how to use virtual calculator

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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  y x 5. e x 6. 10 x 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

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Page 1: How to Use Virtual Calculator

7/23/2019 How to Use Virtual Calculator

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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

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 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

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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

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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.

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 5 | P a g e   How to use Virtual Calculator

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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.

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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.

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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

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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+

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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

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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.

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  sin30 30 sin = 0.5

  cos45 45 cos = 0.707

  tan30 30 tan = 0.577

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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

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  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 

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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

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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  ………… . . () 

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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. 

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  17 | P a g e   How to use Virtual Calculator in Mechanical Engineering 

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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

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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

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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

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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]

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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

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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

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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

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= 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 

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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]

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(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

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(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)

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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

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ECM Calculation

(i) Find average density of an alloy

1

= 1

1+

2

2+

3

3+

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

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= 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 

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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

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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+

 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

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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

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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

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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.

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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

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)

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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- 

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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

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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/ 

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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

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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  

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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:

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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. 

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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”