Week - 1 - Consistency of units
Two tables are formed, one is the value table consisting of the value of quantities stated in different systems of units and the other table shows the conversion factors utilized.
Value Table
|
Unit System |
Quantity |
|||||||||
|
Mass |
Length |
Time |
Force |
Stress |
Energy |
Density |
Young’s Modulus |
Velocity |
Gravity |
|
|
Kg/m/s |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
210*10^(9) |
15.6472 |
9.8 |
|
Kg/cm/ms |
1 |
100 |
1000 |
10^(-4) |
10^(-8) |
10^(-2) |
10^(-6) |
2100 |
1.56472 |
9.8*10^(-4) |
|
Kg/cm/s |
1 |
100 |
1 |
100 |
10^(-2) |
10^(4) |
10^(-6) |
210*10^(7) |
1564.72 |
9.8*10^(2) |
|
g/mm/ms |
1000 |
1000 |
1000 |
1 |
10^(-6) |
1000 |
10^(-6) |
210*10^(3) |
15.6472 |
9.8*10^(-3) |
|
g/cm/s |
1000 |
100 |
1 |
10^(5) |
10 |
10^(7) |
10^(-3) |
210*10^(10) |
1564.72 |
9.8*10^(2) |
|
g/cm/us |
1000 |
100 |
10^(6) |
10^(-7) |
10^(-11) |
10^(-5) |
10^(-3) |
210*10(-2) |
15.6472*10^(-4) |
9.8*10^(-10) |
|
g/mm/s |
1000 |
1000 |
1 |
10^(6) |
1 |
10^(9) |
10^(-6) |
210*10^(9) |
15.6472*10^(3) |
9.8*10^(3) |
|
Ton/mm/s |
10^(-3) |
1000 |
1 |
1 |
10^(-6) |
1000 |
10^(-12) |
210*10^(3) |
15.6472*10^(3) |
9.8*10^(3) |
|
Slug/ft/s |
0.0685218 |
3.28084 |
1 |
0.224809062312 |
0.020885 |
0.73756256 |
0.0019403 |
4.38585 |
51.33595 |
32.152232 |
|
Kg/mm/s |
1 |
1000 |
1 |
1000 |
10^(-3) |
10^(6) |
10^(-9) |
210*10^(6) |
15.6472*10^(3) |
9.8*10^(3) |
|
g/cm/ms |
1000 |
100 |
1000 |
10^(-1) |
10^(-5) |
10 |
10^(-3) |
210*10^(4) |
1.56472 |
9.8*10^(-4) |
|
Kg/mm/ms |
1 |
1000 |
1000 |
10^(-3) |
10^(-9) |
1 |
10^(-9) |
210 |
15.6472 |
9.8*10^(-3) |
*Ton is metric tonne
Conversion Factor Table
|
Unit System |
Quantity |
|||||||||
|
Mass |
Length |
Time |
Force |
Stress |
Energy |
Density |
Young’s Modulus |
Velocity |
Gravity |
|
|
Kg/m/s |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
Kg/cm/ms |
1 |
100 |
1000 |
10^(-4) |
10^(-8) |
10^(-2) |
10^(-6) |
10^(-8) |
0.1 |
10^(-4) |
|
Kg/cm/s |
1 |
100 |
1 |
100 |
10^(-2) |
10^(4) |
10^(-6) |
10^(7) |
100 |
10^(2) |
|
g/mm/ms |
1000 |
1000 |
1000 |
1 |
10^(-6) |
1000 |
10^(-6) |
10^(3) |
1 |
10^(-3) |
|
g/cm/s |
1000 |
100 |
1 |
10^(5) |
10 |
10^(7) |
10^(-3) |
10^(10) |
100 |
10^(2) |
|
g/cm/us |
1000 |
100 |
10^(6) |
10^(-7) |
10^(-11) |
10^(-5) |
10^(-3) |
10(-2) |
10^(-4) |
10^(-10) |
|
g/mm/s |
1000 |
1000 |
1 |
10^(6) |
1 |
10^(9) |
10^(-6) |
10^(9) |
10^(3) |
10^(3) |
|
Ton/mm/s |
10^(-3) |
1000 |
1 |
1 |
10^(-6) |
1000 |
10^(-12) |
10^(3) |
10^(3) |
10^(3) |
|
Slug/ft/s |
0.0685218 |
3.28084 |
1 |
0.224809062312 |
0.020885 |
0.73756256 |
0.0019403 |
0.020885 |
3.28084 |
3.28084 |
|
Kg/mm/s |
1 |
1000 |
1 |
1000 |
10^(-3) |
10^(6) |
10^(-9) |
10^(6) |
10^(3) |
10^(3) |
|
g/cm/ms |
1000 |
100 |
1000 |
10^(-1) |
10^(-5) |
10 |
10^(-3) |
10^(4) |
0.1 |
10^(-4) |
|
Kg/mm/ms |
1 |
1000 |
1000 |
10^(-3) |
10^(-9) |
1 |
10^(-9) |
1 |
1 |
10^(-3) |
The conversion calculations from SI to g/mm/ms is evaluated below:
Mass 1kg =1000 g (conversion factor is 1000)
Length 1m =1000 mm (conversion factor is 1000)
Time 1 s =1000 ms (conversion factor is 1000)
Force 1 N = 1 kg.m/(s^2) = 1000 g. 1000 mm/(10^6 )(ms^2) = 1 (g.mm/(ms^2)) [conversion factor is 1]
Stress 1 Pa = 1N/(m^2) = 1(g.mm/(ms^2))/(10^6)(mm^2) = 10^(-6) (g/ mm.(ms^2)) [conversion factor is 10^-6]
Energy 1J = 1N.m = 1 (g.mm/(ms^2)) * 1000 mm = 1000 (g. (mm/ms)^2) [conversion factor is 1000]
Density 1 (kg/m^3) = 1000 g/ 10^9 (mm^3) = 10^(-6) (g / (mm^3)) [conversion factor is 10^-6]
Young's modulus has same units as stress, therefore 210 GPa = 210*(10^3) (g/ mm.(ms^2)) [conversion factor is 10^-6]
Velocity 15.6472 m/s = 15.6472 mm/ms [conversion factor is 1]
Gravity 9.8 m/(s^2) = 9.8 *1000 mm/ (10^6) (ms^2) = 9.8*10^(-3) (mm/(ms^2)) [conversion factor is 10^-3]