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
Production Engineering
Some functions
Theory of Metal Cutting
1. Exp
Shear angle
2. ln 3. log 4. logyx 5. ex 6.
10x
7.
xy
8.
π
π
Shear strain Velocity relations Merchant Circle Force Relations Turning Specific Energy Linear Interpolation Tool life equation
9. π
Linear regression
10. β
Economics
11.1/x
Metrology
12.sin cos tan sinh cosh tanh
Rolling
13. sin-1 cos-1 tan-1 sinh-1 cosh-
Forging
1
tanh-1
14. Factorial n (n!) 15. Linear Interpolation 16. Linear regression
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
How to use Virtual Calculator
2|Page
General Instructions ο·
Operation procedures and sequence of operations are totally different in Virtual calculator. Hence all students are requested to practice the following procedures.
ο·
It is very weak calculator, canβt handle large equation at a time, we have to calculate part by part.
ο·
Use more and more bracket for calculations
ο·
BODMAS rule should be followed
ο·
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]
ο·
In the starting of any calculation you must click on C [ C means you have to click on this C button]
ο·
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]
ο·
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
Made Easy
1 Exp 2 =
100
By: S K Mondal
How to use Virtual Calculator
3|Page
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
Made Easy
By: S K Mondal
4|Page
How to use Virtual Calculator
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
logyx
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.
Made Easy
By: S K Mondal
How to use Virtual Calculator
5|Page
log550
50 logyx 5
7log550
7 * ( 50 logyx 5 ) =
=
2.430677 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.
Made Easy
By: S K Mondal
How to use Virtual Calculator
6|Page
5 x 102
5 * 2 10X
=
105/3
(5/3) 10X
=
10
1.4β1 1.4
(1.4β1) ) 1.4
10(
500
46.41592
((1.4 β 1)/1.4) 10X =
1.930698
Or you may simplify
10
1.4β1 1.4
0.4
10(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.
Made Easy
By: S K Mondal
How to use Virtual Calculator
7|Page
π2 π1
πΎ πΎβ1
πΎ πΎβ1
π2 βΉ π1
1.4 1.4β1
5 βΉ 3
(5/3) xy 1.4/(1.4 β 1) =
8.
π¦
5.111263
π₯ 5
32
32
π¦
π₯ 5 =
2 π¦
Note: you have to first type value of x then π₯ button then value of y. Logically value of x should be given first then value of y.
We may use xy function also
5
32 = 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
Made Easy
5 +/- =
π₯
=
5
By: S K Mondal
How to use Virtual Calculator
8|Page
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 = ππ =
1 2 1 2
π1 β π2
2
+ π2 β π3
97.74 β 22.96
2
2
+ π3 β π1
+ 22.96 β 20
2
2
+ 20 β 97.74
2
Using bracket also we canβt calculate it directly, we have to use M+
Made Easy
By: S K Mondal
How to use Virtual Calculator
9|Page
x2 =
97.74 β 22.96
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 Therefore, ππ =
=
76.30309
1
97.74 β 22.96
2
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
Made Easy
=
0.9064397
By: S K Mondal
How to use Virtual Calculator
10 | P a g e
Then press 1/x button
Then multiply by 0.45 * 12 cos =
12. sin ο· ο·
cos
1.103217
0.4855991
tan
Calculator must be in degree mode. Always value should be given first then the function.
Made Easy
By: S K Mondal
How to use Virtual Calculator
11 | P a g e
ο·
sin30
30 sin
=
0.5
ο·
cos45
45 cos
ο·
tan30
30 tan =
Made Easy
=
0.707
0.577
By: S K Mondal
How to use Virtual Calculator
12 | P a g e
ο·
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 =
ο·
ο· ο·
ο·
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 2 π
2.0
= π ππ 2 20 = 2.0/(20 sin ) x2
same procedure for
13. sin-1
cos-1
=
17.09726
sinh cosh tanh
tan-1
ο·
Calculator must be in degree mode. If needed in radians calculate by multiplying ο/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.
ο·
sin-10.5
Made Easy
0.5 sin-1
=
30
degree
By: S K Mondal
How to use Virtual Calculator
13 | P a g e
ο·
cos-10.5
0.5 cos-1
=
60
ο·
tan-10.5
0.5 tan-1
=
26.565 degree
ο·
same procedure for
degree
sinh-1 cosh-1 tanh-1
14. Factorial n (n!) ο·
You have to first input the value the n! button.
ο·
3!
3 n!
=
6
ο·
5!
5 n!
=
120
ο·
25!
25 n!
Made Easy
=
1.551121 e+25 = 1.551121 x 1025
By: S K Mondal
14 | P a g e
How to use Virtual Calculator
15. Linear Interpolation formula You have to first calculate upto last form π¦ β π¦1 π₯ β π₯1 = π¦2 β π¦1 π₯2 β π₯1 1.8 β 0.8 π₯ β 10 = 2.0 β 0.8 60 β 10 π₯ β 10 = 60 β 10 Γ
1.8 β 0.8 2.0 β 0.8
π₯ = 10 + 60 β 10 Γ
1.8 β 0.8 2.0 β 0.8
10 + (60 β 10) * (1.8 β 0.8) / (2.0 β 0.8) =
Made Easy
51.66667
By: S K Mondal
How to use Virtual Calculator
15 | P a g e
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 1 2 3
x 1 2 3 βπ₯ = 6 For βπ₯ 1 + 2 + 3 = 6
y 1 2 3 βπ¦ = 6
xy 1 x1 2x2 3x3 βπ₯π¦ = 14
x2 12 22 32 βπ₯ 2 = 14
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₯ or
6 = 3 π΄ + 6π΅
Made Easy
β¦ β¦ β¦ β¦ . . (π) β¦ β¦ β¦ β¦ . . (π)
By: S K Mondal
How to use Virtual Calculator
16 | P a g e
and βπ₯π¦ = π΄βπ₯ + π΅βπ₯ 2 or
14 = 6A + 14 B
β¦ β¦ β¦ β¦ . . (ππ) β¦ β¦ β¦ β¦ . . (ππ)
Solving (i) and (ii) we get A = 0 and B = 1 y = 0 + 1. x is the solution.
Made Easy
By: S K Mondal
How to use Virtual Calculator in Mechanical Engineering
17 | P a g e
Production Engineering Theory of Metal Cutting Shear angle (Ξ¦) ππππ πΌ
π‘ππβ
= 1βππ πππΌ = π‘ππβ
=
ππππ πΌ 1βππ πππΌ
[We have to use one extra bracket in the denominator]
0.45πππ 12 1β0.45π ππ 12
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
+ tanβ‘ (β
β πΌ) πΎ = πππ‘17.3 + tanβ‘ (17.3 β 10) 1
πΎ = π‘ππ 17.3 + tanβ‘ (17.3 β 10) It is a long calculation; we have to use M+ 1 π‘ππ 17.3
= 1 / 17.3 tan
=
tanβ‘ (17.3 β 10) = (17.3 - 10) tan
3.210630 =
M+ then press C button
0.1281029 M+
Then find πΎ Just press button MR
3.338732
πππππππππ ( πΎ) = πππ‘17.3 + tanβ‘ (17.3 β 10) = 3.34
Made Easy
By: S K Mondal
How to use Virtual Calculator in Mechanical Engineering
18 | P a g e
Velocity relations ππ πππ πΌ = π πππ β
β πΌ ππ πππ 10 = 2.5 πππ 22.94 β 10 ππ = 2.5 Γ
πππ 10 πππ 22.94 β 10
2.5 * 10 cos / ((22.94 - 10) cos )
=
2.526173
Merchant Circle (i)
ππ‘
πΉπ = ππ Γ π ππ β
= 285 Γ
3Γ0.51 π ππ 20.15
[we have to use extra bracket for denominator]
285 * 3 * 0.51 / (20.15 sin )
(ii)
=
1265.824
πΉπ = π
πππ β
+ π½ β πΌ ππ π
=
πΉπ 1265.8 = πππ β
+ π½ β πΌ 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 = πΉπ πππ β
β πΉπ‘ π ππβ
πΉπ = 900 πππ 30 β 600 π ππ30 900 * 30 cos - 600 * 30 sin
Made Easy
=
479.4229
By: S K Mondal
How to use Virtual Calculator in Mechanical Engineering
19 | P a g e
Turning (i)
π‘ = ππ πππ = 0.32 π ππ75 0.32 * 75 sin
(ii)
πΉ
π₯ πΉπ‘ = π πππ =
=
0.3091
800
[We have to use extra bracket for denominator]
π ππ 75
800 / ( 75 sin )
=
828.2209
Specific Energy πΉ
π = 1000π ππ =
800 1000 Γ0.2Γ2
[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₯ β π₯1 = π¦2 β π¦1 π₯2 β π₯1 1.8 β 0.8 π₯ β 10 = 2.0 β 0.8 60 β 10 π₯ β 10 = 60 β 10 Γ
1.8 β 0.8 2.0 β 0.8
π₯ = 10 + 60 β 10 Γ
1.8 β 0.8 2.0 β 0.8
10 + (60 β 10) * (1.8 β 0.8) / (2.0 β 0.8) =
Made Easy
51.66667
By: S K Mondal
How to use Virtual Calculator in Mechanical Engineering
20 | P a g e
Tool life equation (i)
π1 π1π = π2 π2π or 100 Γ 10π = 75 Γ 30π or
100
or
4
75
3
30 π
=
10
= 3π
or ππ
4
or π =
ππ
= πππ3
3 4 3
[We have to use extra bracket for denominator]
ππ 3
(4/3) ln / ( 3 ln )
(ii)
=
0.2618593
Find C C = 100 x 1200.3 100 * 120 xy 0.3 =
(iii)
π1 π
π3 = π1 Γ
π3
= 30 Γ
420.4887
60 0.204 30
30 * ( 60 / 30 ) xy 0.204 =
1
(iv)
1
90 0.45 π₯
>
60 0.3 π₯
1
90 0.45 or π₯
or
90 0.3 π₯
Made Easy
34.55664
1
= =
60 0.3 π₯ 60 0.45 π₯
[Make power opposite]
By: S K Mondal
How to use Virtual Calculator in Mechanical Engineering
21 | P a g e
or
π₯ 0.45 π₯ 0.3
or π₯
=
0.15
60 0.45
=
900.3 60 0.45 900.3
or π₯ = 1.636422
= 60 xy 0.45
/ 90 xy 0.30 = 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 1 2 3
X 1 2 3 βπ₯ = 6 For βπ₯ 1 + 2 + 3 = 6
y 1 2 3 βπ¦ = 6
xy 1 x1 2x2 3x3 βπ₯π¦ = 14
x2 12 22 32 βπ₯ 2 = 14
For βπ¦ 1 + 2 + 3 = 6 For βπ₯π¦ 1 * 1 + 2 * 2 + 3 * 3 = 14 For βπ₯ 2 Use M+ button
Made Easy
By: S K Mondal
How to use Virtual Calculator in Mechanical Engineering
22 | P a g e
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₯ or
6 = 3 π΄ + 6π΅
β¦ β¦ β¦ β¦ . . (π) β¦ β¦ β¦ β¦ . . (π)
and βπ₯π¦ = π΄βπ₯ + π΅βπ₯ 2 or
14 = 6A + 14 B
β¦ β¦ β¦ β¦ . . (ππ) 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 πΆπ‘ πΆπ
1βπ π
6.5 0.5
1 β 0.2 0.2
ππ = ππ + ππ = 3 +
To = ( 3 + 6.5 / 0.5 ) (1 β 0.2 ) / 0.2 =
64 min
Now ππ πππ = πΆ or ππ 64
0.2
= 60
60
or ππ = 64 0.2 60 / 64 xy 0.2 =
Made Easy
26.11 m/min
By: S K Mondal
How to use Virtual Calculator in Mechanical Engineering
23 | P a g e
Metrology 3
π = 0.45 π· + 0.001π· 3
π = 0.45 97.98 + 0.001 Γ 97.98 0.45 * 97.98
π
π 3
=
+ 0.001 * 97.98
=
2.172535
Rolling cos πΌ = 1 β
βπ 5 = 1β π· 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)
ππ 12 4
Γ π1 =
π2 = π1 Γ
ππ 22 4
Γ π2
π1 50 = 100 Γ = 100 Γ 2 π2 25
100 * ( 50 / 25) β or 100 * 2 β
(ii)
π₯π = 48 β
=
141.4214
=
141.4214
6 2Γ0.25
ππ
1 2Γ0.25
48 β (6 / 2 / 0.25 ) * (1 / 2 / 0.25 ) ln
(iii)
πΉπ π‘ππππππ = 2
π₯π 0
ππ +
2πΎ π
π₯π β π₯
=
39.68223
π΅ππ₯
we have to first integrate without putting values
Made Easy
By: S K Mondal
How to use Virtual Calculator in Mechanical Engineering
24 | P a g e
πΉπ π‘ππππππ = 2π΅ ππ π₯ +
2πΎ
π₯π π₯ β
π 2πΎ
πΉπ π‘ππππππ = 2π΅ ππ π₯π +
π₯π 2 β
π
π₯2
π₯π
2
0
π₯ π 2 2
πΎ
πΉπ π‘ππππππ = 2π΅ ππ π₯π + π₯π 2 π
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
πΏ
πΉπππππππ = 2
2π
2πΎπ π
πΏβπ₯
π΅ππ₯
πΏβπ₯
ππ₯
π₯π πΏ
πΉπππππππ = 4πΎπ΅
2π
ππ π₯π 2π
πΉπππππππ = 4πΎπ΅
ππ
β
πΉπππππππ =
πΉπππππππ = πΉπππππππ =
4πΎπ΅ 2π β π 2πΎπ΅π π
πΏβπ₯
2π π
πΏ
π₯π 2π
π0 β π π
π
2π π
πΏβπ₯ π
πΏβπ₯ π
β1
2 Γ 4.04 Γ 150 Γ 6 0.25
π
[Note: extra brackets are used] 2Γ0.25 48β39.68 6
β1
(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) =
Made Easy
1.000372
By: S K Mondal
How to use Virtual Calculator in Mechanical Engineering
25 | P a g e
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 Γ
πππ2 ππ Γ ππ 4 ππ
π Γ 82 5 πΉ = 2 Γ 400 Γ ππ 4 4 It is a long calculation, after some part we press multiplication is done . 2 * 400 * (π
* 8 x2 / 4) = Now 40212.38 * (5 / 4) ln
=
button then further
it gives 40212.38 =
8973.135 N
Wire Drawing (i)
ππ = ππ
1+π΅ π΅
1β
π π 2π΅ ππ
1 + 1.7145 5 ππ = 400 Γ 1β 1.7145 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, 1β
5 6.25
2Γ1.7145
= (1 β(5 / 6.25) xy (2 * 1.7145)) =
Now multiply 0.5347402 * 633.3040
=
0.5347402
338.65 MPa
[At that time in your calculator 0.5347402 is present just multiply it with previous value 633.3040]
Made Easy
By: S K Mondal
How to use Virtual Calculator in Mechanical Engineering
26 | P a g e
(ii)
ππ = ππ
1+π΅ π΅
400 = 400 Γ Let or
π ππππ
1β
2π΅
+
ππ
π ππππ ππ
πππππ 1 + 1.7145 1β 1.7145 6.25
2Γ1.7145
6.25
2π΅
Γ ππ
2Γ1.7145
+
πππππ 6.25
2Γ1.7145
Γ 50
=π₯
400 = 400 Γ
Calculate, 400 Γ or
π ππππ
1+1.7145 1.7145
1+1.7145
1 β π₯ + π₯ Γ 50
= 400 * (1 +1.7145) / 1.7145
1.7145
=
633.3
400 = 633.3 1 β π₯ + π₯ Γ 50 633.3β400
or π₯ =
633.3β50
β 0.4 =
or πππππ = 6.25 Γ 0.4
π ππππ
2Γ1.7145
6.25
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
(ii)
=
0.08230286 mm
πΉ = πΏπ‘π πΉ = 2 π + π π‘π = 2 100 + 50 Γ 5 Γ 300 2 * (100+50) * 5 * 300
(iii)
=
450000 N = 450 KN
π· = π 2 + 4ππ π·=
252 + 4 Γ 25 Γ 15
( 25 x2 + 4 * 25 * 15) β
Made Easy
[Extra bracket used] =
46.09772 mm
By: S K Mondal
How to use Virtual Calculator in Mechanical Engineering
27 | P a g e
(iv)
π‘πππππ =
π‘ ππππ‘πππ π π 1 Γπ π 2
1.5
=
π 0.05 Γπ 0.09
1.5 / ( 0.05 ex * 0.09 ex ) =
[Extra bracket for denominator] 1.304038 mm
Casting (i)
π΅π’ππ¦ππππ¦ πππππ = π΅π’ππ¦ππππ¦ πππππ =
ππ 2 4
Γ π πππππ’ππ β πππππ Γ π
π Γ 0.1202 Γ 0.180 Γ 11300 β 1600 Γ 9.81 4
( π
* 0.12 x2 / 4 ) * 0.18 * (11300 - 1600) * 9.81 =
(ii)
193.7161 N
π 2
π‘π = π΅
π΄
Find values of V and A separately and then B * (V / A) x2
=
0
Welding (i)
π ππΆπ
πΌ
+ ππΆπΆ = 1
45 500 + =1 ππΆπ ππΆπΆ
β¦ β¦ . . (π)
55 400 + =1 ππΆπ ππΆπΆ
β¦ β¦ . . (ππ)
Now (ii) x 5 - (i) x 4 will give 55 Γ 5 β 45 Γ 4 = 5β4 = 1 ππΆπ or OCV = 95 V Now from equation (i)
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45 500 + =1 95 ππΆπΆ 500
45
or ππΆπΆ = 1 β 95 or ππΆπΆ =
500 45 95
1β
500 / ( 1 β 45 / 95)
(ii)
=
950 V
π» = πΌ 2 π
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)
(ii)
Drilling time ( T ) =
=
0
πΏ+π+π΄+π ππ
L = 50 mm π=
π· 15 = = 15/ (2 β59 tan ) = 4.5 ππ 2π‘πππΌ 2 Γ π‘ππ59
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) =
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ECM Calculation (i)
Find average density of an alloy 1 π₯1 π₯2 π₯3 π₯4 = + + + π π1 π2 π3 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 π₯1 π₯2 π₯3 π₯4 = + + + πΈ πΈ1 πΈ2 πΈ3 πΈ4 or or
1 πΈ 1 πΈ
= =
π₯ 1 π£1 πΈ1
+
0.7Γ2 58.71
π₯ 2 π£2
+
πΈ2
+
0.2Γ2 51.99
π₯ 3 π£3 πΈ3
+
+
π₯ 4 π£4
0.05Γ2 55.85
πΈ4
+
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
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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
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Strength of Materials (Only for the type of equations which are not yet covered)
Elongation (i)
πΏ=
ππΏ π΄πΈ
or πΏ =
or πΏ =
10Γ10 3 Γ1000 π Γ5 2 Γ200Γ10 3 4
100Γ4
ππ
ππ
π Γ52 Γ2
[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)
0.5Γ12.5Γ10 β6 Γ20 1+
50Γ0.5 π Γ0.01 2 Γ200 Γ10 6 4
First calculate
50Γ0.5 π Γ0.01 2 4
Γ200Γ10 6
=
50Γ0.5Γ4 πΓ0.012 Γ200Γ10 6
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
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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 =
ππ βππ π π
+ ππππ 2
80 β 20 2
ππππ₯ =
+ 402
[One bracket for denominator one bracket for square and one for square root] (((80-20) / 2 ) x2 + 40 x2 )
For
π1,2 =
ππ₯ +ππ¦ 2
First calculate
+
=
ππ₯ βππ¦ 2 2
50 MPa
2 + ππ₯π¦
ππ₯ +ππ¦ 2
And then calculate
ππ₯ βππ¦ 2
2 2 + ππ₯π¦
Deflection of Beams (iv)
πΏ=
π€πΏ4 8πΈπΌ
=
10Γ10 3 Γ54 8Γ781250
10 * 3 10x * 5 xy 4 / (8 * 781250 ) =
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Bending stresses (v)
π
9.57Γ10 = ππ¦ = πΌ
3
Γ0.1
0.1Γ0.2 12
=
3
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
or
π·4 =
=
80Γ10 9 Γπ 1Γ180
32Γ409.256Γ180 π2Γ
1β0.74 Γ80Γ10 9
First calculate 32 * 409.256 * 180 = 2357315 Then calculate π 2 Γ 1 β 0.74 Γ 80 Γ 109 π
x2 * (1 β 0.7 xy 4) * 80 * 9 10x Now π· 4
=
2357315 5.999930Γ10 11
=
5.999930e+11
= 0.000003928904
Just press β button twice , D = 0.04452130 m = 44.52 mm
Spring (vii)
πΏ=
8ππ· 3 π
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πΊπ 4
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8Γ200Γ10 3 Γ10 β6 Γ10 80Γ10 9 Γ84 Γ10 β12 8*200*310x 6 +/- 10x 10 /(80* 9 10x 8 xy 4 * 12 +/- 10x ) =
0.04882813 m
= 48.83 mm
Theories of column (viii) πππ
=π
2 πΈπΌ
[For one end fixed and other end free]
4πΏ2 3
10 Γ 10 =
π Γπ 4 64
π 2 Γ210Γ10 9 Γ 4Γ4 2
3
4
9
or 10 Γ 10 Γ 4 Γ 42 Γ 64 = π2 Γ 210 Γ 10 Γ π Γ π
or π 4 =
10Γ10 3 Γ4Γ42 Γ64
π 3 Γ210Γ10 9
First calculate 10 Γ 103 Γ 4 Γ 42 Γ 64 10 * 3 10x * 4 * 4 x2 * 64
= 4.096000e+7
Then calculate π 3 Γ 210 Γ 109 π
x3 * 210 * 9 10x πππ€ π4 =
= 6.511319e+12
4.096000e + 7 = 0.000006290584 6.511319π + 12
Just press β button twice, d = 0.05008097 m β 50 mm
Theories of Failure (ix)
ππ = ππ =
1 2 1 2
π1 β π2
2
+ π2 β π3
97.74 β 22.96
2
2
+ π3 β π1
+ 22.96 β 20
2
2
+ 20 β 97.74
2
Using bracket also we canβt calculate it directly, we have to use M+ 97.74 β 22.96
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x2 =
5592.048
M+ then press C button
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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 Therefore, ππ =
= 1 2
76.30309 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.
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Theory of Machines (Only for the type of equations which are not yet covered)
Frequency (i)
ππ =
1
π
2π
π
=
1
40Γ10 3
2π
100
(40 * 10 x3 / 100 ) β / 2 / π
=
3.183099
Transmissibility ratio (ii)
ππ
=
1+ 2ππ 2 1βπ 2 2 + 2ππ 2 1 + 2 Γ 0.15 Γ 18.85
ππ
=
1 β 18.852
2
First calculate 2ππ (2 * 0.15 PressM+ Next find 1 β π 2
2
2
+ 2 Γ 0.15 Γ 18.85
2
2
= 2 Γ 0.15 Γ 18.85
* 18.85 ) x2
= 1 β 18.852
(1 β 18.85 x2 ) x2
=
=
2
31.97903 This data is needed again so
2
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)
π1 +
π12 2000
+
ππ 1000
+
ππ ππ
= π1 +
π12 2000
+
ππ 1000
+
ππ ππ
1602 9.81 Γ 10 1002 9.81 Γ 6 ππ 3200 + + + 0 = 2600 + + + 2000 1000 2000 1000 ππ M+ 3200
M+ =
M+
Press M+
M-
M-
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 MNow Press MR and it is answer = 607.8392400000004
ππ 1602 9.81 Γ 10 1002 9.81 Γ 6 = 3200 + + β 2600 β β ππ 2000 1000 2000 1000
Entropy Change (ii)
ππ β ππ = ππ ππ
ππ ππ
ππ β ππ = 1.005 ππ M+
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β π
ππ
ππ ππ
300 50 β 0.287ππ 350 150 M-
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First calculate
1.005 ππ
300 350
1.005 * (300 / 350 ) ln = Then calculate 0.287ππ
-0.1549214 Press M+ then press C button
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 First calculate
1250 β 450 β 303ππ
1250 450 1250 450
(1250-450)-303 * (1250 / 450) ln
=
490.4397
Then multiply with 2000 Γ 0.5 490.4397 * 2000 * 0.5 =
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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)
π=
π=
2ππΏ π‘ π βπ‘ π π ππ π 2 1 πΎπ΄
π ππ π 3 2 + πΎπ΅
2 Γ π Γ 1 Γ 1200 β 600 0.025 0.055 ππ ππ 0.01 + 0.025 19 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 =
β΄ π=
Made Easy
944.7186
W/m
2 Γ π Γ 1 Γ 1200 β 600 = 944.72 π/π 0.025 0.055 ππ ππ 0.01 + 0.025 19 0.2
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Unsteady Conduction (ii)
π ππ
πβπ
= π βππ = π βπ΅π πΉπ π
π
298 β 300 β3 = π β425πΓ2.3533 Γ10 30 β 300 or ππ
298β300
or ππ
30β300
= β425π Γ 2.3533 Γ 10β3
30β300
= 425π Γ 2.3533 Γ 10β3
298β300
30β300
or π
=
ππ 298 β300 425Γ2.3533 Γ10 β3
((30-300) / (298-300)) ln = Note: Several times use of
/ 425 = =
/ 2.3533 =
/ 3 +/- 10x =
4.904526 S
is good for this calculator.
Heat Exchanger (iii)
πΏπππ· =
π π βππ ππ
ππ ππ
=
90β40 90 40
ππ
(90 / 40) ln = then press 1/x then multiply with numerator * (90 β 40) = 61.65760
Radiation (iii)
Interchange factor
π12 =
1 1 π΄1 1 + β1 π1 π΄2 π2
First calculate
=
1 1 2Γ10 β3 1 + β1 0.6 100 0.3
2Γ10 β3
1
100
0.3
β1
(2 * 3 +/- 10x / 100) * (1 / 0.3 β 1 ) =
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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‘
= π12 ππ΄1 π14 β π24
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
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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 2 ππ‘β2 + πΌ 1 β πΌ 3 ππ‘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+ 0.4 * 95
M+ =
0.4 * 0.6 * 82
38
M+
M+
Press M+ then press C button
= 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:
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Data 1 2 3
x 1 2 3 βπ₯ = 6 For βπ₯ 1 + 2 + 3 = 6
Y 1 2 3 βπ¦ = 6
Xy 1 x1 2x2 3x3 βπ₯π¦ = 14
x2 12 22 32 2 βπ₯ = 14
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₯ or
6 = 3 π΄ + 6π΅
β¦ β¦ β¦ β¦ . . (π) β¦ β¦ β¦ β¦ . . (π)
and βπ₯π¦ = π΄βπ₯ + π΅βπ₯ 2 or
14 = 6A + 14 B
β¦ β¦ β¦ β¦ . . (ππ) β¦ β¦ β¦ β¦ . . (ππ)
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)
2ππ
π=
π=
πΌπ
Γ
πΌπ +πΌπ πΌπ
2 Γ 30000 Γ 3500 2.5 + 10 Γ 2.5 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
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