Week - 1 - Consistency of Units
LS-Dyna Consistency of Units
Aim: Value of the following measurements are given as follows:
- 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
Now, here are a few systems of units:
- 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
Write the given measurements in the above different system of units. Also, mention the conversion factors.
**The assignment should show detailed calculation for conversion from SI unit to gm/mm/ms unit system. For others only the answers in the form of a table are sufficient with the unit systems as rows and measured quantities as columns. **
Solution:
- Fundamental Quantity: The Fundamental Quantity is independent Physical Quantity that is not possible to express in other Physical Quantity.
- Derived Quantity: Derived quantities are quantities that are calculated from two or more measurements. Derived quantities cannot be measured directly. They can only be computed.
- Below are the fundamental quantities that will be used in this task:
- 1 kg = 1e3 g = 1e-3 tonne = 0.06852 slug
- 1 m = 100 cm = 1e3 mm = 3.2808 ft
- 1 s = 1e3 ms = 1e6 = µs
Assuming the SI units for Length, Mass, and Time, we will proceed to convert kg/m/s system to g/mm/ms system.
|
SI System (kg, m, s) |
(g, mm, ms) system |
|
MASS 1kg |
1000 g |
|
LENGTH 1m |
1000 mm |
|
TIME 1s |
1000 ms |
|
FORCE 1N |
1N = 1 kg m/s2 |
|
STRESS 1 Pa |
1Pa = 1 N/m2 = 1 kg/m s2 |
|
ENERGY 1Nm |
1J = 1Nm = 1 kg m2/s2 |
|
DENSITY 1kg/m3 |
1 kg/m3 |
|
YOUNG'S Modulus 210GPa |
210 GPa = 210e9 Pa = 210e9 kg/m s2 |
|
Velocity 56.33KMPH |
56.33 km/h = 15.647 m/s |
|
GRAVITY 9.8m/s2 |
9.8 m/s2 = 9.8 * [1000 mm/ (1000 ms)2] |
Conversion Table
|
Unit System |
Mass |
Length |
Time |
Force |
Stress |
Energy |
|
SI Unit (kg m s) |
1 kg |
1 m |
1 s |
1N = 1 kg m/s2 |
1Pa = 1 N/m2 = 1 kg/m s2 |
1J = 1Nm = 1 kg m2/s2 |
|
kg cm ms |
1 kg |
102 cm |
103 ms |
10-4 kg cm/ms2 |
10-8 kg/cm ms2 |
10-2 kg cm2/ms2 |
|
kg cm s |
1 kg |
102 cm |
1 s |
102 kg cm/s2 |
10-2 kg/cm s2 |
104 kg cm2/s2 |
|
g mm ms |
103 g |
103 mm |
103 ms |
1 g mm/ms2 |
10-6 g/mm ms2 |
103 g mm2/ms2 |
|
g cm s |
103 g |
102 cm |
1 s |
105 g cm/s2 |
10 g/cm s2 |
107 g cm2/s2 |
|
g cm µs |
103 g |
102 cm |
106 µs |
10-7 g cm/µs2 |
10-11 g/cm µs2 |
10-5 g cm2/µs2 |
|
g mm s |
103 g |
103 mm |
1 s |
106 g mm/s2 |
1 g/mm s2 |
109 g mm2/s2 |
|
tonne mm s |
10-3 tonne |
103 mm |
1 s |
1 tonne mm/s2 |
10-6 tonne/mm s2 |
103 tonne mm2/s2 |
|
slug ft s |
0.068 slug |
3.28 ft |
1 s |
0.2246 slug ft/s2 |
0.0208 slug/ft s2 |
0.7366 slug ft2/s2 |
|
kg mm s |
1 kg |
103 mm |
1 s |
103 kg mm/s2 |
10-3 kg/mm s2 |
106 kg mm2/s2 |
|
g cm ms |
103 g |
102 cm |
103 ms |
10-1 g cm/ms2 |
10-5 g/cm ms2 |
10 g cm2/ms2 |
|
kg mm ms |
1 kg |
103 mm |
103 ms |
10-3 kg mm/ms2 |
10-9 kg/mm ms2 |
1 kg mm2/ms2 |
|
Unit System |
Density |
Young's Modulus 210GPa |
Velocity = 56.33 km/h |
Gravity = 9.8 m/s2 |
|
SI Unit ( kg m s) |
1 kg/m3 |
210 Gpa = 210e9 kg/m s2 |
56.33 km/h = 15.647 m/s |
9.8 m/s2 |
|
kg cm ms |
10-6 kg/cm3 |
2100 kg/cm ms2 |
1.5647 cm/ms |
9.8 x 10-4 cm/ms2 |
|
kg cm s |
10-6 kg/cm3 |
210e7 kg/cm s2 |
1564.7 cm/s |
9.8 x 102 cm/s2 |
|
g mm ms |
10-6 g/mm3 |
210e3 g/mm ms2 |
15.647 mm/ms |
9.8 x 10-3 mm/ms2 |
|
g cm s |
10-3 g/cm3 |
210e10 g/cm s2 |
1564.7 cm/s |
9.8 x 102 cm/s2 |
|
g cm µs |
10-3 g/cm3 |
2.10 g/cm µs2 |
15.647 x 10-4 cm/µs |
9.8 x 10-10 cm/µs2 |
|
g mm s |
10-6 g/mm3 |
2.10e11 g/mm s2 |
15647 mm/s |
9.8 x 103 mm/s2 |
|
tonne mm s |
10-12 tonne/mm3 |
210e3 tonne/mm s2 |
15647 mm/s |
9.8 x 103 mm/s2 |
|
slug ft s |
1.93 x 10-3 slug/ft3 |
4.368e9 slug/ft s2 |
51.322 ft/s |
32.144 ft/s2 |
|
kg mm s |
10-9 kg/mm3 |
210e6 kg/mm s2 |
15647 mm/s |
9.8 x 103 mm/s2 |
|
g cm ms |
10-3 g/cm3 |
210e4 g/cm ms2 |
1.5647 cm/ms |
9.8 x 10-4 cm/ms2 |
|
kg mm ms |
10-9 kg/mm3 |
210 kg/mm ms2 |
15.647 mm/ms |
9.8 x 10-3 mm/ms2 |
Note: Conversion factors are highlighted in Bold.