Week - 1 - Consistency of units

Objective

• Maintaining the unit consistency with varying unit systems.
• Finding the conversion factor for each different system.
• Assembling all systems to a table.

MASS 1kg

• 1000g

LENGTH 1m

• 1000mm

TIME 1s

• 1000ms

FORCE 1N

• F=mass*acceleration

=>1kg*1m/s²

=>(1000g*1000mm)/(1000ms)²

=>10^6/10^6 g mm/ms²

=>1 g mm/ms²

PRESSURE 1PA

• 1Pa =1N/1M²

=> (1kg*1m/s²⁾/1M²

=>((1000g*1000mm)/(1000ms)²)/(1000mm)²

=>(g*mm/ms²) *mm^-2)

=>1000g/ (1000)²ms²*1000mm

=>1*10^-6g/ms² mm

conversion factor is 10^-6

ENERGY 1Nm=1 Joule

• 1 Joule =1N*1M

1N =1 g mm/ms²{above derivation}

1Joule => (1000g*1000mm/(1000ms)²) *1000mm

=>10⁹g mm²/10⁶ms²

=>10⁹g mm² *10^-6 ms²

ANS =>10³ g mm²/ms²

Conversion factor=10³

DENSITY 1Kg/m3

=>1000g/(1000mm)³

=>g/(1000mm)²

Ans =>10^-6g /mm²

Conversion factor=10^-6

YOUNG'S Modulus 210GPa

1pa =>1*10^-6g/ms²mm mm {above derivation}

1 Giga =>1*10⁹

=> (1*10^-6) *(1*10⁹)

1Gpa =>1*10³g/ms² mm

210Gpa =>210*10³ g/ms²mm

Conversion factor=10^-3

Velocity 56.33KMPH

Velocity =Km/H

1Km =10⁶mm

1 hour => 60 minutes

1 Minute =>60 seconds

=>60*60 seconds=3600 seconds

1ms =3600*1000

=>36*10⁵

Km/H => (10⁶)/ (36*10⁵)

=0.277 Mm/ms

56.33Km/H =56.33*0.277

ANS =>15.60Mm/Ms

Conversion factor=1

GRAVITY 9.8m/s2

Gravity =M/s²

=>1000mm/(1000ms)²

=>1*10^-3mm/ms²

9.8mm/ms² =>9.8*10^-3mm/ms²

ANS =>9.8*10^-3mm/ms²

Conversion factor=1

THE CONVERSION FACTOR

Unit system=>Kg m s

• FORCE 1N=>1kg*1m/s2
• conversion factor =1

• STRESS 1Pa=>kg/m*s²
• conversion factor =1

• ENERGY 1Nm=>kg m²/s²
• conversion factor =1

• DENSITY 1Kg/m3=>Kg/m³
• conversion factor =1

• YOUNG'S Modulus 210GPa=>210e⁺⁹kg/m s²
• conversion factor =10⁹

• 33kmph=>15.64 m/s
• conversion factor =1

• m/s2=>9.8 m/s²
• conversion factor =1

Unit system=>kg cm ms

• FORCE=>1*10^-4kg cm/ms
• conversion factor=10^-4

• STRESS=>1*10^-8kg/cm*ms²
• conversion factor=10^-8

• ENERGY=>1*10^-3kg cm²/ms²
• conversion factor=10^-3
• DENSITY=>10-6 kg/cm3
• conversion factor =10-6

• YOUNG'S Modulus=>2100 kg/cm ms2
• conversion factor =10

• 33=>1.564cm/ms
• conversion factor =1
• GRAVITY 9.8=>9.8*10-4 cm/ms2
• conversion factor=10-4

• Unit system=> Kg cm s
• FORCE 1N=> 102 kg*cm/s2
• conversion factor =102

• STRESS 1Pa=> 10^-3kg/cm*s²
• conversion factor =10^-3

• ENERGY 1Nm=>10⁴kgcm²/s²
• conversion factor =10⁴

• DENSITY 1Kg/m3=>10^-6 kg/cm
• conversion factor =10^-6
• YOUNG'S Modulus 210GPa=>210e⁺⁷kg/cm s²
• conversion factor =10⁷

• 33=>1564 cm/s
• conversion factor =1

• Gravity =>9.8*10²cm/s²
• conversion factor =10²

Unit system=> gm mm ms

• FORCE => 1 gm*mm/ms²
• conversion factor =1

• STRESS => 1*10^-6g/ms²mm
• conversion factor =10^-6

• ENERGY =>10³g mm²/ms²
• conversion factor =10³

• DENSITY =>10^-6g /mm²
• conversion factor =10^-6

• YOUNG'S Modulus 210=>210*10³ g/ms²mm
• conversion factor =10³

• 33=>15.64mm/Ms
• conversion factor =1

• Gravity =>9.8*10^-3 mm/ms²
• conversion factor =10^-3

Unit system=> gm cm s

• FORCE => 10⁵g*cm/s²
• conversion factor =10⁵

• STRESS => 10 g/cm*s²
• conversion factor =10

• ENERGY =>10⁶g cm²/s²
• conversion factor =10⁶

• DENSITY =>10^-3g/cm³
• conversion factor =10^-3

• YOUNG'S Modulus 210=>2.1*10¹²g/cm s²
• conversion factor =10¹²

• 33=> 1564 cm/s
• conversion factor =1
• Gravity =>9.8*10²cm/s²
• conversion factor =10²

Unit system=> g cm us

• FORCE => 10^-7 g*cm/us²
• conversion factor =10^-7

• STRESS => 10^-11g/cm*us²
• conversion factor =10^-11

• ENERGY =>10^-5g cm²/us²
• conversion factor =10^-5

• DENSITY =>10^-3g/cm³
• conversion factor =10^-3

• YOUNG'S Modulus 210=>2.1 g/cm us²
• conversion factor =1

• 33=> 15.6*10^-4cm/us
• conversion factor =10^-4
• Gravity =>9.8*10^-10cm/us²
• conversion factor =10^-10

Unit system=> g mm s

• FORCE => 10⁶g*mm/s²
• conversion factor =10⁶

• STRESS => 1 g/mm*s²
• conversion factor =1

• ENERGY =>10⁹g mm²/s²
• conversion factor =10⁹

• DENSITY => 10^-6 g/mm³
• conversion factor =10^-6

• YOUNG'S Modulus 210=>2.1*10¹¹g/mm s²
• conversion factor =10¹¹

• 33=> 1564mm/s
• conversion factor =1
• Gravity =>9.8*10³mm/s²
• conversion factor =10³

Unit system=> ton mm s

• FORCE => 1 t/mm*s²
• conversion factor =1

• STRESS => 10^-6t/mm*s²
• conversion factor =10^-6

• ENERGY =>10³t *mm²/s
• conversion factor =10³

• DENSITY => 10^-12 t/mm³
• conversion factor =10^-12

• YOUNG'S Modulus 210=>210e⁺³t/mm s²
• conversion factor =10³

• 33=> 15647 mm/s
• conversion factor =1
• Gravity =>9.8*10³mm/s²
• conversion factor =10³

Unit system=> slug ft s

• FORCE => 0.2246 slug/ft*s²
• conversion factor =1

• STRESS => 0.0208 slug/s²ft
• conversion factor =1

• ENERGY =>0.7366 slug*ft²/s
• conversion factor =1

• DENSITY => 1.93*10^-3 slug/ft³
• conversion factor =10^-3

• YOUNG'S Modulus 210=>4.368e⁺⁹slug/ft s²
• conversion factor =10⁹

• 33=> 51.32 ft/s
• conversion factor =1
• Gravity =>32.144 ft/s²
• conversion factor =1

Unit system=> kg mm s

• FORCE => 10³ kg*mm/s²
• conversion factor =10³

• STRESS => 10^-3kg/mm*s²
• conversion factor =10^-3

• ENERGY => 10⁶ g mm²/s²
• conversion factor =10⁶

• DENSITY => 10^-9 kg/mm³
• conversion factor =10^-9

• YOUNG'S Modulus 210=>2.1*10⁸ kg/mm s²
• conversion factor =10⁸

• 33=> 1564mm/s
• conversion factor =1
• Gravity =>9.8*10³mm/s²
• conversion factor =10³

Unit system=> g cm ms

• FORCE => 1*10^-1g cm/ms²
• conversion factor =10^-1

• STRESS => 1*10^-5g/cm*ms²
• conversion factor =10^-5

• ENERGY => 10 g cm²/ms²
• conversion factor =10

• DENSITY => 10^-3 g/cm³
• conversion factor =10^-3

• YOUNG'S Modulus 210=> 2.1e⁺⁶g/cm ms²
• conversion factor =10⁶

• 33=> 1.56cm/ms
• conversion factor =1
• Gravity =>9.8*10^-4 cm/ms²
• conversion factor =10^-4

Unit system=> kg mm ms

• FORCE => 10^-3 kg*mm/ms²
• conversion factor =10^-3

• STRESS => 10^-9kg/mm*ms²
• conversion factor =10^-9

• ENERGY => 1 kg mm²/ms²
• conversion factor =1

• DENSITY => 10^-9 kg/mm³
• conversion factor =10^-9

• YOUNG'S Modulus 210=> 2.10e²kg/mm ms²
• conversion factor =10²

• 33=> 15.647 mm/ms
• conversion factor =1
• Gravity =>9.8*10 ^-3 mm/ms²
• conversion factor =10^-3

QUANTITIES	Mass (Kg)	LENGTH (m)	TIME (S)	FORCE (N)	STRESS (Pa)	ENERGY (Nm)	DENSITY (Kg/m^3)	YOUNG'S Modulus (GPA)	Velocity (m/s)	GRAVITY (m/s^2)
SYSTEMS	1	1	1	1	1	1	1	210	56.33	9.81
kg m s	1kg	1m	1s	1kg*1m/s^2	1pa=kg/m*s^2	1Nm=1Joule =kg m^2/s^2	Kg/m^3	210e^+9kg/m s^2	15.64 m/s	9.8 m/s^2
Kg cm ms	1 kg	10^2cm	10^3ms	1*10^-4kg cm/ms^2	1*10^8 kg/cm*ms^2	1*10^-3kg cm^2/ms^2	10^-6kg/cm^3	2100 kg/cm ms^2	1.564cm/ms	9.8*10^-4 cm/ms^2
Kg cm s	1kg	10^2cm	1s	10^2 kg*cm/s^2	1*10^-3 kg/cm*s^2	10^4kgcm^2/s^2	10^-6kg/cm^3	210^e+7kg/cm s^2	1564 cm/s	9.8*10^2cm/s^2
gm mm ms	10^3gm	10^3mm	10^3ms	1 gm*mm/ms^2	1*10^-6g/ms^2 mm	10^3g mm2/ms2	10 ^-6g /mm^2	210*10^3 g/ms^2mm	15.64mm/Ms	9.8*10^-3mm/ms^2
g cm s	10^3gm	10^2cm	1s	10^5g*cm/s^2	10 g/cm*s^2	10^6g cm^2/s^2	10^-3g/cm^3	2.1*10^12g/cm s^2	1564 cm/s	9.8*10^2cm/s^2
g cm us	10^3gm	10^2cm	10^6us	10^-7g*cm/us^2	10^-11g/cm*us^2	10^-5g cm^2/us^2	10^-3g/cm^3	2.1 g/cm us^2	15.6*10^-4 cm/us	9.8*10^-10 cm/us^2
g mm s	10^3gm	10^3mm	1s	10^6g*mm/s^2	1 g/mm*s^2	10^9g mm^2/s^2	10^-6 g/mm^3	2.1*10^11g/mm s^2	1564mm/s	9.8*10^3mm/s^2
ton mm s	10^-3 ton	10^3mm	1s	1 t/mm*s^2	10^-6 t/mm*s^2	10^3t *mm^2/s	10^-12t/mm^3	210^e^+3t/mm s^2	15647 mm/s	9.8*10^3mm/s^2
slug ft s	0.068 slug	3.28ft	1s	0.2246 slug/fts^2	0.0208 slug/s^2ft	0.7366 slug*ft^2/s	1.93*10-3 slug/ft^3	4.368e^+9slug/ft s^2	51.32 ft/s	32.144 ft/s^2
kg mm s	1kg	10^3mm	1s	10^3kg*mm/s^2	10^-3kg/mm*s^2	10^6g mm^2/s^2	10^-9kg/mm^3	2.1*10^8 kg/mm s^2	1564mm/s	9.8*10^ 3mm/s^2
g cm ms	10^3gm	10^2cm	10^3ms	1*10^-1g cm/ms^2	1*10^-5 g/cm*ms^2	10 g cm^2/ms^2	10^-3g/cm^3	2.1e^+6g/cm ms^2	1.56cm/ms	9.8*10^ -4cm/ms^2
kg mm ms	1kg	10^3mm	10^3ms	10^-3kg*mm/ms^2	10^-9kg/mm*ms^2	1 kg mm^2/ms^2	10^-9kg/mm^3	2.10^e2kg/mm ms^2	15.647 mm/ms	9.8*10 ^ -3 mm/ms^2

CONCLUSION

• Through this assignment we learn the various conversion method of one-unit system to another unit system
• Learn about conversion factor
• LS-DYNA doesn't have a default system of units.
• User needs a consistent system of units as per their choice. This warrants that to use LS-DYNA in different circumstances, users have to be conversant with converting quantities from one system of units to another.