Week - 1 - Consistency of Units
AIM:- To Convert the given SI Units into different system of units.
Objective:-
- Convert the given SI units into different standard units.
- Write the Detailed factors involves in conversion for gm mm ms
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/s2
Calculation & Result:-
- The calculation for conversion from SI unit for gm/mm/ms unit
|
Unit system |
gm mm ms |
Conversion factor |
|
Mass |
1000 gm | Conversion factor=103 |
| Length | 1000 mm | Conversion factor=103 |
| Time | 1000 ms | Conversion factor=103 |
| FORCE |
1N = 1Kg * 1m/s2 = (1000 gm * 1000 mm) / (1000 ms *1000 ms) = (1 gm * mm ) / ms2 |
Conversion factor=1 |
| STRESS |
1Pa = N / m2 = 1 kg / (m * s2) = 1000gm/1000mm (1000 ms *1000 ms) = 10-6 gm /(mm*ms2) |
Conversion factor=10-6 |
| ENERGY | 1Nm = 1(Kg * m2 /s2)
= [1000gm*(1000mm*1000mm)]/(1000ms*1000ms) = 103 gm*mm2/ms2 |
Conversion factor=103 |
| DENSITY |
1Kg/m3 = 1000 gm /(1000mm*1000mm*1000mm) = 103 gm/ 109 ms3 = 10-6gm/ms3 |
Conversion factor=10-6 |
| YOUNG’S Modulus 210GPa |
210GPa = 210 * 109 * (N /m2)] -------{ 1 GPa = 109 X (N / m2)} = 210 * 109 * (10-6 gm /mm*ms2) = 210 * 103 gm/mm*ms2 |
Conversion factor=103 |
| Velocity |
1KMPH = 106mm / (3600 *1000 ms) ------{ 1KM = 106mm} = 10/36 = 0.277 mm/ms ------{ 1hr = 3600 *1000 ms} 56.33KMPH = 56.33 x 0.277 = 15.64 mm/ms |
Conversion factor=5/18 |
| GRAVITY 9.8m/s |
1 m/s2 = 1000 mm/(1000 ms X 1000 ms) = 10-3 mm/ms2 9.8m/s2 = 9.8 X 10-3 mm/ms2 |
Conversion factor=10-3 |
- The calculation for conversion from SI unit for-
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
|
Unit system |
Mass |
Length |
Time |
Force |
Stress |
Energy |
Density |
Young’s Modulus |
Velocity |
Gravity |
|
kg m s |
1kg |
1m |
1s |
1 N =1 kg*m/s2 |
1 Pa = 1 kg/(m* s2) |
1 J = 1Nm = 1 kg*m2/s2 |
1kg/m3 |
210 GPa = 210e+9 kg/(m*s2) |
15.647 m/s |
9.8 m/s2 |
|
kg cm ms |
1kg |
102cm |
103ms |
10-4 kg*cm/ms2 |
10-8 kg/(cm*ms2) |
10-2 kg*cm2/ms2 |
10-6 kg/cm3 |
2100 kg/(cm*ms2) |
1.5647 cm/ms |
9.8*10-4 cm/ms2 |
|
kg cm s |
1kg |
102cm |
1s |
102 kg*cm/s2 |
10-2 kg/(cm*s2) |
104 kg*cm2/s2 |
10-6 kg/cm3 |
210e+7 kg/(cm*s2) |
1564.7 cm/s |
9.8*102 cm/s2 |
|
g mm ms |
103g |
103mm |
103ms |
1 g*mm/ms2 |
10-6 g/(mm*ms2) |
103 g*mm2/ms2 |
10-6 g/mm3 |
210e+3 g/(mm*ms2) |
15.647 mm/ms |
9.8*10-3 mm/ms2 |
|
g cm s |
103g |
102cm |
1s |
105 g*cm/s2 |
10 g/(cm*s2) |
107 g*cm2/s2 |
10-3 g/cm3 |
210e+10 g/(cm*s2) |
1564.7 cm/s |
9.8*102 cm/s2 |
|
g cm μs |
103g |
102cm |
106μs |
10-7 g*cm/μs2 |
10-11 g/(cm*μs2) |
10-5 g*cm2/μs2 |
10-3 g/cm3 |
2.10 g/(cm*μs2) |
15.647*10-4 cm/ μs |
9.8*10-10 cm/μs2 |
|
g mm s |
103g |
103mm |
1s |
106 g*mm/ s2 |
1 g/(mm*s2) |
109 g*mm2/s2 |
10-6 g/mm3 |
2.10 e+11 g/(mm*s2) |
15647 mm/s |
9.8*103 mm/s2 |
|
Ton mm s |
10-3ton |
103mm |
1s |
1 ton*mm/s2 |
10-6 ton/(mm*s2) |
103 ton*mm2/s2 |
10-12 ton/mm3 |
210e+3 ton/(mm*s2) |
15647 mm/s |
9.8*103 mm/s2 |
|
slug ft s |
0.068slug |
3.28 ft |
1s |
0.2246 slug*ft/ s2 |
0.0208 slug/(ft*s2) |
0.7366 slug*ft2/s2 |
1.93*10-3 slug/ft3 |
4.368 e+9 slug/(ft*s2) |
51.322 ft/s |
32.144 ft/s2 |
|
kg mm s |
1kg |
103mm |
1s |
103 kg*mm/s2 |
10-3 kg/(mm*s2) |
106 kg*mm2/s2 |
10-9 kg/mm3 |
210e+6 kg/(mm*s2) |
15647 mm/s |
9.8*103 mm/s2 |
|
g cm ms |
103g |
102cm |
103ms |
10-1 g*cm/ms2 |
10-5 g/(cm*ms2) |
10 g*cm2/ms2 |
10-3 g/cm3 |
210e+4 g/(cm*ms2) |
1.5647 cm/ms |
9.8*10-4 cm/ ms2 |
|
kg mm ms |
1kg |
103mm |
103ms |
10-3 kg*mm/ms2 |
10-9 kg/(mm*ms2) |
1 kg*mm2/ms2 |
10-9 kg/mm3 |
210 kg/(mm*ms2) |
15.647 mm/ms |
9.8*10-3 mm/ms2 |
Link & References:-
NOTE-LS-DYNA doesn't have a default system of units. User needs to input material properties and physical dimensions according to a consistent system of units as per their choice.
LS Dyna - https://www.dynasupport.com/howtos/general/consistent-units
Learning Outcome:-
- Learn to convert SI units
- Understand the factors involves in conversion.