Week - 1 - Consistency of units
AIM
Convert the given measurements from Si unit system to other differant system of units
OBJECTIVE
- MASS 1kg
- LENGTH 1m
- TIME 1s
These are the fundemental quantities in SI unit system
- FORCE 1N
- STRESS 1Pa
- ENERGY 1Nm
- DENSITY 1Kg/m3
- YOUNG'S Modulus 210GPa
- Velocity 56.33KMPH
- GRAVITY 9.8m/s2
These are the derived quantities which basically derived from the fundemental quantities.
We need to convert all these quanties from SI unit system to the following unit systems.
- Kg cm ms
- Kg cm s
- gm mm ms
- kg m s
- g cm s
- g cm us
- g mm s
- ton mm s
- slug ft s
- kg mm s
- g cm ms
- kg mm ms
Detailed calculation for conversion from Si System ( kg /m /s ) to gm /mm /ms
1) Mass = 1 kg
1 kg = 1000 gm
So conversion factor = 10^3
2) Length = 1 m
1m = 1000 mm
So conversion factor = 10^3
3) Time = 1 s
1 s = 1000 ms
So conversion factor = 10^3
4) Force = 1 Newton
1N = 1 kgm/s^2 = (10^3 gm x 10^3 mm) / (10^3 )^2
= 1 gm mm/ms^2
So conversion factor = 10^0
5) Stress = 1 Pa
1 Pa = 1N/m^2
= 1(gm mm/ms^2)/ 10^6 mm^2
= 10^-6 gm/(mm ms^2)
So Conversion factor = 10^-6
6) Energy = 1 Nm
= 1 (gm mm/ms^2) x 10^3 mm
= 10^3 (gm mm^2 )/ms^2
So conversion Factor = 10^3
7) Density = 1 Kg /m^3
= 10^3 gm/(10^3)^3 mm^3
= 10^-6 g/mm^3
So Conversion factor = 10^-6
8) Young's Modulus ,E = 210 GPa
= 210 x 10^9 N/m^2
= (210 x 10^9 gm mm)/ (ms^2 x 10^6 mm^2)
= 210 x 10^3 gm/mm ms^2
So Conversion factor = 10^-6
Conversion factor is nothing but the number which we should be multipling with a quantity in one unit system to convert that quantity into another unit system.
Here Conversion Factor = 210 x10^3/210x10^9 = 10^-6
9) Velocity = 56.33 KMPH
= (56.33 x 10^3 m) / 3600 sec
= 15.64 m/s
= 15.64 mm/ms
So conversion factor = 10^0
10) Gravity = 9.8 m/s^2
= 9.8 x 10^3 mm/(10^3)^2 ms^2
= 9.8 x 10^-3 mm/ms^2
here in SI system of units, accleration due to gravity is 9.8 m/s^2 .But in gm/mm/ms unit system, its value is 9.8 x10^-3 mm/ms^2.So we need to multiply 10^-3 to the value of gravity in SI system to get the value of gravity in gm/mm/ms unit system.
So Conversion factor = 10^-3
Tabular form of all the conversions
| MASS 1 Kg | Conversion Factor | LENGTH 1m | Conversion Factor | TIME 1s | Conversion Factor | FORCE 1N | Conversion Factor | STRESS 1Pa | Conversion Factor | ENERGY 1Nm | Conversion Factor | DENSITY 1Kg/m3 | Conversion Factor | YOUNG'S Modulus 210GPa | Conversion Factor | Velocity 56.33KMPH | Conversion Factor | GRAVITY 9.8m/s2 | Conversion Factor | |
| Kg cm ms | 1 | 10^0 | 1 | 10^2 | 1 | 10^3 | 1 | 10^-4 | 1 | 10^-8 | 1 | 10^-2 | 1 | 10^-6 | 210x10^0 | 10^-8 | 1.564 | 10^-1 | 9.8x10^-4 | 10^-4 |
| Kg cm s | 1 | 10^0 | 1 | 10^2 | 1 | 10^3 | 1 | 10^2 | 1 | 10^-2 | 1 | 10^4 | 1 | 10^-6 | 210x10^7 | 10^-2 | 1564 | 10^2 | 9.8x10^2 | 10^2 |
| gm mm ms | 1 | 10^3 | 1 | 10^3 | 1 | 10^3 | 1 | 10^0 | 1 | 10^-6 | 1 | 10^3 | 1 | 10^-6 | 210x10^3 | 10^-6 | 15.64 | 10^0 | 9.8 | 10^-3 |
| kg m s | 1 | 10^0 | 1 | 10^0 | 1 | 10^0 | 1 | 10^0 | 1 | 10^0 | 1 | 10^0 | 1 | 10^0 | 210x10^9 | 10^9 | 15.64 | 10^0 | 9.8 | 10^0 |
| g cm s | 1 | 10^3 | 1 | 10^2 | 1 | 10^0 | 1 | 10^5 | 1 | 10^1 | 1 | 10^7 | 1 | 10^-3 | 210x10^10 | 10^1 | 1564 | 10^2 | 9.8x10^2 | 10^2 |
| g cm us | 1 | 10^3 | 1 | 10^2 | 1 | 10^6 | 1 | 10^-7 | 1 | 10^-11 | 1 | 10^-5 | 1 | 10^-3 | 210x10^-2 | 10^-11 | 15.64x10^-4 | 10^-4 | 9.8x10-10 | 10^-10 |
| g mm s | 1 | 10^3 | 1 | 10^3 | 1 | 10^0 | 1 | 10^6 | 1 | 10^0 | 1 | 10^9 | 1 | 10^-6 | 210x10^9 | 10^0 | 15.64x10^3 | 10^3 | 9.8x10^3 | 10^3 |
| ton mm s | 1 | 10^-3 | 1 | 10^3 | 1 | 10^0 | 1 | 10^0 | 1 | 10^-6 | 1 | 10^3 | 1 | 10^-12 | 210x10^3 | 10^-6 | 15.64x10^3 | 10^3 | 9.8x10^3 | 10^3 |
|
slug ft s |
0.0685218 | 0.068512 | 3.28084 | 3.28084 | 1 | 10^0 | 0.224809 | 0.224809 | 0.02088543 | 0.02088543 | 0.737562 | 0.737562 | 0.001940 | 0.001940 | 4.385 | 2.088x10^7 | 5.01793 | 3.2x10^-1 | 3.21522 | 3.2x10^0 |
| kg mm s | 1 | 10^0 | 1 | 10^3 | 1 | 10^0 | 1 | 10^3 | 1 | 10^-3 | 1 | 10^6 | 1 | 10^-9 | 210x10^6 | 10^-3 | 15.64x10^3 | 10^3 | 9.8x10^3 | 10^3 |
| g cm ms | 1 | 10^3 | 1 | 10^2 | 1 | 10^3 | 1 | 10^2 | 1 | 10^-2 | 1 | 10^4 | 1 | 10^-3 | 210x10^-7 | 10^-16 | 1.564 | 10^-1 | 9.8x10^-4 | 10^-4 |
| kg mm ms | 1 | 10^0 | 1 | 10^3 | 1 | 10^3 | 1 | 10^-3 | 1 | 10^-9 | 1 | 10^0 | 1 | 10^-9 | 210 | 10^-9 | 15.64 | 10^0 | 9.8x10^-3 | 10^-3 |
Learning Outcome
Learned about the process of converting quantities in one unit system to other unit system.This should be learned because the LS Dyna is not having a unit system.So the user must be consistent with the unit system he is using in a job.