Week - 1 - Consistency of units
Objective : To convert the given units in different system of units which is given in the question.
Given values :
I. Mass(M) = 1kg
II. Length(L) = 1m
III. Time(t) = 3s
IV. Force(F) = 1N
V. Stress = 1Pa
VI. Energy(E) = 1J
VII. Density(p) = 1kg/m3
VIII. Youngs Modulus(Y) = 210GPa
IX. Velocity(V) = 56.33kmph
X. Acceleration due to gravity(g) = 9.81m/s2
Calculations :
Here calculations are done stepwise and with detail manner. At last we can model a table for the values which we calculated and for all other conversions.
I. gm mm ms :
Here we are converting above given units into this type.
Main conversions to calculate below systems are 1kg = 1000gm,
1m = 1000mm and 1s = 1000ms
1. Force (F) = 1N ,
where N = kg * m/s2(i),
we can put main values in equation(i) formulae i.e,
N = 1000gm * 1000mm/(1000)^2 ms2 = 1e+0 gm * mm/ms2 or 1N.
Then we can conclude that conversion factor is '1e+0'.
2. Stress = 1Pa,
where St = N/m2 = kg * m/( s2 * m2) = kg /(m * s2)(ii),
we can put main values in equation(ii) formulae i.e,
St = 1000gm/(1000mm * 1000^2 ms2) = 1e-6 gm/(mm * ms2) or 1MPa.
Then we conclude that conversion factor is '1e-6'.
3. Energy = 1J
E = 1 N * m = kg * m * m/s2 = Kg * m2/s2(iii)
now we can put main conversion values in equation(iii) i.e,
E = 1000gm * 1000^2 m2/(1000^2 ms2) = 1e+3 gm * m2/(ms2) or 1mJ.
Then we conclude that conversion factor is '1e+3'.
4. Density = 1kg/m3(iv)
now we can put main conversion values in equation(iv) i.e,
p = 1000gm/(1000^3 mm3) = 1e-6 gm/m3.
Then we can conclude that conversion factor is '1e-6'.
5. Youngs Modulus = 210GPa
Y = 210 * 1e+9 N/m2(v)
now we can put main conversion values in equation(v) i.e,
Y = 210 * 1e+9 * 1e-6 gm/(mm * ms2) = 210 * 1e+3 gm/(mm * ms2) or 2.1e+5.
Then we can conclude that conversion factor is '2.1e+5'.
6. Velocity = 56.33 kmph
V = 56.33 km/hr, here 1hr = 3600 s = 3600e+3 ms = 3.6e+6 ms, 1km = 1000m = 1e+6mm
now, V = 56.33 * 1e+6 mm/(3.6e+6 ms) = 15.647 mm/ms.
Then we can conclude that conversion factor is '15.647'.
7. Acceleration due to gravity = 9.81 m/s2
now, g = 9.81 * 1000 mm/(1000^2 ms2) = 9.81e-3 mm/ms2.
Then we can conclude that conversion factor is '9.81e-3'.
This is the table for entire sytem conversion factors :
| Systems/Units |
Mass (m) |
Length (L) |
Time (t) |
Force (F) |
Stress (St) |
Energy (E) |
Density (p) |
Youngs Modulus (Y) |
Velocity (V) |
Acceleration due to gravity (g) |
| 1. gg mm ms | 1e+3 | 1e+3 | 1e+3 | 1e+0 | 1e-6 | 1e+3 | 1e-6 | 2.1e+5 | 15.647 | 9.81e-3 |
| 2. kg cm ms | 1e+0 | 1e+2 | 1e+3 | 1e-4 | 1e-8 | 1e-2 | 1e-6 | 2.1e+3 | 15.647e-1 | 9.81e-4 |
| 3. kg cm s | 1e+0 | 1e+2 | 1e+0 | 1e+2 | 1e-2 | 1e+4 | 1e-6 | 2.1e+9 | 15.647e+2 | 9.81e+2 |
| 4. kg m s | 1e+0 | 1e+0 | 1e+0 | 1e+0 | 1e+0 | 1e+0 | 1e+o | 2.1e+11 | 15.647e+0 | 9.81e+0 |
| 5. gm cm s | 1e+3 | 1e+2 | 1e+0 | 1e+5 | 1e+1 | 1e+7 | 1e-3 | 2.1e+12 | 15.647e+2 | 9.81e+2 |
| 6. gm cm us | 1e+3 | 1e+2 | 1e+6 | 1e-7 | 1e-11 | 1e-5 | 1e-3 | 2.1e+0 | 15.647e-4 | 9.81e-10 |
| 7. gm mm s | 1e+3 | 1e+3 | 1e+0 | 1e+6 | 1e+0 | 1e+9 | 1e-6 | 2.1e+11 | 15.647e+3 | 9.81e+3 |
| 8. ton mm s | 1e-3 | 1e+3 | 1e+0 | 1e+0 | 1e-6 | 1e+3 | 1e-12 | 2.1e+5 | 15.647e+3 | 9.81e+3 |
| 9. slug ft s | 6.85e-2 | 3e-1 | 1e+0 | 2.05e-2 | 2.28e-1 | 4.1e-5 | 2.5e+0 | 4.78e+10 | 4.694e+0 | 2.9e+0 |
| 10. kg mm s | 1e+0 | 1e+3 | 1e+0 | 1e+3 | 1e-3 | 1e+6 | 1e-9 | 2.1e+8 | 15.647e+3 | 9.81e+3 |
| 11. gm cm ms | 1e+3 | 1e+2 | 1e+3 | 1e-1 | 1e-5 | 1e-1 | 1e-3 | 2.1e+6 | 15.647e-1 | 9.81e-4 |
| 12. kg mm ms | 1e+0 | 1e+3 | 1e+3 | 1e-3 | 1e-9 | 1e+0 | 1e-9 | 2.1e+2 | 15.647e+0 | 9.81e-3 |
Conclusion :
Thus we have learnt how to convert the different systems in SI units and calculated the conversion factors for different systems, this will help during the analysis when we have to give boundary conditions for model in LS-Dyna.