Week - 1 - Consistency of Units
Aim:
To understand the conversion of unit system and to maintain consistency in unit system.
Conversion of given SI units to g/mm/ms
Given SI units:
MASS 1kg
LENGTH 1m
TIME 1s
FORCE 1N
STRESS 1Pa
ENERGY 1Nm
DENSITY 1Kg/m3
YOUNG'S Modulus 210GPa
Velocity 56.33KMPH
GRAVITY 9.8m/s2
- Mass = 1 kilogram in SI system, where kilo = 1000
Therefore, Mass = 1 kg = 1000 grams = 1000 g
- Length = 1 m is its SI unit,
1 m = 100 cm
1 cm= 10 mm
Therefore, 1 m = 100*10 = 1000 mm
conversion factor = 1000
- Time = 1 second is its SI unit.
Milli = 0.001
Therefore, 1 ms = 0.001 s, i.e., 1 s = 1000 ms
conversion factor=1000
- Force = Mass * acceleration
=kg * m/s^2 = 1000g*(1000 mm / (1000)^2 ms^2) = 1
conversion factor = 1
- Stress = Force / Area = N /m^2 =
= 1/(1000)^2 = 1e-6 Pa
conversion factor = 1e-6
- Energy = force * displacement = Nm
= 1(g mm/ms^2)*1000mm = 1000
conversion factor = 1000
- Density = mass/volume = kg/m^3 = 1000 g/ (1000^3) m^3 = 1 e -6
conversion factor = 1e-6
- Younges Modules = Gpa = 10^9* 1 N /m^2 = 1 e 9 * 1e-6 = 1000
conversion factor = 1000
- Velocity = 33KMPH = 56.33*(1000*1000 mm)/3600*1000 ms = 15.64 mm/ms
conversion factor = 5/18
- Gravity = 9.81 m/s^2 = 9.81 *(1000 mm / (1000^2) ms^2) = 9.81 * 10^-3
conversion factor = 10^-3.
|
MASS (M) |
LENGTH (L) |
TIME (T) |
FORCE F=(M*(L/s^2)) |
STRESS (F/A) |
ENERGY (F*L) |
DENSITY (M/L^3) |
YOUNG'S Modulus 210Gpa* |
Velocity (L/T) 15.64* |
GRAVITY 9.81* |
|
|
Kg cm ms |
1 |
100 |
1000 |
1e-4 |
1e-8 |
1e-2 |
1e-6 |
1e-8 |
0.1 |
1e-4 |
|
Kg cm s |
1 |
100 |
1 |
1e2 |
1e-2 |
1e4 |
1e-6 |
1e-2 |
100 |
1e2 |
|
gm mm ms |
1e3 |
1000 |
1000 |
1 |
1e-6 |
1e3 |
1e-6 |
1e-6 |
1 |
1e-3 |
|
kg m s |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
g cm s |
1e3 |
100 |
1 |
1e5 |
10 |
1e7 |
1e-3 |
10 |
100 |
1e2 |
|
g cm micro sec |
1e3 |
100 |
1e6 |
1e-7 |
1e-11 |
1e-5 |
1e-3 |
1e-11 |
1e-4 |
1e-10 |
|
g mm s |
1e3 |
1000 |
1 |
1e6 |
1 |
1e9 |
1e-6 |
1 |
1e3 |
1e3 |
|
ton mm s |
1e-3 |
1000 |
1 |
1 |
1e-6 |
1e3 |
1e-12 |
1e-6 |
1e3 |
1e3 |
|
slug ft s |
6.8 e-2 |
3.28 |
1 |
0.22 |
0.0208 |
0.7216 |
1.92e-3 |
0.0208 |
3.28 |
3.28 |
|
kg mm s |
1 |
1000 |
1 |
1e3 |
1e-3 |
1e6 |
1e-9 |
1e-3 |
1e3 |
1e3 |
|
g cm ms |
1e3 |
100 |
1000 |
0.1 |
1e-5 |
10 |
1e-3 |
1e-5 |
0.1 |
1e-4 |
|
kg mm ms |
1 |
1000 |
1000 |
1e-3 |
1e-9 |
1 |
1e-9 |
1e-9 |
1 |
1e-3 |
Conclusion:
Most of the commercial FEA software’s don not have unit system setting in them, the user has to maintain a consistent unit system while entering the values, in this report detailed unit system conversion is explained and the conversion factor for many other unit system is presented in the table above.