Week - 1 - Consistency of Units

UNIT CONVERSIONS

AIM:

To convert the given measurements in to the specified system of units

PROCEDURE:

The units in the SI system will be in Meter (m), Kilogram (Kg), Second (s), Newton (N). So the youngs modulus (E) of 210 GPa can be written as;

210GPa = 210e+9 Pa = 210e+9 N/m2

Since we require the E in kg/mm/ms unit system.

210e+9 N/m2 = 210e+9 x 1e-6 n/mm2

1N/m2 = 1N/(1e+3mm)2 , 1m = 1e+3 mm

= 210e+3 N/mm2

1N/m2 = 1e-6 N/mm2

1N = 1kg x m/s2

= 1Kg x 1e+3 mm/(1e+3ms)2

= 1Kg x 1e+3mm/ 1e+6ms2

= 1Kg x mm/ 1e+3ms2

= 1e-3 Kg x mm/ ms2 = 1e-3 N

while substituting the e+3 and e-3 cancels and ends up with 210

Thus we can enter 210Gpa as 210 in LS-DYNA as per Kg/mm/ms unit system and if we multiply with 1e-9 then it wll cancels the powers in SI unit systen by leaving the magnitude as per the required unit system so its considered as the conversion factor.

Units conversion:

System of Units	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
Kg cm ms	1kg	100cm	1000ms	1e-4 kg cm/ms2	1e-8 kg/ cm. ms2	1e-2 kg cm2/ms2	1+e-6 kg/cm3	2100 Kg/cm ms2	1.5647 cm/ms	9.8e-4 cm/ms2
Kg cm s	1kg	100cm	1s	1e+2 kg cm/s2	1e-2 kg/cm.s2	1e+4 kg cm2/s2	1+e-6 kg/cm3	210e+7 Kg/ cm s2	15.647e+2 cm/s	9.8e+2 cm/s2
gm mm ms	1000gm	1000mm	1000ms	1 gm mm/ms2	1e-6 gm/mm ms2	1e+3 mm2/ms2	1+e-6 gm/mm3	210e+3 gm /mm ms2	15.647 mm/ms	9.8e-3 mm/ms2
kg m s	1kg	1m	1s	1N	Pa (N/m2)	1 kg m2/s2 (J)	1 kg/m3	210e+9 Pa	15.647 m/s	9.8 m/s2
g cm s	1000g	100cm	1s	1e+5 gm cm/s2	1e+1 gm/cm s2	1e+7 gm cm2/s2	1e-3 g/cm3	210e+10 g/ cm s2	15.647e+2 cm/s	9.8e+2 cm/s2
g cm μs	1000g	100cm	1e+6μs	1e-7 gm cm/μs2	1e-11 gm/cm μs2	1e-5 gm cm2/μs2	1e-3 g/cm3	210e-2 g/cm μs2	15.647e-4 cm/μs	9.8e-10 cm/μs2
g mm s	1000g	1000mm	1s	1e+6 gm mm/s2	1 g/mm s2	1e+9 gm mm2/s2	1+e-6 g/mm3	210e+9 g/mm s2	15.647e+3 mm/s	9.8e+3 mm/s2
ton mm s	1e-3 ton	1000mm	1s	1 ton mm/s2	1e-6 ton/mm s2	1e+3 ton mm2/s2	1e-12 ton/mm3	210e+3 ton /mm s2	15.647e+3 mm/s	9.8e+3 mm/s2
slug ft s	0.068slug	3.28ft	1s	0.223 slug ft/s2	0.02 slug/ft s2	0.731slug ft2/s2	1.9e-3 slug/ft3	4.3536e+9 slug/ ft s2	51.3228 ft/s	32.144 ft/s2
kg mm s	1kg	1000mm	1s	1e+3 kg mm/s2	1e-3 kg/mm s2	1e+6 kg mm2/s2	1e-9 kg/mm3	210e+6 Kg/mm s2	15.647e+3 mm/s	9.8e+3 mm/s2
g cm ms	1000g	100cm	1000ms	1e-1 g mm/ms2	1e-5 gm/cm ms2	1e+1 gm cm2/ms2	1e-3 g/cm3	210e+4 g/sm ms2	1.5647 cm/ms	9.8e-4 cm/ms2
kg mm ms	1kg	1000mm	1000ms	1e-3 kg mm/ms2	1e-9 kg/mm ms2	1kg mm2/ms2	1e-9 kg/mm3	210 kg/mm ms2	15.647 mm/ms	9.8e-3 mm/ms2

conversion factors:

System of Units	MASS 1kg	LENGTH 1m	TIME 1s	FORCE 1N	STRESS 1Pa	ENERGY 1Nm	DENSITY 1Kg/m3	YOUNG'S Modulus 210GPa	Velocity 56	GRAVITY
Kg cm ms	1	100	100	1e-4	1e-8	1e-2	1+e-6	1e-8	0.0277	1e-4
Kg cm s	1	100	1	1e+2	1e-2	1e+4	1+e-6	1e-2	27.77	1e+2
gm mm ms	1000	1000	1000	1	1e-6	1e+3	1+e-6	1e-6	0.277	1e-3
kg m s	1	1	1	1	1	1 kg	1	1	0.277	1
g cm s	1000	100	1	1e+5	1e+1	1e+7	1e-3	1e+1	27.77	1e+2
g cm μs	1000g	100	1e+6	1e-7	1e-11	1e-5	1e-3	1e-11	2.77e-5	1e-10
g mm s	1000	1000	1s	1e+6	1	1e+9	1+e-6	1	277.77	1e+3
ton mm s	1e-3	1000	1s	1	1e-6	1e+3	1e-12	1e-6	277.77	1e+3
slug ft s	0.068	3.28	1	0.223	0.02	0.731	1.92e-3	0.0207	0.9111	3.28
kg mm s	1	1000	1	1e+3	1e-3	1e+6	1e-9	1e-3	277.77	1e+3
g cm ms	1000	100	1000	1e-1	1e-5	1e+1	1e-3	1e-5	0.0277	1e-4
kg mm ms	1	1000	1000	1e-3	1e-9	1	1e-9	1e-9	0.277	1e-3

Calculations:

SI unit to gm/mm/ms.

1Kg = 1e+3 gm

1m = 1e+3 mm

1s = 1e+3 ms.

FORCE 1N

= 1 Kg x m/s2

= 1e+3 gm x 1e+3 mm/ (1e+3ms)2

= [1e+3 x 1e+3 x 1e-6] gm.mm/ms2

= 1 gm.mm/ms2

STRESS 1Pa

= 1N/m2

= 1N/ (1e+3mm)2

= 1e-6 gm/ ms2.mm

ENERGY 1Nm

= 1e+3 gm mm2/ms2

DENSITY 1kg/m3

= 1e+3 gm/1e+9 mm3

= 1e-6 gm/mm3

YOUNG'S Modulus 210GPa

= 210e+9 N/m2

= 210e+9 N/1e+6mm2

= 210e+3 gm /mm ms2

Velocity 56.33KMPH

= 56.33 x 1e+6 mm /3600 x 1e+3 ms

= 15.647 mm/ms

CONCLUSION:

The given measurements were converted in to different unit systems as per the specification and the detailed calculation is done in order to convert the units.