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. logyx
5. ex
6. 10x
7. xy
8. ππ
9. π
10. β
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
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, canβt 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 β Bracket
O β Order (Power and roots)
D β Division
M β Multiplication
A β Addition
S β 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 β button.
Some functions
1. Exp
It is actually power of 10
102 1 Exp 2 = 100
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 often.
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
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.
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 β 1) 4 * ( 5 x 3.4 β 1 ) eX = 3.554444e+7
6. 10X
102 2 10X = 100
Note: you have to first type value of x then 10X button.
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
101.4β1
1.4 10((1.4β1)
1.4) ((1.4 β 1)/1.4) 10X = 1.930698
Or you may simplify
101.4β1
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 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
π2
π1
πΎπΎβ1
βΉ π2
π1
πΎ πΎβ1
βΉ 5
3
1.4 1.4β1
(5/3) xy 1.4/(1.4 β 1) = 5.111263
8. π₯π¦
325
32 π₯π¦
5 = 2
Note: you have to first type value of x then π₯π¦
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 canβt use 32 xy 1/5 β wrong
9. π₯
β5 5 +/- = π₯ = 5
8 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
10. β
β5 5 β = 2.236068
Note: you have to first type value then β button.
32 + 42 = 32 + 42 = ( 3 x2 + 4 x2 ) β = 5
But
ππ =1
2 π1 β π2 2 + π2 β π3 2 + π3 β π1 2
ππ =1
2 97.74 β 22.96 2 + 22.96 β 20 2 + 20 β 97.74 2
Using bracket also we canβt calculate it directly, we have to use M+
9 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
97.74 β 22.96 x2 = 5592.048 M+ then press C button
22.96 β 20 x2 = 8.7616 M+ then press C button
20 β 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 β button 107.9089
[ it is = 97.74 β 22.96 2 + 22.96 β 20 2 + 20 β 97.74 2 ]
Now divide it with β2
107.9089 / 2 β = 76.30309
Therefore, ππ =1
2 97.74 β 22.96 2 + 22.96 β 20 2 + 20 β 97.74 2 = 76.30309
After the calculation you must press MC button.
11. 1/x
This is generally used at middle of calculation.
0.45πππ 12
1 β 0.45π ππ12
We first calculate 1 β 0.45sin12 then use 1/x button.
1 β 0.45 * 12 sin = 0.9064397
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.
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
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 β B ) = sin (30-10.5)
(30 β 10.5 ) sin = 0.3338
cos ( Ο + Ξ² - Ξ± ) = cos (20.15 + 33 -10 )
( 20.15 + 33 - 10) cos = 0.729565
tan (Ξ¦ - Ξ± ) = tan (17.3 β 10)
(17.3 β 10 ) tan = 0.128103
π
π ππ 2π =
2.0
π ππ 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
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
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
π¦ β π¦1
π¦2 β π¦1=
π₯ β π₯1
π₯2 β π₯1
1.8 β 0.8
2.0 β 0.8=
π₯ β 10
60 β 10
π₯ β 10 = 60 β 10 Γ1.8 β 0.8
2.0 β 0.8
π₯ = 10 + 60 β 10 Γ1.8 β 0.8
2.0 β 0.8
10 + (60 β 10) * (1.8 β 0.8) / (2.0 β 0.8) = 51.66667
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 βπ¦ = π΄π + π΅βπ₯ β¦β¦β¦β¦ . . (π)
Next step multiply both side of original equation by x
xy = Ax + Bx2
Again take summation of both sides βπ₯π¦ = π΄βπ₯ + π΅βπ₯2 β¦β¦β¦β¦ . . (ππ)
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
βπ₯ = 6 βπ¦ = 6 βπ₯π¦ = 14 βπ₯2 = 14
For βπ₯ 1 + 2 + 3 = 6
For βπ¦ 1 + 2 + 3 = 6
For βπ₯π¦ 1 * 1 + 2 * 2 + 3 * 3 = 14
For βπ₯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 βπ₯2 = 14
Now βπ¦ = π΄π + π΅βπ₯ β¦β¦β¦β¦ . . (π)
or 6 = 3 π΄ + 6π΅ β¦β¦β¦β¦ . . (π)
16 | P a g e How to use Virtual Calculator
Made Easy By: S K Mondal
and βπ₯π¦ = π΄βπ₯ + π΅βπ₯2 β¦β¦β¦β¦ . . (ππ)
or 14 = 6A + 14 B β¦β¦β¦β¦ . . (ππ)
Solving (i) and (ii) we get A = 0 and B = 1
y = 0 + 1. x is the solution.
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 (Ξ¦)
π‘ππβ =ππππ πΌ
1βππ πππΌ=
ππππ πΌ
1βππ πππΌ [We have to use one extra bracket in the denominator]
π‘ππβ =0.45πππ 12
1β0.45π ππ12
First find the value of π‘ππβ
0.45 * 12 cos / ( 1 β 0.45 * 12 sin ) = 0.4855991
Then find β
Just press button tan-1 25.901
Shear strain (Ξ³)
πΎ = πππ‘β + tan(β β πΌ)
πΎ = πππ‘17.3 + tan(17.3 β 10)
πΎ =1
π‘ππ 17.3+ tan(17.3 β 10)
It is a long calculation; we have to use M+
1
π‘ππ 17.3 = 1 / 17.3 tan = 3.210630 M+ then press C button
tan(17.3 β 10) = (17.3 - 10) tan = 0.1281029 M+
Then find πΎ
Just press button MR 3.338732
πππππππππ ( πΎ) = πππ‘17.3 + tan(17.3 β 10) = 3.34
18 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Velocity relations
ππ π
=πππ πΌ
πππ β β πΌ
ππ 2.5
=πππ 10
πππ 22.94 β 10
ππ = 2.5 Γπππ 10
πππ 22.94 β 10
2.5 * 10 cos / ((22.94 - 10) cos ) = 2.526173
Merchant Circle
(i) πΉπ = ππ Γππ‘
π ππβ = 285 Γ
3Γ0.51
π ππ20.15 [we have to use extra bracket for denominator]
285 * 3 * 0.51 / (20.15 sin ) = 1265.824
(ii) πΉπ = π πππ β + π½ β πΌ
ππ π =πΉπ
πππ β + π½ β πΌ =
1265.8
πππ 20.15 + 33 β 10
[We have to use extra bracket for denominator]
1265.8 / ((20.15 + 33 - 10) cos ) = 1735.005
Force Relations
πΉπ = πΉππππ β β πΉπ‘π ππβ
πΉπ = 900 πππ 30 β 600 π ππ30
900 * 30 cos - 600 * 30 sin = 479.4229
19 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Turning
(i) π‘ = ππ πππ = 0.32 π ππ75
0.32 * 75 sin = 0.3091
(ii) πΉπ‘ =πΉπ₯
π πππ=
800
π ππ75 [We have to use extra bracket for denominator]
800 / ( 75 sin ) = 828.2209
Specific Energy
π =πΉπ
1000ππ=
800
1000Γ0.2Γ2 [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
π¦ β π¦1
π¦2 β π¦1=
π₯ β π₯1
π₯2 β π₯1
1.8 β 0.8
2.0 β 0.8=
π₯ β 10
60 β 10
π₯ β 10 = 60 β 10 Γ1.8 β 0.8
2.0 β 0.8
π₯ = 10 + 60 β 10 Γ1.8 β 0.8
2.0 β 0.8
10 + (60 β 10) * (1.8 β 0.8) / (2.0 β 0.8) = 51.66667
20 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Tool life equation
(i) π1π1π = π2π2
π
or 100 Γ 10π = 75 Γ 30π
or 100
75=
30
10 π
or 4
3= 3π
or ππ 4
3 = πππ3
or π =ππ
4
3
ππ3 [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) π3 = π1 Γ π1
π3 π
= 30 Γ 60
30
0.204
30 * ( 60 / 30 ) xy 0.204 = 34.55664
(iv) 90
π₯
1
0.45>
60
π₯
1
0.3
or 90
π₯
1
0.45=
60
π₯
1
0.3
or 90
π₯
0.3=
60
π₯
0.45 [Make power opposite]
21 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
or π₯0.45
π₯0.3 =600.45
900.3
or π₯0.15 =600.45
900.3 = 60 xy 0.45 / 90 xy 0.30 = 1.636422
or π₯ = 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 analysis
Let us assume the equation which best fit the given data
y = A + Bx
First take summation of both sides βπ¦ = π΄π + π΅βπ₯ β¦β¦β¦β¦ . . (π)
Next step multiply both side of original equation by x
xy = Ax + Bx2
Again take summation of both sides βπ₯π¦ = π΄βπ₯ + π΅βπ₯2 β¦β¦β¦β¦ . . (ππ)
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
βπ₯ = 6 βπ¦ = 6 βπ₯π¦ = 14 βπ₯2 = 14
For βπ₯ 1 + 2 + 3 = 6
For βπ¦ 1 + 2 + 3 = 6
For βπ₯π¦ 1 * 1 + 2 * 2 + 3 * 3 = 14
For βπ₯2 Use M+ button
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 βπ₯2 = 14
Now βπ¦ = π΄π + π΅βπ₯ β¦β¦β¦β¦ . . (π)
or 6 = 3 π΄ + 6π΅ β¦β¦β¦β¦ . . (π)
and βπ₯π¦ = π΄βπ₯ + π΅βπ₯2 β¦β¦β¦β¦ . . (ππ)
or 14 = 6A + 14 B β¦β¦β¦β¦ . . (ππ)
Solving (i) and (ii) we get A = 0 and B = 1
y = 0 + 1. x is the solution.
Economics in metal cutting
ππ = ππ +πΆπ‘
πΆπ
1 β π
π
ππ = 3 +6.5
0.5
1 β 0.2
0.2
To = ( 3 + 6.5 / 0.5 ) (1 β 0.2 ) / 0.2 = 64 min
Now πππππ = πΆ
or ππ 64 0.2 = 60
or ππ =60
640.2
60 / 64 xy 0.2 = 26.11 m/min
23 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Metrology
π = 0.45 π·3
+ 0.001π·
π = 0.45 97.983
+ 0.001 Γ 97.98
0.45 * 97.98 ππ
3 = + 0.001 * 97.98 = 2.172535
Rolling
cos πΌ = 1 ββπ
π·= 1 β
5
600
πΆ = 1 - 5 / 600 = cos-1 = 7.40198o
If you want πΌ in radian after calculating 7.40198 just press * π/180 and you will
get πΌ = 0.129189 ππππππ
Forging
(i) ππ1
2
4Γ π1 =
ππ22
4Γ π2
π2 = π1 Γ π1
π2= 100 Γ
50
25= 100 Γ 2
100 * ( 50 / 25) β = 141.4214
or 100 * 2 β = 141.4214
(ii) π₯π = 48 β 6
2Γ0.25 ππ
1
2Γ0.25
48 β (6 / 2 / 0.25 ) * (1 / 2 / 0.25 ) ln = 39.68223
(iii) πΉπ π‘ππππππ = 2 ππ +2πΎ
π π₯π β π₯ π΅ππ₯
π₯π
0
we have to first integrate without putting values
24 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
πΉπ π‘ππππππ = 2π΅ ππ π₯ +2πΎ
π π₯π π₯ β
π₯2
2
0
π₯π
πΉπ π‘ππππππ = 2π΅ ππ π₯π +2πΎ
π π₯π
2 βπ₯π
2
2
πΉπ π‘ππππππ = 2π΅ ππ π₯π +πΎ
ππ₯π
2
πΉππ‘ππππππ = 2 Γ 150 Γ 16.16 Γ 39.68 + 4.04
6 Γ 39.682
2 * 120 * ( 16.16 * 39.68 + ( 4.04 / 6 ) * 39.68 x2 ) = 510418.2
πΉπ π‘ππππππ = 510418.2 π
πΉπππππππ = 2 2πΎπ2ππ
πΏβπ₯ π΅ππ₯
πΏ
π₯π
πΉπππππππ = 4πΎπ΅ π2ππ
πΏβπ₯ ππ₯
πΏ
π₯π
πΉπππππππ = 4πΎπ΅ π
2ππ
πΏβπ₯
β2ππ
π₯π
πΏ
πΉπππππππ =4πΎπ΅
β2ππ
π0 β π
2ππ
πΏβπ₯π
πΉπππππππ = 2πΎπ΅π
π π
2π
π πΏβπ₯π β 1 [Note: extra brackets are used]
πΉπππππππ = 2 Γ 4.04 Γ 150 Γ 6
0.25 π
2Γ0.25
6 48β39.68
β 1
(2 * 4.04 * 150 * 6 / 0.25) * (((2 * 0.25/6) * (48 β 39.68)) ex - 1) =
This is very large calculation; this weak calculator canβt 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 β 39.68)) ex - 1) = 1.000372
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
πΉπππππππ = 29098.82 π
πΉπππ‘ππ = πΉππ‘ππππππ + πΉππππππ = 510418.2 + 29098.82 = 539517 π = 539.52 πΎπ
Extrusion
πΉ = 2ππ Γπππ
2
4Γ ππ
ππ
ππ
πΉ = 2 Γ 400 Γ π Γ 82
4 ππ
5
4
It is a long calculation, after some part we press = button then further
multiplication is done .
2 * 400 * (π * 8 x2 / 4) = it gives 40212.38
Now 40212.38 * (5 / 4) ln = 8973.135 N
Wire Drawing
(i) ππ = ππ 1+π΅
π΅ 1 β
ππ
ππ
2π΅
ππ = 400 Γ 1 + 1.7145
1.7145 1 β
5
6.25
2Γ1.7145
It is a long calculation,
First calculate, 400 Γ 1+1.7145
1.7145 = 400 * (1 +1.7145) / 1.7145 = 633.3040
Then calculate,
1 β 5
6.25
2Γ1.7145
= (1 β(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]
26 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
(ii) ππ = ππ 1+π΅
π΅ 1 β
πππππ
ππ
2π΅
+ πππππ
ππ
2π΅
Γ ππ
400 = 400 Γ 1 + 1.7145
1.7145 1 β
πππππ
6.25
2Γ1.7145
+ πππππ
6.25
2Γ1.7145
Γ 50
Let πππππ
6.25
2Γ1.7145
= π₯
or 400 = 400 Γ 1+1.7145
1.7145 1 β π₯ + π₯ Γ 50
Calculate, 400 Γ 1+1.7145
1.7145 = 400 * (1 +1.7145) / 1.7145 = 633.3
or 400 = 633.3 1 β π₯ + π₯ Γ 50
or π₯ = 633.3β400
633.3β50 β 0.4 =
πππππ
6.25
2Γ1.7145
or πππππ = 6.25 Γ 0.4 1
2Γ1.7145
or πππππ = 6.25 * 0.4 xy (1 / 2 / 1.7145) = 4.784413 mm
Sheet Metal Operation
(i) πΆ = 0.0032π‘ π
πΆ = 0.0032 Γ 1.5 Γ 294
0.0032 * 1.5 * 294 β = 0.08230286 mm
(ii) πΉ = πΏπ‘π
πΉ = 2 π + π π‘π = 2 100 + 50 Γ 5 Γ 300
2 * (100+50) * 5 * 300 = 450000 N = 450 KN
(iii) π· = π2 + 4ππ
π· = 252 + 4 Γ 25 Γ 15 [Extra bracket used]
( 25 x2 + 4 * 25 * 15) β = 46.09772 mm
27 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
(iv) π‘πππππ =π‘ππππ‘πππ
πν1 Γπν2=
1.5
π0.05 Γπ0.09 [Extra bracket for denominator]
1.5 / ( 0.05 ex * 0.09 ex ) = 1.304038 mm
Casting
(i) π΅π’ππ¦ππππ¦ πππππ =ππ2
4Γ π πππππ’ππ β πππππ Γ π
π΅π’ππ¦ππππ¦ πππππ = π Γ 0.1202
4 Γ 0.180 Γ 11300 β 1600 Γ 9.81
( π * 0.12 x2 / 4 ) * 0.18 * (11300 - 1600) * 9.81 = 193.7161 N
(ii) π‘π = π΅ π
π΄
2
Find values of V and A separately and then
B * (V / A) x2 = 0
Welding
(i) π
ππΆπ+
πΌ
ππΆπΆ= 1
45
ππΆπ+
500
ππΆπΆ= 1 β¦β¦ . . (π)
55
ππΆπ+
400
ππΆπΆ= 1 β¦β¦ . . (ππ)
Now (ii) x 5 - (i) x 4 will give
55 Γ 5 β 45 Γ 4
ππΆπ= 5 β 4 = 1
or OCV = 95 V
Now from equation (i)
28 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
45
95+
500
ππΆπΆ= 1
or 500
ππΆπΆ= 1 β
45
95
or ππΆπΆ =500
1β45
95
500 / ( 1 β 45 / 95) = 950 V
(ii) π» = πΌ2π π‘ = 300002 Γ 100 Γ 10β6 Γ 0.005
30000 x2 * 100 * 6 +/- 10x * 0.005 = 450 J
Machine Tools
(i) Turning time ( T ) = πΏ+π΄+π
ππ
( L + A + O ) / ( f * N ) = 0
(ii) Drilling time ( T ) = πΏ+π+π΄+π
ππ
L = 50 mm
π =π·
2π‘πππΌ=
15
2 Γ π‘ππ59 = 15/ (2 β59 tan ) = 4.5 ππ
A = 2 mm
O = 2 mm
f = 0.2 mm/rev
N = 500 rpm
π = 50 + 4.5 + 2 + 2
0.2 Γ 500
(50 + 4.5 + 2 + 2 ) / (0.2 * 500) = 0.585 min
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
π=
π₯1
π1+
π₯2
π2+
π₯3
π3+
π₯4
π4
or 1
π=
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
π = 8.069989 π/ππ
(ii) Find equivalent weight of an alloy
1
πΈ=
π₯1
πΈ1+
π₯2
πΈ2+
π₯3
πΈ3+
π₯4
πΈ4
or 1
πΈ=
π₯1π£1
πΈ1+
π₯2π£2
πΈ2+
π₯3π£3
πΈ3+
π₯4π£4
πΈ4
or 1
πΈ=
0.7Γ2
58.71+
0.2Γ2
51.99+
0.05Γ2
55.85+
0.05Γ3
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
πΈ = 27.42593
Alternate Method β 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
30 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
πΈ = 27.42593
Alternate Method β 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
πΈ = 27.42593
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) πΏ =ππΏ
π΄πΈ
or πΏ =10Γ103Γ1000
πΓ52
4Γ200Γ103
ππ
or πΏ =100Γ4
πΓ52Γ2 ππ
[After cancelling common terms from numerator and denominator and one extra
bracket in the denominator has to be put]
100 * 4 / ( π * 5 x2 * 2) = 2.546480 mm
Thermal Stress
(ii) 0.5Γ12.5Γ10β6Γ20
1+50Γ0.5
πΓ0.012
4 Γ200Γ106
First calculate 50Γ0.5
πΓ0.012
4Γ200Γ106
=50Γ0.5Γ4
πΓ0.012Γ200Γ106
50 * 0.5 * 4 / (π * 0.01 x2 * 200 * 6 10x ) = 0.001591550
Then add 1
0.001591550 + 1 = 1.001592
Then press button 1/x
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 Γ 12.5 Γ 10β6 Γ 20
0.9984105 * 0.5 * 12.5 * 6 +/- 10x * 20 = 0.0001248013
Principal stress and principal strain
(iii) ππππ = ππβππ
π π
+ ππππ
ππππ₯ = 80 β 20
2
2
+ 402
[One bracket for denominator one bracket for square and one for square root]
(((80-20) / 2 ) x2 + 40 x2 ) = 50 MPa
For π1,2 =ππ₯+ππ¦
2+
ππ₯βππ¦
2
2+ ππ₯π¦
2
First calculate ππ₯+ππ¦
2
And then calculate ππ₯βππ¦
2
2
+ ππ₯π¦2
Deflection of Beams
(iv) πΏ =π€πΏ4
8πΈπΌ=
10Γ103Γ54
8Γ781250
10 * 3 10x * 5 xy 4 / (8 * 781250 ) = 1 mm
33 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Bending stresses
(v) π = ππ¦πΌ
= 9.57Γ103
Γ0.1
0.1Γ0.2
3
12
Pa
=9.57 Γ 103 Γ 12
0.23
9.57 * 3 10x * 12 / (0.2 xy 3 ) = 1.435500e+7 Pa = 14.355 MPa
Torsion
(vi) π
π½=
πΊπ
πΏ
409.256
π
32 1β0.74 π·4
=80Γ109Γπ
1Γ180
or π·4 =32Γ409.256Γ180
π2Γ 1β0.74 Γ80Γ109
First calculate 32 * 409.256 * 180 = 2357315
Then calculate π2 Γ 1 β 0.74 Γ 80 Γ 109
π x2 * (1 β 0.7 xy 4) * 80 * 9 10x = 5.999930e+11
Now π·4 =2357315
5.999930Γ1011 = 0.000003928904
Just press β button twice , D = 0.04452130 m = 44.52 mm
Spring
(vii) πΏ =8ππ·3π
πΊπ4
34 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
8Γ200Γ103Γ10β6Γ10
80Γ109Γ84Γ10β12
8*200*310x6 +/- 10x10 /(80* 9 10x 8 xy 4 * 12 +/- 10x ) = 0.04882813 m
= 48.83 mm
Theories of column
(viii) πππ = π2πΈπΌ
4πΏ2 [For one end fixed and other end free]
10 Γ 103 =π2Γ210Γ109Γ
πΓπ4
64
4Γ42
or 10 Γ 103 Γ 4 Γ 42 Γ 64 = π2 Γ 210 Γ 109 Γ π Γ π4
or π4 =10Γ103Γ4Γ42Γ64
π3Γ210Γ109
First calculate 10 Γ 103 Γ 4 Γ 42 Γ 64
10 * 3 10x * 4 * 4 x2 * 64 = 4.096000e+7
Then calculate π3 Γ 210 Γ 109
π x3 * 210 * 9 10x = 6.511319e+12
πππ€ π4 =4.096000e + 7
6.511319π + 12= 0.000006290584
Just press β button twice, d = 0.05008097 m β 50 mm
Theories of Failure
(ix) ππ =1
2 π1 β π2 2 + π2 β π3 2 + π3 β π1 2
ππ =1
2 97.74 β 22.96 2 + 22.96 β 20 2 + 20 β 97.74 2
Using bracket also we canβt calculate it directly, we have to use M+
97.74 β 22.96 x2 = 5592.048 M+ then press C button
35 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
22.96 β 20 x2 = 8.7616 M+ then press C button
20 β 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 β button 107.9089
[ it is = 97.74 β 22.96 2 + 22.96 β 20 2 + 20 β 97.74 2 ]
Now divide it with β2
107.9089 / 2 β = 76.30309
Therefore, ππ =1
2 97.74 β 22.96 2 + 22.96 β 20 2 + 20 β 97.74 2 = 76.30309
After the calculation must press MC button.
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) ππ =1
2π
π
π=
1
2π
40Γ103
100
(40 * 10 x3 / 100 ) β / 2 / π = 3.183099
Transmissibility ratio
(ii) ππ = 1+ 2ππ 2
1βπ2 2+ 2ππ 2
ππ = 1 + 2 Γ 0.15 Γ 18.85 2
1 β 18.852 2 + 2 Γ 0.15 Γ 18.85 2
First calculate 2ππ 2 = 2 Γ 0.15 Γ 18.85 2
(2 * 0.15 * 18.85 ) x2 = 31.97903 This data is needed again so
PressM+
Next find 1 β π2 2 = 1 β 18.852 2
(1 β 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)
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) π1 +π1
2
2000+
ππ
1000+
ππ
ππ= π1 +
π12
2000+
ππ
1000+
ππ
ππ
3200 +1602
2000+
9.81 Γ 10
1000+ 0 = 2600 +
1002
2000+
9.81 Γ 6
1000+
ππ
ππ
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
ππ
ππ= 3200 +
1602
2000+
9.81 Γ 10
1000β 2600 β
1002
2000β
9.81 Γ 6
1000
Entropy Change
(ii) ππ β ππ = ππ ππ ππ
ππ β π ππ
ππ
ππ
ππ β ππ = 1.005 ππ 300
350 β 0.287ππ
50
150
M+ M-
38 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
First calculate 1.005 ππ 300
350
1.005 * (300 / 350 ) ln = -0.1549214 Press M+ then press C button
Then calculate 0.287ππ 50
150
0.287 * (50 /150 ) ln = -0.3153016 Press M-
Just press MR and it is the answer 0.16038020000000003
β΄ βπ = 0.16 πΎπ½/πΎππΎ
Available Energy
(iii) π΄πΈ = πππ π2 β π1 β ππ ππ π2
π1
π΄πΈ = 2000 Γ 0.5 1250 β 450 β 303ππ 1250
450
First calculate 1250 β 450 β 303ππ 1250
450
(1250-450)-303 * (1250 / 450) ln = 490.4397
Then multiply with 2000 Γ 0.5
490.4397 * 2000 * 0.5 = 490439.7 KJ = 490.44 MJ
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) π =2ππΏ π‘πβπ‘π
ππ π2π1
πΎπ΄+
ππ π3π2
πΎπ΅
π =2 Γ π Γ 1 Γ 1200 β 600
ππ 0.0250.01
19+
ππ 0.0550.025
0.2
First calculate denominator ππ
0.025
0.01
19+
ππ 0.055
0.025
0.2
But it is very weak calculator canβt 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 Γ π Γ 1 Γ 1200 β 600
0.2505944 * 2 * π * 600 = 944.7186 W/m
β΄ π =2 Γ π Γ 1 Γ 1200 β 600
ππ 0.0250.01
19+
ππ 0.0550.025
0.2
= 944.72 π/π
40 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Unsteady Conduction
(ii) π
ππ=
πβππ
ππβππ= πβπ΅ππΉπ
298 β 300
30 β 300= πβ425πΓ2.3533Γ10β3
or ππ 298β300
30β300 = β425π Γ 2.3533 Γ 10β3
or ππ 30β300
298β300 = 425π Γ 2.3533 Γ 10β3
or π =ππ
30β300
298β300
425Γ2.3533Γ10β3
((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) πΏπππ· =ππβππ
ππ ππππ
=
90β40
ππ 90
40
(90 / 40) ln = then press 1/x then multiply with numerator * (90 β 40) = 61.65760
Radiation
(iii) Interchange factor
π12 =1
1
ν1+
π΄1π΄2
1
ν2β1
=1
1
0.6+
2Γ10β3
100
1
0.3β1
First calculate 2Γ10β3
100
1
0.3β 1
(2 * 3 +/- 10x / 100) * (1 / 0.3 β 1 ) = 0.00004666666
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
f12 =0.5999830 β0.6
Now ππππ‘ = π12ππ΄1 π14 β π2
4
ππππ‘ = 0.6 Γ 5.67 Γ 10β8 Γ 2 Γ 10β3 8004 β 3004
First calculate 0.6 Γ 5.67 Γ 10β8 Γ 2 Γ 10β3
0.6 * 5.67 * 8 +/- 10x * 2 * 3 +/- 10x = 6.804000e-11
Then multiply with 8004 β 3004
6.804000e-11 * (800 xy 4 - 300 xy 4) = 27.31806 W
ππππ‘ = 0.6 Γ 5.67 Γ 10β8 Γ 2 Γ 10β3 8004 β 3004 = 27.32 π
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) π’π = πΌππ‘ + πΌ 1 β πΌ ππ‘β1 + πΌ 1 β πΌ 2ππ‘β2 + πΌ 1 β πΌ 3ππ‘β3
π’π = 0.4 Γ 95 + 0.4 Γ 0.6 Γ 82 + 0.4 Γ 0.62 Γ 68 + 0.4 Γ 0.63 Γ 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
π’π = 0.4 Γ 95 + 0.4 Γ 0.6 Γ 82 + 0.4 Γ 0.62 Γ 68 + 0.4 Γ 0.63 Γ 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 βπ¦ = π΄π + π΅βπ₯ β¦β¦β¦β¦ . . (π)
Next step multiply both side of original equation by x
xy = Ax + Bx2
Again take summation of both sides βπ₯π¦ = π΄βπ₯ + π΅βπ₯2 β¦β¦β¦β¦ . . (ππ)
Just solve this two equations and find A and B
Example:
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
βπ₯ = 6 βπ¦ = 6 βπ₯π¦ = 14 βπ₯2 = 14
For βπ₯ 1 + 2 + 3 = 6
For βπ¦ 1 + 2 + 3 = 6
For βπ₯π¦ 1 * 1 + 2 * 2 + 3 * 3 = 14
For βπ₯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 βπ₯2 = 14
Now βπ¦ = π΄π + π΅βπ₯ β¦β¦β¦β¦ . . (π)
or 6 = 3 π΄ + 6π΅ β¦β¦β¦β¦ . . (π)
and βπ₯π¦ = π΄βπ₯ + π΅βπ₯2 β¦β¦β¦β¦ . . (ππ)
or 14 = 6A + 14 B β¦β¦β¦β¦ . . (ππ)
Solving (i) and (ii) we get A = 0 and B = 1
y = 0 + 1. x is the solution.
44 | P a g e How to use Virtual Calculator in Mechanical Engineering
Made Easy By: S K Mondal
Optimum run size
(iii) π = 2ππ
πΌπΓ
πΌπ+πΌπ
πΌπ
π = 2 Γ 30000 Γ 3500
2.5Γ
2.5 + 10
10
First calculate 2Γ30000 Γ3500
2.5 Γ
2.5+10
10
(2 * 30000 *3500 / 2.5) * ((2.5 + 10) / 10) = 1.050000e+8
Then just press β
1.050000e+8 β = 10246.95
END
If you got the above points, of the way of calculation then you should be happy enough
because we finally succeeded in its usage.
βEk Ghatiya Calculator ka Sahi Upyogβ
Top Related