Consistency of Units

AIM: Convert the given measurements into different system of units and finding their corresponding conversation factors

OBJECTIVE:

• CALCULATE THE CONVERSION FROM SI UNITS TO gm/mm/ms unit system
• REST OF THE VALUES PLOT ON THE TABLE FROM SI UNIT TO REQUIRED UNIT VALUES

MEASUREMENTS GIVEN:

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

SYSTEM OF UNITS:

Kg cm ms

Kg cm s

gm mm ms

kg m s

g cm s

g cm `mu`s

g mm s

ton mm s

slug ft s

kg mm s

g cm ms

kg mm ms

why for conververtion/ Needed for conversion:

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.

CONVERSIONS AND CONVERSION FACTORS:

from SI unit to (gm/mm/ms) unit system

CONVERSION FOR MASS:

MASS: 1kg`=`1000gm

CONVERSION FACTOR `=``10^3`

LENGTH: 1m`=`100mm

CONVERSION FACTOR `=``10^3`

TIME: 1s`=`1000ms

CONVERSION FACTOR `=``10^3`

FORCE: 1N

`=`1kg`*`1m/`s^2`

`=`1000g`*`1000mm/`(1000ms)^2`

`=``10^6*10^-6(g*mm )``/ms^2`

`=`1`(g*mm)`/`ms^2`

CONVERSION FACTOR `=`1

STRESS: 1Pa

`=`1N/`m^2``={`1kg`*`(1m/`s^2`)}/`m^2``=`1kg/`(m*s^2)`

`=`1000g/{1000mm`*``(1000ms)^2`}

`=``10^-6`g/(`mm*ms^2`)

CONVERSION FACTOR `=``10^-6`

ENERGY: 1Nm

`=`1kg`*`1m/`s^2``*m`

`=`{`1000g*(100mm)^2`}/`(1000ms)^2`

`=``(10^9 g*mm^2)`/`(10^6 ms^2)`

`=``10^3``(g*mm^2`/`ms^2)`

CONVERSION FACTOR `=``10^3`

DENSITY: kg/`m^3`

`=`1000g/(1000mm)`^3`

`=``10^-6`g/mm`^3`

CONVERSION FACTOR `=``10^-6`

YOUNGS MODULUS: 210GPa

`=``210e^+9`kg/`(m*s^2)`

`=``210e^+9``*10-6g`/`(mm*ms^2)`

`=``210e^+3`g/`(mm*ms^2)`

`=`210`*10^3`g/`(mm*ms^2)`

CONVERSION FACTOR `=``10^3`

VELOCITY:56.33Kmph

`=`56.33`*`{`10^6 mm`/(3600`*`1000ms)

`=`15.647 mm/ms

CONVERSION FACTOR `=`5/18

GRAVITY: 9.8m/`s^2`

`=`9.8`*`1000mm/(1000ms`)^2`

`=`9.8`*`10`^-3`mm/m`s^2`

CONVERSION FACTOR `=``10^-3`

TABLE UNIT SYSTEMS AND MEASURED QUANTITIES:

SI UNIT	MASS	LENGTH	TIME	FORCE	STRESS	ENERGY	DENSITY	YOUNGS MODULUS	VELOCITY	GRAVITY
Kg cm ms	1kg	`10^2`cm	`10^3`ms	`10^-4`kg`*`cm/`ms^2`	`10^-8kg`/cm`*ms^2`	`10^-2kg*cm`/`ms^2`	`10^-6kg`/`cm^3`	2100kg/cm`*ms^2`	1.5647cm/ms	9.8`*10^-4cm`/`ms^2`
Kg cm s	1kg	`10^2`cm	1s	100kg`*cm`/`s^2`	`10^-2kg`/cm`*s^2`	`10^4kg*cm^2`/`s^2`	`10^-6kg`/`cm^3`	210`*10^7kg`/`cm*s^2`	1564.72cm/s	9.8`*10^2cm`/`s^2`
gm mm ms	`10^3`g	`10^3`mm	`10^3`ms	1g`*mm`/`ms^2`	`10^-6`g/mm`*``ms^2`	`10^3g``*mm^2`/`ms^2`	`10^-6g`/`mm^3`	210`*10^3g`/`mm*ms^2`	15.647mm/ms	9.8`*10^-3mm`/`ms^2`
kg m s	1kg	1m	1s	1kg`*m`/`s^2`	1kg/`m*s^2`	1kg`*m^2`/`s^2`	1kg/`m^3`	210`*10^9kg`/`m*s^2`	15.647m/s	9.8m/`s^2`
g cm s	`10^3`g	`10^2`cm	1s	`10^5`g`*cm`/`s^2`	10g/cm`*s^2`	`10^7g*cm^2`/`s^2`	`10^-3g`/cm^3`	210`*10^10g`/`cm*s^2`	1564.72cm/s	9.8`*10^2cm`/`s^2`
g cm `mu`s	`10^3`g	`10^2`cm	`10^6mus`	`10^-7`g``*cm`/`mus^2`	`10^-11`g/`cm*mus^2`	`10^-5g*cm^2`/`s^2`	`10^-3g`/cm^3`	2.10g/`cm*mus^2`	15.647`*10^-4cm`/`mus`	9.8`*10^-10cm`/`mus^2`
g mm s	`10^3`g	1`0^3`mm	1s	`10^6g```*mm`/`s^2`	1g/`mm*s^2`	`10^9g*mm^2`/`s^2`	`10^-6g`/`mm^3`	210`*10^9g`/`mm*s^2`	15647.2mm/s	9.8`*10^3mm`/`s^2`
ton mm s	1`0^-4`tonne	1`0^3`mm`	1s	`10^-1``tonne`*mm`/`s^2`	`10^-7`tonne/`mm*s^2`	`10^2`tonne`*mm^2`/`s^2`	`10^-13`tonne/`mm^3`	210`*10^2`tonne/`mm*s^2`	15647.2mm/s	9.8`*10^3mm`/`s^2`
slug ft s	0.068slug	3.28ft	1s	.223slug`*`ft/`s^2`	0.0207slug/ft`*s^2`	0.7314slug`*ft^2`/`s^2`	`19*10^-4slug`/`ft^3`	4.347`*10^9slug`/`ft*s^2`	51.34ft/s	32.14ft/`s^2`
kg mm s	1kg	1`0^3`mm`	1s	`10^3kg``*mm`/`s^2`	`10^-3kg`/`mm*s^2`	`10^6kg*mm^2`/`s^2`	`10^-9kg`/`mm^3`	210`*10^6g`/`mm*s^2`	15647.2mm/s	9.8`*10^3mm`/`s^2`
g cm ms	`10^3`g	`10^2`cm	`10^3`ms	`10^-1g*cm`/`ms^2`	`10^-5g`/`cm*s^2`	10g`*cm^2`/m`s^2`	`10^-3g`/`cm^3`	210`*10^4g`/`cm*ms^2`	1.5647cm/ms	9.8`*10^-4cm`/`ms^2`
kg mm ms	1kg	1`0^3`mm`	`10^3`ms	`10^-3kg*mm`/`ms^2`	`10^-9kg`/`mm*ms^2`	1kg`*mm^2`/m`s^2`	`10^-9kg`/`mm^3`	210kg/`mm*ms^2`	15.647mm/ms	9.8`*10^-3mm`/`ms^2`

CONCLUSION:

The given challege of Conversion of SI units to required units has been done and plotted on the table.

The derived conversion for gm/mm/ms also done