Week - 1 - Consistency of units
Objective: To understand the conversion factors for the various unit system, as the unit systems used vary according to the industries. Following are some example values of the quantities.
Following Table gives the Conversion Factor for various values in the various unit system.
| Mass 1 kg | Length 1m | Time 1s | Force 1N | Stress 1Pa | Energy 1Nm | Density 1Kg/m3 | Youngs Modulus 210GPa | Velocity 56.33Kmph | Gravity 9.8 m/s2 | |
| Kg/cm/ms | 1 kg | 100cm | 1000ms | `10^-4` | `10^-8` | `10^-2` | `10^-6` | `10` | `1.563` | `10^-4` |
| Kg/cm/s | 1kg | 100cm | 1s | `10^2` | `10^-2` | `10^4` | `10^-6` | `10^7` | `1563.88` |
`10^2` |
| gm/mm/ms | 1000gm | 1000mm | 1000ms | `1` | `10^-6` | `10^3` | `10^-6` | `10^3` | `15.638` | `10^-3` |
| Kg/m/s | 1kg | 1m | 1s | 1 | `1` | 1 | 1 | `10^9` | `15.638` | 1 |
| gm/cm/s | 1000gm | 100cm | 1s | `10^5` | `10` | `10^7` | `10^-3` | `10^10` | `1563.8` | `10^2` |
| gm/cm/us | 1000gm | 100cm | 1000000us | `10^-7` | `10^-13` | `10^-5` | `10^-3` | `10^-12` | `0.0015638` | `10^-10` |
| gm/mm/s | 1000gm | 1000mm | 1s | `10^6` | `1` | `10^9` | `10^-6` | `1` | `15.638` | `10^3` |
| ton/mm/s | 0.001ton | 1000mm | 1s | `1` | `10^-6` | `10^-3` | `10^-6` | `10^3` | `15.638` | `10^3` |
| slug/ft/s | 0.0685 slug | 3.2808 ft | 1s | `0.2248` | `0.020` | `10.7584` | `0.00194` | `4.38*10^9` | `51.505` | `32.17` |
| Kg/mm/s | 1kg | 1000mm | 1s | `10^3` | `10^-3` | `10^6` | `10^-9` | `10^6` | `15.638` | `10^3` |
| gm/cm/ms | 1000gm | 100cm | 1000ms | `10^-1` | `10^-5` | `10` | `10^-3` | `10^4` | `1.5638` | `10^-4` |
| Kg/mm/ms | 1kg | 1000mm | 1000ms | `1` | `10^-6` | `1` | `10^-9` | `1` | `15.638` | `10^-3` |
- Calculation for Force
Force (N) in gm/mm/ms
`F=1000 * 1000/(1000)^2 = 1N`
- Stress Calculation:
gm/mm/ms
`1 Pa = 1/(100*1000^2 )= 10^-8`
Unit conversion factor is `10^-8`
- Energy Calculation : (N-m)
gm/mm/ms
`E= 1000*1000^2/(1000^2 )= 10^3`
Unit conversion factor is `10^-3`
- Densitygm
gm/mm/ms
`Density= 1000^/(1000^3 )= 10^-6`
Unit conversion factor is `10^-6`
- Youngs Modulus
gm/mm/ms
`Youngs Modus= 210*10^9*1000/(1000^2 *1000)= 210*10^3`
Unit conversion factor is `10^-3`
- Velocity 56.53 Kmph
gm/mm/ms
`Velocity= 56.53*1000^2/(3.6*10^6 )= 56.53*0.277= 15.70 mm/ms`
Unit conversion factor is `0.2777`
- Gravity(9.8 m/s^2)
gm/mm/ms
`Gravity= 9.8*1000/(1000^3 )= 9.8*10^-3`
Unit conversion factor is `10^-3`