Week - 1 - Consistency of Units
AIM:
Convert the given measurements into a different system of units and find their corresponding conversion factors.
GIVEN DATA:
Some measurements have been given,
- 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/s)
Some systems of units are given,
PURPOSE:
LS-DYNA doesn't have a default system of units. User needs to input the material properties and physical dimensions according to a consistent system of units as per their choice. This warrants that to use LS-DYNA in different circumstances, users have to be conversant with converting quantities from one system of units to another.
CONVERSATIONS:
>>> From SI units to gm/mm/ms unit system
Mass: 1kg = 1000gm ------- (conversion factor 10^3)
Length: 1m = 1000mm ------- (Conversion factor 10^3)
Time: 1s = 1000ms ------- (Conversion factor 10^3)
Force: 1N = 1kg * 1m/s^2
= 1000g/{1000mm * (1000ms)^2}
= 10^-6g /(mm * ms^2) ------ (Conversion Factor 10^-6)
Stress: 1Pa = 1n/m^2 = {1kg*(1m/s^2)}/m^2 = 1kg/(m*s^2)
= 1000g/{1000mm * (1000ms)^2}
= 10^-6g/(mm*ms^2) -------(Conversion Factor 10^-6)
Energy: 1j = 1Nm =(1kg*1m/s^2)*m = 1(kg*m^2/s^2)
= (1000g*1000mm^2)/(1000ms^2)
= (10^9*g*mm^2)/(10^6ms^2)
= 10^3(g*mm2/ms2) ------- (Conversion factor 10^3)
Density: 1kg/m^3 = 1000g/(1000mm^3)
= 10^-6 g/mm^3 ------(Conversion factor 10^-6)
Young's Modulus: 210 Gpa = 210e+9kg/(m*s^2) = 210e+9*10^-6g/(mm*ms^2)
= 210e+3 g/(mm*m s^2)
= 210*10^3 g/(mm*m s^2) ------(Conversion factor 10^3)
Velcoity: 56.33 Kmph = 56.33 * {10^6mm/(3600*1000ms)}
= 15.647 mm/ms ------(Conversion factor 5/18)
Gravity: 9.8 m/s^2 = 9.8*1000mm/(1000ms)^2
= 9.8*10^-3 mm/ms^2 ------(Conversion factor 10^-3)
TABLE:
Unit systems as rows and Measured quantities as columns:
| Unit system(SI unit) | Mass | Length | Time | Force | Stress | Energy |
| kg.m.s | 1kg | 1m | 1s |
1N=1 kg*m/s^2 |
1pa = 1kg/(m*s^2) |
1J =1Nm = 1kg*m^2/s^2*10^-2
|
| kg.cm.ms | 1kg | 10^2cm | 10^3ms |
kg*cm/ms^2 10^-4 |
kg/(cm*ms^2) 10^-8 |
kg*cm^2/ms^2 10^-2 |
| kg.cm.s | 1kg | 10^2cm | 1s |
kg*cm/s^2 10^2 |
Kg/(cm*s^2) 10^-2 |
kg*cm^2/s^2 10^4 |
| g.mm.ms | 10^3g | 10^3mm | 10^3ms |
g*mm/ms^2 1 |
g/(mm*ms^2) 10^-6 |
g*mm^2/ms^2 10^3 |
| g.cm.s | 10^3g | 10^2cm | 1s |
g*cm/s^2 10^5 |
g/(cm*s^2) 10 |
g*cm^2/s^2 10^7 |
| g.cm.μs | 10^3g | 10^2cm | 10^6 μs |
g*cm/μs^2 10^-7 |
g/(cm*μs^2) 10^-11 |
g*cm^2/μs^2 10^-5 |
| g.mm.s | 10^3g | 10^3mm | 1s |
g*mm/s^2 10^6 |
g/(mm*s^2)
|
g*mm^2/s^2 10^9 |
| Ton.mm.s | 10^3 ton | 10^3mm | 1s |
ton*mm/s^2 1 |
ton/(mm*s^2) 10^-6 |
ton*mm^2/s^2 10^3 |
| slug.ft.s | 0.068 slug | 3.28 ft | 1s |
slug*ft/s^2 o.2246 |
slug/(ft*s^2) 0.0208 |
slug*ft^2/s^2 0.7366 |
| kg.mm.s | 1kg | 10^3mm | 1s |
kg*mm/s^2 10^3 |
kg/(mm*s^2) 10^-3 |
kg*mm^2/s^2 10^6 |
| g.cm.ms | 10^3g | 10^2cm | 10^3ms |
g*cm/ms^2 10^-1 |
g/(cm*ms^2) 10^-5 |
g*cm^2/ms^2 10 |
| kg.mm.ms | 1kg | 10^3mm | 10^3ms |
kg*mm/ms^2 10^-3 |
kg/(mm*ms^2) 10^-9 |
kg*mm^2/ms^2 1 |
CONCLUSION:
The conversation of units has been completed.
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