Week - 1 - Consistency of Units
Aim
To convert SI unit (MKS) to different unit system
Indroduction
Different industries uses different system of units as per the their convenience. The unit for the basic measurement quantities, mass, distance and time- dictate how the other quantities will be expressed. for example automobile industries use kg, mm,ms as their standard unit system.Construction industries are likely to use tonne, m,s as their unit system, In watch industries uses mg `mum` s. Similarly, PCB simulation in electronic industry uses gm `mum`, ms as their unit system.
LS-DYNA doesn't have a default system of units. User need to input materials 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 has to be conversant with converting quantities from one system of unit to another.
Procedure
Given
Mass 1kg length 1m Time 1s Force 1N Stress 1Pa Energy 1Nm Density `1(kg)/m^3`
Young's Modulus 210 GPa
Velocity 56.33 KMPH
Gravity `9.8 m/s^2`
- gm mm ms
Force (N)
`1kg*1m/s^2` = `1000gm*(1000mm)/(1000ms)^2` = `1gm(mm)/(ms)^2`
Stress `(N/m^2)`
`1N/m^2` = `((1gm*(mm))/(ms)^2 )/(1000mm)^2` = `10^-6``(gm)/((mm)(ms)^2)`
Energy (Nm)
1Nm = `1gm*(mm)/(ms)^2*1000mm` = `10^3 gm (mm^2)/(ms^2)`
Density (`(kg)/m^3`)
`1(kg)/m^3`= `(1000gm)/((1000mm)^3)` = `10^-6 (gm)/(mm^3)`
Young's modulus(GPa)
210GPa = 210*`10^9 N/m^2`= 210*`10^9 *(10^-6 (gm)/((mm)(ms)^2))` = 210*`10^3``(gm)/((mm)(ms)^2)`
Velocity (`m/s`)
56.33 KMPH = `56.33*(10^3 m/h)` = `56330*(1000mm)/(3600*1000ms)` = `15.64 (mm)/(ms)`
Gravity (`m/s^2`)
9.8 `m/s^2` = 9.8`*10^3(mm)/(1000ms)^2` = `9.8*10^-3 (mm)/(ms)^2`
Similarly,
| Unit System |
Mass (1kg) |
Length (1m) |
Time(1s) |
Force (1N) |
Stress (1Pa=`N/m^2`) |
Energy (1J`=Nm`) |
Density (`1(kg)/m^3`) |
| kg cm ms | 1 kg | 100 cm | `10^3` ms | `10^-4kg*(cm)/(ms^2)` | `10^-8(kg)/(cm*ms^2)` | `10^-2(kg*cm^2)/(ms^2)` | `10^-6(kg)/(cm^3)` |
| kg cm s | 1 kg | 100 cm | 1 s | `10^2 kg*(cm)/(s^2)` | `10^-2(kg)/(cm*s^2)` | `10^4(kg*cm^2)/(s^2)` | `10^-6(kg)/(cm^3)` |
| g mm ms | `10^3`g | `10^3 mm` | `10^3`ms | `1g*(mm)/(ms^2)` | `10^-6(g)/(mm*ms^2)` | `10^3(g*mm^2)/(ms^2)` | `10^-6(g)/(mm^3)` |
| kg m s | 1 kg | 1 m | 1 s | `1kg*(m)/(s^2)` | `1(kg)/(m*s^2)` | `1(kg*m^2)/(s^2)` | `1(kg)/(m^3)` |
| g cm s | `10^3`g | 100 cm | 1 s | `10^5g*(cm)/(s^2)` | `10(g)/(cm*s^2)` | `10^7(g*cm^2)/(s^2)` | `10^-3(g)/(cm^3)` |
| g cm `mus` | `10^3`g | 100 cm | `10^6 mus` | `10^-7g*(cm)/(mus^2)` | `10^-11(g)/(cm*mus^2)` | `10^-5(g*cm^2)/(mus^2)` | `10^-3(g)/(cm^3)` |
| g mm s | `10^3`g | `10^3`mm | 1s | `10^6g*(mm)/(s^2)` | `1(g)/(mm*s^2)` | `10^9(g*mm^2)/(s^2)` | `10^-6(g)/(mm^3)` |
| ton mm s |
`10^-3` ton |
`10^3`mm | 1s | 1ton`*(mm)/s^2` | `10^-6`ton`/(mm*s^2)` | `10^3`ton`*(mm^2)/(s^2)` | `10^-12`ton/(`mm^3`) |
| slug ft s | 0.0685 slug | 3.281 ft | 1s | `0.2247 slug*(ft)/s^2` | `0.0208(slug)/(ft*s^2)` | `0.7373(slug*ft^2)/(s^2)` | `1.9394(slug)/(ft^3)` |
| kg mm s | 1 kg | `10^3`mm | 1s | `10^3kg*(mm)/(s^2)` | `10^-3(kg)/(mm*s^2)` | `10^6(kg*mm^2)/(s^2)` | `10^-9(kg)/(mm^3)` |
| g cm ms | `10^3`g | 100 cm | `10^3`mm | `10^-1g*(cm)/(ms^2)` | `10^-5(g)/(cm*ms^2)` | `10(g*cm^2)/(ms^2)` | `10^-3(g)/(cm^3)` |
| kg mm ms | 1 kg | `10^3`mm | `10^3`ms | `10^-3kg*(mm)/(ms^2)` | `10^-9(kg)/(mm*ms^2)` | `1(kg*mm^2)/(ms^2)` | `10^-9(kg)/(mm^3)` |
In above table, Number shows conversion factor from SI unit to different units system.
|
Unit system |
Young's Modulus(`N/m^2`) |
Velocity(m/s) |
Accleration due to gravity(`m/s^2`) |
| kg cm ms | `210*10^9*10^-8(kg)/(cm*ms^2)` | `15.64*10^-1(cm)/(ms)` | `9.8*10^-4(cm)/(ms^2)` |
| kg cm s | `210*10^9*10^-2(kg)/(cm*s^2)` | `15.64*10^2(cm)/(s)` | `9.8*10^2(cm)/s^2` |
| g mm ms | `210*10^9*10^-6(g)/(mm*ms^2)` | `15.64*1(mm)/(ms)` | `9.8*10^-3(mm)/(ms^2)` |
| kg m s | `210*10^9*1(kg)/(m*s^2)` | `15.64*1(m)/(s)` | `9.8*1m/s^2` |
| g cm s | `210*10^9*10(g)/(cm*s^2)` | `15.64*10^2(cm)/(s)` | `9.8*10^2(cm)/s^2` |
| g cm `mus` | `210*10^9*10^-11(g)/(cm*mus^2)` | `15.64*10^-4(cm)/(mus)` | `9.8*10^-10(cm)/(mus^2)` |
| g mm s | `210*10^9*1(g)/(mm*s^2)` | `15.64*10^3(mm)/(s)` | `9.8*10^3(mm)/s^2` |
| ton mm s |
`210*10^9*10^-6` ton`/(mm*s^2)` |
`15.64*10^3(mm)/(s)` | `9.8*10^3(mm)/s^2` |
| slug ft s | `210*10^9*0.0208(slug)/(ft*s^2)` | `15.64*3.281(ft)/(s)` | `9.8*3.281(ft)/s^2` |
| kg mm s | `210*10^9*10^-3(kg)/(mm*s^2)` | `15.64*10^3(mm)/(s)` | `9.8*10^3(mm)/s^2` |
| g cm ms | `210*10^9*10^-5(g)/(cm*ms^2)` | `15.64*10^-1(cm)/(ms)` | `9.8*10^-4(cm)/(ms^2)` |
| kg mm ms | `210*10^9*10^-9(kg)/(mm*ms^2)` | `15.64*1(mm)/(ms)` | `9.8*10^-3(mm)/(ms^2)` |
In above table, except the given value, number shows conversion factor.
Conclusion
The unit conversion from SI to different unit system is performed and conversion factor is calculated.