Week - 1 - Consistency of Units
Aim: To determine the conversion factor for different unit systems.
Theory: Different industries use different system of units as per their convenience. The units for the basic measurement quantities, mass distance and time - dictate how the other derived quantities will be expressed. For example, automotive industries use kg,mm,ms as their standard unit system. Construction industries are likely to use tonne,m,s as their unit system. Similarly, PCB simulation in electronic industry uses gm, micrometer,ms as their system of units.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. This warrants that to use LS-DYNA in different circumstances, users has to be conversant with converting quantities from one system of units to another.
Conversion of SI to gm,cm,s
1kg = 1000g;
1metre = 100cm;
1N = 1Kg*m/s2 = 1000g * 100cm / s2 = 10^5 gcm/s2;
Energy = 1J = 1Nm = 1N * 100cm = 100Ncm;
Stress = 1Pa = 1N/m2 = 1N/(100)^2 cm2 = 10^-4 N/cm2;
Density = Kg/m3 = 1000 g / (100)^3 = 10^-3 g/cm^3 ;
Young's modulas = 210GPa = 210G*N/m2 = 210*10^9*1N/(100)^2 = 210*10^5 N/cm2
velocity = 56.33kmph=56.33*10^3*100/60*60 = 1564.722 cm/s
| property/ unit system | Kg,m,s | Kg,cm,s | gm,mm,ms | Kg,m,s | gm,cm,s | gm,cm,us | gm,mm,s | ton,mm,s | slug,ft,s | Kg,mm,s | gm,cm,ms | Kg,mm,ms |
| Mass(Kg) | 1 | 1 | 1.00E-03 | 1 | 1.00E-03 | 1.00E-03 | 1.00E-03 | 1000 | 14 | 1 | 1.00E-03 | 1 |
| Length(m) | 1 | 1.00E-02 | 1.00E-03 | 1 | 2.00E-02 | 1.00E-02 | 1.00E-03 | 1.00E-03 | 0.3048 | 1.00E-03 | 1.00E-02 | 1.00E-03 |
| time(s) | 1 | 1 | 1.00E-03 | 1 | 1 | 1.00E-06 | 1 | 1 | 1 | 1 | 1.00E-03 | 1.00E-03 |
| Force(N) | 1 | 1.00E-02 | 1 | 1 | 1.00E-05 | 1.00E+07 | 1.00E-06 | 1 | 4.2672 | 1.00E+03 | 10 | 1.00E+03 |
| energy(J) | 1 | 1.00E-04 | 1.00E-03 | 1 | 1.00E-07 | 1.00E+05 | 1.00E-09 | 1.00E-03 | 1.3 | 1 | 0.1 | 1.00E+00 |
| stress(Pa) | 1 | 1.00E+02 | 1.00E+06 | 1 | 1.00E-01 | 1.00E+11 | 1 | 1.00E-06 | 45.85 | 1.00E+09 | 1.00E+05 | 1.00E+09 |
| density(Kg/m3) | 1 | 1.00E+06 | 1.00E+06 | 1 | 1.00E+03 | 1.00E+03 | 1.00E+06 | 1.00E+06 | 494.4 | 1.00E+09 | 1.00E-03 | 1.00E+09 |
| youngs Modulas | 210GPa | 2.10E+09 | 2.10E+05 | 210GPa | 2.10E+12 | 2.10E+12 | 2.10E+11 | 2.10E+05 | 9.65E+12 | 2.10E+08 | 2.10E+06 | 2.10E+02 |
| velocity | 15.65 m/s | 1565 cm/s | 15.65 mm/ms | 15.65 m/s | 1565 cm/s | 1.565e-3 cm/us | 1.565e+4 mm/s | 15650 mm/s | 184.76 ft/s | 15650 mm/s | 1.56 | 15.65 mm/ms |
| acceleration | 9.81 | 981 | 9.81E-03 | 9.81 | 981 | 9.81E-10 | 9810 | 9810 | 31.392 ft/s2 | 9810 | 9.81E-04 | 9.81E-03 |
Conclusion : In this task ,I learn about the conversion of various unit systems. Now I can easily convert one system of unit to other.