
7log550 7 * ( 50 logy
x 5 ) = 17.01474
Note: In this case ( ) is must. if you press 7 * 50 logyx it becomes
350 logx Base y and give wrong answer. But see in case of 5 log50 we simply use
5 * 50 log = 8.494850 and no need of ( ).
5. eX
e2 2 eX = 7.389056
Note: you have to first type value of x then eX button.
5 e2 5 * 2 eX = 36.94528
4 e(5 x 3.4 – 1) 4 * ( 5 x 3.4 – 1 ) eX = 3.554444e+7
6. 10X
102 2 10X = 100
Note: you have to first type value of x then 10X button.
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 6/44
6 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
5 x 102 5 * 2 10X = 500
105/3 (5/3) 10X = 46.41592
101.4−1
1.4 10(
(1.4−1)
1.4) ((1.4− 1)/1.4) 10X = 1.930698
Or you may simplify
101.4−1
1.4 10(
0.4
1.4) (0.4/1.4)10X = 1.930698
7. Xy
23 2 xy 3 = 8
Note: you have to first type value of x then xy button then value of y. Logically
value of x should be given first then value of y.
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 7/44
7 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
21
−1
⟹ 21
−1 ⟹ 5
3 1.41.4−1
(5/3) xy 1.4/(1.4 – 1) = 5.111263
8.
325
32 5 = 2
Note: you have to first type value of x then button then value of y. Logically
value of x should be given first then value of y.
We may use xy function also 325
= 321/5 = 32 xy (1/5) = 2
But in this case (1/5) is must you can’t use 32 xy 1/5 → wrong
9. −5 5 +/- = = 5
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 8/44
8 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
10. √
√5 5 √ = 2.236068
Note: you have to first type value then √ button.
32 + 42 = 32 + 42 = ( 3 x2 + 4 x2 ) √ = 5
But
=1 2 1 − 22 + 2 − 32 + 3 − 12
=1 2 97.74 − 22.962 + 22.96 − 202 + 20 − 97.742
Using bracket also we can’t calculate it directly, we have to use M+
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 9/44
9 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
97.74 − 22.96 x2 = 5592.048 M+ then press C button
22.96 − 20 x2 = 8.7616 M+ then press C button
20
−97.74
x2 = 6043.508 M+ then press C button
Now Press MR button 11644.32 [ It is total value which is under root]
Now press √ button 107.9089
[ it is = 97.74 − 22.962 + 22.96 − 202 + 20 − 97.742 ]Now divide it with √2
107.9089 / 2 √ = 76.30309
Therefore, =1 2 97.74 − 22.962 + 22.96 − 202 + 20 − 97.742 = 76.30309
After the calculation you must press MC button.
11. 1/x
This is generally used at middle of calculation.
0.4512
1 − 0.4512
We first calculate 1 – 0.45sin12 then use 1/x button.
1 – 0.45 * 12 sin = 0.9064397
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 10/44
10 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
Then press 1/x button 1.103217
Then multiply by 0.45 * 12 cos = 0.4855991
12. sin cos tan
Calculator must be in degree mode.
Always value should be given first then the function.
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 11/44
11 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
sin30 30 sin = 0.5
cos45 45 cos = 0.707
tan30 30 tan = 0.577
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 12/44
12 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
sin230 (30 sin ) x2 = 0.25
cos245 (45 cos ) x2 = 0.5
tan230 (30 tan ) x2 = 0.3333333
sin (A – B ) = sin (30-10.5)
(30 – 10.5 ) sin = 0.3338
cos ( φ + β - α ) = cos (20.15 + 33 -10 )
( 20.15 + 33 - 10) cos = 0.729565
tan (Φ - α ) = tan (17.3 – 10)
(17.3 – 10 ) tan = 0.128103
2 =
2.0 220 = 2.0/(20 sin ) x2 = 17.09726
same procedure for sinh cosh tanh
13. sin
-1
cos
-1
tan
-1
Calculator must be in degree mode. If needed in radians calculate by
multiplying /180. We may use in rad mode but i will not recommend it because
students forget to change the mode to degree and further calculations may go
wrong.
sin-10.5 0.5 sin-1 = 30 degree
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 13/44
13 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
cos-10.5 0.5 cos-1 = 60 degree
tan-10.5 0.5 tan-1 = 26.565 degree
same procedure for sinh-1
cosh-1
tanh-1
14. Factorial n (n!)
You have to first input the value the n! button.
3! 3 n! = 6
5! 5 n! = 120
25! 25 n! = 1.551121 e+25 = 1.551121 x 1025
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 14/44
14 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
15. Linear Interpolation formula
You have to first calculate upto last form
− 12 − 1
= − 12 − 1
1.8
−0.8
2.0 − 0.8=
−10
60 − 10
− 10 = 60 − 10 ×1.8 − 0.8
2.0 − 0.8
= 1 0 + 60 − 10 ×1.8 − 0.8
2.0 − 0.8
10 + (60 – 10) * (1.8 – 0.8) / (2.0 – 0.8) = 51.66667
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 15/44
15 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
16. Linear regression analysis
Let us assume the equation which best fit the given data
y = A + Bx
First take summation of both sides ∑ = + ∑ ………… . . ()
Next step multiply both side of original equation by x
xy = Ax + Bx2
Again take summation of both sides ∑ = ∑ + ∑2 ………… . . ()
Just solve this two equations and find A and B
Example:
Data x y xy x2
1 1 1 1 x1 12
2 2 2 2 x 2 22
3 3 3 3 x 3 32
∑ = 6 ∑ = 6 ∑ = 14 ∑2 = 14
For ∑ 1 + 2 + 3 = 6
For ∑ 1 + 2 + 3 = 6
For ∑ 1 * 1 + 2 * 2 + 3 * 3 = 14
For
∑2 Use M+ button
12 1 x2 M+ then press C button
22 2 x2 M+ then press C button
32 3 x2 M+ then press C button
Then press MR button, Therefore∑2 = 14
Now ∑ = + ∑ ………… . . ()
or 6 = 3 + 6 ………… . . ()
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 16/44
16 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
and ∑ = ∑ + ∑2 ………… . . ()
or 14 = 6A + 14 B ………… . . ()
Solving (i) and (ii) we get A = 0 and B = 1
y = 0 + 1. x is the solution.
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 17/44
17 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Production Engineering
Theory of Metal Cutting
Shear angle (Φ)
∅ =
1− =1− [We have to use one extra bracket in the denominator]
∅ =0.45121−0.4512
First find the value of
∅
0.45 * 12 cos / ( 1 – 0.45 * 12 sin ) = 0.4855991
Then find ∅
Just press button tan-1 25.901
Shear strain (γ)
= ∅ + tan (∅ − )
= 17.3 + tan (17.3 − 10)
=1 17.3
+ tan (17.3− 10)
It is a long calculation; we have to use M+
1 17.3 = 1 / 17.3 tan = 3.210630 M+ then press C button
tan (17.3 − 10) = (17.3 - 10) tan = 0.1281029 M+
Then find
Just press button MR 3.338732
( ) = 17.3 + tan (17.3 − 10) = 3.34
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 18/44
18 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Velocity relations
=
∅ −
2.5
= 1022.94 − 10 = 2.5 ×
1022.94 − 10 2.5 * 10 cos / ((22.94 - 10) cos ) = 2.526173
Merchant Circle
(i) = ×∅ = 285 ×
3×0.5120.15 [we have to use extra bracket for denominator]
285 * 3 * 0.51 / (20.15 sin ) = 1265.824
(ii) = ∅ + − =
∅ + − =1265.820.15 + 33 − 10
[We have to use extra bracket for denominator]
1265.8 / ((20.15 + 33 - 10) cos ) = 1735.005
Force Relations
= ∅−∅
= 900
30
−600
30
900 * 30 cos - 600 * 30 sin = 479.4229
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 19/44
19 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Turning
(i) = = 0.32 75
0.32 * 75 sin = 0.3091
(ii) = =
80075 [We have to use extra bracket for denominator]
800 / ( 75 sin ) = 828.2209
Specific Energy
=
1000 =8001000×0.2×2 [We have to use extra bracket for denominator]
800 / ( 1000 * 0.2 * 2 ) = 2
Linear Interpolation formula You have to first calculate upto last form
− 12 − 1
= − 12 − 1
1.8 − 0.8
2.0 − 0.8=
− 10
60 − 10
− 10 = 60 − 10 × 1.8 − 0.82.0 − 0.8
= 1 0 + 60 − 10 ×1.8 − 0.8
2.0 − 0.8
10 + (60 – 10) * (1.8 – 0.8) / (2.0 – 0.8) = 51.66667
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 20/44
20 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Tool life equation
(i) 11 = 22
or 100 × 10 = 75 × 30
or100
75= 30
10
or4
3= 3
or 4
3 = 3
or = 4
33 [We have to use extra bracket for denominator]
(4/3) ln / ( 3 ln ) = 0.2618593
(ii) Find C
C = 100 x 1200.3
100 * 120 xy 0.3 = 420.4887
(iii) 3 = 1 × 13 = 3 0 × 60
300.204
30 * ( 60 / 30 ) xy 0.204 = 34.55664
(iv) 90 1
0.45> 60 1
0.3
or 90 1
0.45= 60 1
0.3
or 90 0.3 = 60 0.45 [Make power opposite]
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 21/44
21 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
or0.450.3
=600.45
900.3
or
0.15 =
600.45
900.3 = 60 xy 0.45 / 90 xy 0.30 = 1.636422
or = 1.636422 1
0.15
For finding x the just press button xy (1 / 0.15 ) = 26.66667
[Because in the calculator 1.636422 already present]
(v) Linear regression analysisLet us assume the equation which best fit the given data
y = A + Bx
First take summation of both sides ∑ = + ∑ ………… . . ()
Next step multiply both side of original equation by x
xy = Ax + Bx2
Again take summation of both sides ∑ = ∑ + ∑2 ………… . . ()
Just solve this two equations and find A and B
Example:
Data X y xy x2
1 1 1 1 x1 12
2 2 2 2 x 2 22
3 3 3 3 x 3 32∑ = 6 ∑ = 6 ∑ = 14 ∑2 = 14
For ∑ 1 + 2 + 3 = 6
For ∑ 1 + 2 + 3 = 6
For ∑ 1 * 1 + 2 * 2 + 3 * 3 = 14
For ∑2 Use M+ button
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 22/44
22 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
12 1 x2 M+ then press C button
22 2 x2 M+ then press C button
32 3 x2 M+ then press C button
Then press MR button, Therefore ∑2 = 14
Now ∑ = + ∑ ………… . . ()
or 6 = 3 + 6 ………… . . ()
and ∑ = ∑ + ∑2 ………… . . ()
or 14 = 6A + 14 B
…………. . (
)
Solving (i) and (ii) we get A = 0 and B = 1
y = 0 + 1. x is the solution.
Economics in metal cutting
= + 1 − = 3 +
6.5
0.5 1 − 0.2
0.2
To = ( 3 + 6.5 / 0.5 ) (1 – 0.2 ) / 0.2 = 64 min
Now
=
or 640.2 = 60
or =60
640.2
60 / 64 xy 0.2 = 26.11 m/min
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 23/44
23 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Metrology
= 0.45 3+ 0.001
= 0.45 97.98
3
+ 0.001 × 97.98
0.45 * 97.98 3 = + 0.001 * 97.98 = 2.172535
Rolling
cos = 1 − ∆
= 1 − 5
600
= 1 - 5 / 600 = cos-1 = 7.40198o
If you want in radian after calculating 7.40198 just press * /180 and you will
get = 0.129189
Forging
(i) 1
2
4 × 1 = 2
2
4 × 2
2 = 1 × 12
= 100 × 50
25= 100 × 2
100 * ( 50 / 25) √ = 141.4214
or 100 * 2 √ = 141.4214
(ii) = 48 − 6
2×0.25 1
2×0.25
48 – (6 / 2 / 0.25 ) * (1 / 2 / 0.25 ) ln = 39.68223
(iii)
= 2
+
2 −
0
we have to first integrate without putting values
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 24/44
24 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
= 2 +2 − 2
2
0
= 2
+
2
2
−22
= 2 + 2
= 2 × 1 5 0 × 16.16 × 39.68 + 4.04
6 × 39.682
2 * 120 * ( 16.16 * 39.68 + ( 4.04 / 6 ) * 39.68 x2 ) = 510418.2
= 510418.2
= 2 22 −
= 42 −
= 4 2 −− 2
=4− 2 0 − 2 −
= 2 2 − − 1 [Note: extra brackets are used]
= 2 × 4 . 0 4 × 1 5 0 × 6
0.25 2×0.256 48−39.68 − 1
(2 * 4.04 * 150 * 6 / 0.25) * (((2 * 0.25/6) * (48 – 39.68)) ex - 1) =
This is very large calculation; this weak calculator can’t handle at once, we have
to calculate part by part
First calculate (2 * 4.04 * 150 * 6 / 0.25) = 29088
Then calculate (((2 * 0.25/6) * (48 –
39.68)) ex
- 1) = 1.000372
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 25/44
25 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Now multiply both 29088 * 1.000372 = 29098.82
= 29098.82
=
+
= 510418.2 + 29098.82 = 539517
= 539.52
Extrusion
= 2 ×2
4×
= 2 × 4 0 0 ×
× 82
4
5
4
It is a long calculation, after some part we press = button then further
multiplication is done .
2 * 400 * ( * 8 x2 / 4) = it gives 40212.38
Now 40212.38 * (5 / 4) ln = 8973.135 N
Wire Drawing
(i) = 1+ 1 − 2 = 400 ×
1 + 1.71451.7145
1 − 5
6.252×1.7145
It is a long calculation,
First calculate, 400 ×
1+1.7145
1.7145 = 400 * (1 +1.7145) / 1.7145 = 633.3040
Then calculate,
1 − 5
6.252×1.7145 = (1 – (5 / 6.25) xy (2 * 1.7145)) = 0.5347402
Now multiply 0.5347402 * 633.3040 = 338.65 MPa
[At that time in your calculator 0.5347402 is present just multiply it with
previous value 633.3040]
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 26/44
26 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
(ii) = 1+ 1 − 2 + 2×
400 = 400 ×1 + 1.7145
1.7145
1
− 6.25
2×1.7145
+
6.25
2×1.7145
× 50
Let 6.25 2×1.7145
=
or 400 = 400 ×1+1.7145
1.71451− + × 50
Calculate, 400 ×1+1.7145
1.7145 = 400 * (1 +1.7145) / 1.7145 = 633.3
or 400 = 633.31− + × 50
or = 633.3
−400
633.3−50 ≈ 0.4 = 6.25 2×1.7145
or = 6.25 × 0.4 1
2×1.7145
or = 6.25 * 0.4 xy (1 / 2 / 1.7145) = 4.784413 mm
Sheet Metal Operation
(i) = 0.0032 = 0.0032 × 1.5 × 294
0.0032 * 1.5 * 294 √ = 0.08230286 mm
(ii) = = 2 + = 2100 + 50 × 5 × 3 0 0
2 * (100+50) * 5 * 300 = 450000 N = 450 KN
(iii) = 2 + 4
=
252 + 4 × 2 5 × 1 5
[Extra bracket used]
( 25 x2 + 4 * 25 * 15) √ = 46.09772 mm
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 27/44
27 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
(iv) =1 × 2
=1.50.05 ×0.09 [Extra bracket for denominator]
1.5 / ( 0.05 ex * 0.09 ex ) = 1.304038 mm
Casting
(i) =2
4× − ×
=
× 0.1202
4 × 0.180 ×
11300
−1600
× 9.81
( * 0.12 x2 / 4 ) * 0.18 * (11300 - 1600) * 9.81 = 193.7161 N
(ii) = 2
Find values of V and A separately and then
B * (V / A) x2 = 0
Welding
(i) + = 1
45
+
500
= 1 …… . . ()
55 + 400 = 1 …… . . ()
Now (ii) x 5 - (i) x 4 will give5 5 × 5 − 4 5 × 4 = 5 − 4 = 1
or OCV = 95 V
Now from equation (i)
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 28/44
28 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
45
95+
500 = 1
or500 =
1
−45
95
or = 5001−45
95 500 / ( 1 – 45 / 95) = 950 V
(ii) = 2 = 300002 ×100×10−6 × 0.005
30000 x2 * 100 * 6 +/- 10x * 0.005 = 450 J
Machine Tools
(i) Turning time ( T ) =+ +
( L + A + O ) / ( f * N ) = 0
(ii) Drilling time ( T ) = ++ +
L = 50 mm
=
2 =152 × 59 = 15/ (2 ∗59 tan ) = 4.5
A = 2 mm
O = 2 mm
f = 0.2 mm/rev
N = 500 rpm
=5 0 + 4 . 5 + 2 + 20.2 × 500
(50 + 4.5 + 2 + 2 ) / (0.2 * 500) = 0.585 min
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 29/44
29 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
ECM Calculation
(i) Find average density of an alloy
1
= 1
1+
2
2+
3
3+
4
4
or1 =
0.7
8.9+
0.2
7.19+
0.05
7.86+
0.05
4.51
First calculate
0.7 / 8.9 +0.2 / 7.19 +0.05 / 7.86 +0.05 / 4.51 = 0.1239159
Then just press 1/x button
= 8.069989 / (ii) Find equivalent weight of an alloy
1 =11
+22
+33
+44
or1 =
111+
222+
333+
444
or
1
=
0.7×2
58.71 +
0.2×2
51.99 +
0.05×2
55.85 +
0.05×3
47.9
First calculate
0.7 * 2 / 58.71+0.2 * 2 / 51.99+0.05 * 2 / 55.85+0.05 * 3 / 47.9 = 0.03646185
Then just press 1/x button
= 27.42593
Alternate Method – 1:
First calculate
0.7 * 2 / 58.71 = 0.02384602
Then 0.02384602 + 0.2 * 2 / 51.99 = 0.03153981
Then 0.03153981 + 0.05 * 2 / 55.85 = 0.03333032
Then 0.03333032 + 0.05 * 3 / 47.9 = 0.03646185
Then just press 1/x button
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 30/44
30 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
= 27.42593
Alternate Method – 2: Use M+ button
0.7 * 2 / 58.71 = 0.02384602 press M+ button the press C button
0.2 * 2 / 51.99 = 0.007693788 press M+ button the press C button
0.05 * 2 / 55.85 = 0.001790511 press M+ button the press C button
0.05 * 3 / 47.9 = 0.003131524 press M+ button the press MR button
Then just press 1/x button
= 27.42593
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 31/44
31 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Strength of Materials
(Only for the type of equations which are not yet covered)
Elongation
(i) =
or =10×103×1000×52
4×200×103
or =100×4
×52×2
[After cancelling common terms from numerator and denominator and one extra
bracket in the denominator has to be put]
100 * 4 / ( * 5 x2 * 2) = 2.546480 mm
Thermal Stress
(ii) 0.5×12.5×10−6×20
1+50×0.5×0.012
4×200×106
First calculate50×0.5×0.012
4×200×106 =
50×0.5×4×0.012×200×106 50 * 0.5 * 4 / ( * 0.01 x2 * 200 * 6 10x ) = 0.001591550
Then add 1
0.001591550 + 1 = 1.001592
Then press button 1/x
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 32/44
32 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
0.9984105
Then multiply with 0.5 × 12.5 × 10−6 × 20
0.9984105 * 0.5 * 12.5 * 6 +/- 10x
* 20 = 0.0001248013
Principal stress and principal strain
(iii)
=
−
+
= 80 − 20
22
+ 402
[One bracket for denominator one bracket for square and one for square root]
(((80-20) / 2 ) x2 + 40 x2 ) = 50 MPa
For 1,2 = +2
+ −2 2
+ 2
First calculate+
2
And then calculate −2
2
+ 2
Deflection of Beams
(iv) =4
8 =10×103×548×781250
10 * 3 10x * 5 xy 4 / (8 * 781250 ) = 1 mm
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 33/44
33 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Bending stresses
(v)
=
= 9.57×10
3×0.1
0.1×0.2
3
12 Pa
=9.57 × 103 × 12
0.23
9.57 * 3 10x * 12 / (0.2 xy 3 ) = 1.435500e+7 Pa = 14.355 MPa
Torsion
(vi) =
409.256321−0.744
=80×109×
1×180
or
4
=
32×409.256×180
2×1−0.74×80×109
First calculate 32 * 409.256 * 180 = 2357315
Then calculate 2 × 1 − 0.74 × 8 0 × 1 09
x2 * (1 – 0.7 xy 4) * 80 * 9 10x = 5.999930e+11
Now
4 =
2357315
5.999930×1011 = 0.000003928904
Just press √ button twice , D = 0.04452130 m = 44.52 mm
Spring
(vii)
=
83
4
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 34/44
34 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
8×200×103×10−6×1080×109×84×10−12
8*200*310x6 +/- 10x10 /(80* 9 10x 8 xy 4 * 12 +/- 10x ) = 0.04882813 m
= 48.83 mm
Theories of column
(viii)
= 2
4
2 [For one end fixed and other end free]
10×103 = 2×210×109××4
64
4×42
or 10 × 103
× 4 × 42 × 6 4 = 2 ×210×109
× × 4
or 4 =10×103×4×42×643×210×109
First calculate 10×103 × 4 × 42 × 64
10 * 3 10x * 4 * 4 x2 * 64 = 4.096000e+7
Then calculate 3 ×210×109
x3 * 210 * 9 10x = 6.511319e+12
4 =4.096000e + 7
6.511319 + 12= 0.000006290584
Just press √ button twice, d = 0.05008097 m ≈ 50 mm
Theories of Failure
(ix) =1 2 1 − 22 + 2 − 32 + 3 − 12
=1 2 97.74 − 22.962 + 22.96 − 202 + 20 − 97.742
Using bracket also we can’t calculate it directly, we have to use M+
97.74 − 22.96 x2 = 5592.048 M+ then press C button
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 35/44
35 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
22.96 − 20 x2 = 8.7616 M+ then press C button
20 − 97.74 x2 = 6043.508 M+ then press C button
Now Press MR button 11644.32 [ It is total value which is in under root]
Now press √ button 107.9089
[ it is = 97.74 − 22.962 + 22.96 − 202 + 20 − 97.742 ]Now divide it with √2
107.9089 / 2 √ = 76.30309
Therefore,
=
1
2
97.74
−22.96
2 +
22.96
−20
2 +
20
−97.74
2
= 76.30309
After the calculation must press MC button.
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 36/44
36 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Theory of Machines
(Only for the type of equations which are not yet covered)
Frequency
(i) =1
2 =1
2 40×103
100
(40 * 10 x3 / 100 ) √ / 2 / = 3.183099
Transmissibility ratio
(ii) = 1+2 2 1−22+2 2
= 1 + 2 × 0.15 × 18.852
1
−18.852
2 +
2 × 0.15 × 18.85
2
First calculate 22 = 2 × 0.15 × 18.852
(2 * 0.15 * 18.85 ) x2 = 31.97903 This data is needed again so
PressM+
Next find 1 − 22 =1 − 18.8522
(1 – 18.85 x2 ) x2 = 125544.4
Now find the value of numerator
Press MR + 1 = then press 5.742737
Then find denominator
Press MR + 125544.4 = then press 354.3676
Now Find (TR)
Press 1/x and * 5.742737 = 0.01620559
TR = 0.01620559 (Answer)
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 37/44
37 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Thermodynamics
(Only for the type of equations which are not yet covered)
SFEE
(i) 1 +1
2
2000+
1000
+ = 1 +
12
2000+
1000
+
3200 +1602
2000+
9.81 × 10
1000+ 0 = 2600 +
1002
2000+
9.81 × 6
1000+
M+ M+ M+ M- M- M-
3200 = Press M+ then press C button
160 x2 / 2000 = Press M+ then press C button
9.81 * 10 / 1000 = Press M+ then press C button
2600 = Press M- then press C button
100 x2 / 2000 = Press M- then press C button
9.81 * 6 / 1000 = Press M-
Now Press MR and it is answer = 607.8392400000004 = 3200 +1602
2000+
9.81 × 10
1000− 2600 − 1002
2000− 9.81 × 6
1000
Entropy Change
(ii) − = − − = 1.005 300
350 − 0.287 50
150
M+ M-
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 38/44
38 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
First calculate 1.005 300
350
1.005 * (300 / 350 ) ln = -0.1549214 Press M+ then press C button
Then calculate 0.287 50
150 0.287 * (50 /150 ) ln = -0.3153016 Press M-
Just press MR and it is the answer 0.16038020000000003
∴ ∆ = 0.16/
Available Energy
(iii) = 2 − 1 − 21
= 2000 × 0.5 1250 − 450 − 303 1250
450
First calculate 1250 − 450 − 303 1250
450
(1250-450)-303 * (1250 / 450) ln = 490.4397
Then multiply with 2000 × 0.5
490.4397 * 2000 * 0.5 = 490439.7 KJ = 490.44 MJ
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 39/44
39 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Heat and Mass Transfer
(Only for the type of equations which are not covered yet)
Conduction
(i) =2− 21
+ 32
=
2 ×
× 1 ×
1200
−600
0.0250.01 19+ 0.0550.0250.2
First calculate denominator0.025
0.01
19+
0.055
0.025
0.2
But it is very weak calculator can’t calculate two ln in a operation
Calculate
(0.025 / 0.01) ln / 19 = 0.04822583 Press M+ then press C button
Then
(0.055 / 0.025) ln / 0.2 = 3.942287 Press M+
Then press MR it is denominator 3.9905128299999996
Now Press 1/x button 0.2505944
Multiply with Numerator 2 ×
× 1 ×
1200
−600
0.2505944 * 2 * * 600 = 944.7186 W/m
∴ =2 × × 1 × 1200− 600 0.025
0.01
19+ 0.055
0.025
0.2
= 944.72/
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 40/44
40 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Unsteady Conduction
(ii)
=
−
−=
−
298− 300
30− 300= −425×2.3533×10−3
or 298−300
30−300 = −425 × 2.3533 × 10−3
or 30−300
298−300 = 425 × 2.3533 × 10−3
or = 30
−300
298−300425×2.3533×10−3
((30-300) / (298-300)) ln = / 425 = / 2.3533 = / 3 +/- 10x = 4.904526 S
Note: Several times use of = is good for this calculator.
Heat Exchanger
(iii) = − =90−40 90
40
(90 / 40) ln = then press 1/x then multiply with numerator * (90 – 40) = 61.65760
Radiation
(iii) Interchange factor 12 =1
11+ 1 2
12−1 =
1
1
0.6+
2×10−3
100 1
0.3−1
First calculate 2×10−3
100 1
0.3− 1
(2 * 3 +/- 10x / 100) * (1 / 0.3 – 1 ) = 0.00004666666
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 41/44
41 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Then add 1/0.6
0.00004666666 + 1 / 0.6 ) = 1.666714
Then press 1/x
0.5999830
f 12 =0.5999830≈0.6
Now
=
12
1
14
− 24
= 0.6 × 5.67 × 10−8 × 2 × 1 0−38004 − 3004 First calculate 0.6 × 5.67 × 10−8 × 2 × 1 0−3
0.6 * 5.67 * 8 +/- 10x * 2 * 3 +/- 10x = 6.804000e-11
Then multiply with 8004 − 3004 6.804000e-11 * (800 xy 4 - 300 xy 4) = 27.31806 W
= 0.6 × 5.67 × 10−8 × 2 × 1 0−38004 − 3004 = 27.32
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 42/44
42 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Industrial Engineering
(Only for the type of equations which are not yet covered)
Forecasting
(i) = + 1 − −1 + 1 − 2−2 + 1 − 3−3
= 0.4 × 95 + 0.4 × 0.6 × 82 + 0.4 × 0.62 ×68+0. 4×0. 63 × 70
M+ M+ M+ M+
0.4 * 95 = 38 Press M+ then press C button
0.4 * 0.6 * 82 = 19.68 Press M+ then press C button
0.4 * 0.6 x2 * 68 = 19.68 Press M+ then press C button
0.4 * 0.6 x3 * 70 = 6.048 Press M+
Then press MR button 73.52
= 0.4 × 95 + 0.4 × 0.6 × 82 + 0.4 × 0.62 ×68+0. 4×0. 63 × 70 =73.52
Regression Analysis
(ii) Let us assume the equation which best fit the given data
y = A + Bx
First take summation of both sides ∑ = + ∑ ………… . . ()
Next step multiply both side of original equation by x
xy = Ax + Bx2
Again take summation of both sides ∑ = ∑ + ∑2 ………… . . ()
Just solve this two equations and find A and B
Example:
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 43/44
43 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Data x Y Xy x2
1 1 1 1 x1 12
2 2 2 2 x 2 22
3 3 3 3 x 3 32
∑= 6
∑= 6
∑= 14
∑2 = 14
For ∑ 1 + 2 + 3 = 6
For ∑ 1 + 2 + 3 = 6
For ∑ 1 * 1 + 2 * 2 + 3 * 3 = 14
For ∑2 Use M+ button
12 1 x2 M+ then press C button
22 2 x2 M+ then press C button
32 3 x2 M+ then press C button
Then press MR button, Therefore ∑2 = 14
Now ∑ = + ∑ ………… . . ()
or 6 = 3
+ 6
…………. . (
)
and ∑ = ∑ + ∑2 ………… . . ()
or 14 = 6A + 14 B ………… . . ()
Solving (i) and (ii) we get A = 0 and B = 1
y = 0 + 1. x is the solution.
7/23/2019 How to Use Virtual Calculator
http://slidepdf.com/reader/full/how-to-use-virtual-calculator 44/44
44 | P a g e How to use Virtual Calculator in Mechanical Engineering
Optimum run size
(iii)
=
2
×
+
= 2 × 30000 × 3500
2.5× 2.5 + 10
10
First calculate 2×30000×3500
2.5 × 2.5+10
10
(2 * 30000 *3500 / 2.5) * ((2.5 + 10) / 10) = 1.050000e+8
Then just press √
1.050000e+8 √ = 10246.95
END
If you got the above points, of the way of calculation then you should be happy enoughbecause we finally succeeded in its usage.
“Ek Ghatiya Calculator ka Sahi Upyog”