Week - 1 - Consistency of units

CONSISTENCY OF UNITS

OBJECTIVES :

To convert the SI unit system measurement quantities to given unit systems.

CONVERSION TABLES :

UNIT SYSTEM	MASS 1kg	LENGTH 1m	TIME 1s	FORCE 1N	STRESS 1Pa	ENERGY 1N m
kg m s	1 kg	1m	1s	1 kg.m/s^2	1kg*m/s^2/m^2 =1 kg/m*s^2	1kg*m^2/s^2
kg cm ms	1kg	100 cm	1000ms	1kg.100cm/ (1000ms)^2 =0.0001 or 10^-4 kg*cm/ms^2	1kg/(100cmx (1000ms)^2) = 0.00000001 or 10^-8 kg/cm*ms^2	1kgx(100cm)^2 / (1000ms)^2 = 10^-2 kg*cm^2/ms^2
kg cm s	1 kg	100 cm	1s	1kgx100cm/ 1s =10^2 kg*cm/s	1kg/100cmx1s = 10^-2 kg/cm*s^2	1kg(100cm)^2 /s^2 = 10^4 kg*cm^2/s^2
gm mm s	1000g	1000mm	1s	1000gx1000mm /s^2 = 10^6 g*mm/s^2	1000g/ (1000mmxs^2) = 1 g/mm*s^2	1000gx(1000mm)^2 /s^2 = 10^9 g*mm/s^2
g cm s	1000g	100	1s	1000gx100cm /s^2 =10^5 g*cm/s^2	1000g/ (100cmxs^2) =10g/cm.s^2	1000gx100cm^2/s^2 =10^7g*cm^2/s^2
g mm us	1000g	1000mm	10^-6us	1000gx1000mm /10^-6us = 1 gm*mm/us	1000g/(1000mmx (10^-6us)^2 = 10^12 g/mm*us^2	1000gx(1000mm)^2 /(10^-6 ms)^2 = 10^20g*mm^2/us^2
ton mm s	.001 ton	1000mm	1s	.001x1000mm /s^2 = 1 ton*mm/s	.001ton/ 1000mmxs^2 = 10^-6 ton/mm*s^2	0.001tonx(1000mm)^2 /s^2 = 10^3 ton*mm^2/s^2
slug ft s	.068 slug	3.28ft	1s	.068slugx3.28ft /s^2 = 0.223 slug*ft/s^2	0.068slug/ (3.28ftxs^2) = 0.02 slug/ft*s^2	.068slugx(3.28ft^2)/ s^2 = 0.731 slug*ft^2/s^2
kg mm s	1kg	1000mm	1s	(1kgx1000mm)/ s^2 = 10^3 kg*mm/s^2	1kg/ (1000mmxs^2) = 10^3kg/mm*s^2	1kgx(1000mm)^2/s^2 = 10^6kg/mm^2/s^2
g cm ms	1000	100	1000ms	(1000gx100cm)/ (1000ms)^2 = 10^-1 g*cm/ms^2	1000g/(100cmx (1000ms)^2) = 10^-5 g/cm*ms^2	(1000gx(100cm)^2)/ (1000ms)^2 = 10 g*cm/ms^2
kg mm ms	1kg	1000mm	1000ms	(1kgx1000mm)/ (1000ms)^2 = 10^-3 kg*mm/s^2	1kg/ (1000mmx (1000ms)^2) = 10^-9 kg/mm*ms^2	(1kgx(1000mm)^2)/ (1000ms)^2 = 1 kg*mm^2/ms^2

UNIT SYSTEM	DENSITY 1Kg/m3	YOUNG'S Modulus 210GPa	Velocity 56.33KMPH	GRAVITY 9.8m/s2
kg m s	1 kg/m^3	210x10^9 N/m^2 =210x10^9 kg/m*s^2	56.33x0.277 =15.6 m/s	9.8 m/s^2
kg cm ms	1kg/(100cm)^3 =0.000001 or 10^-6 kg/cm^3	210x10^9kg/ (100cm x (1000ms)^2) = 210 x10^1 kg/cm*ms^2	(15.6x100cm)/ 1000ms = 15.6x10^-1 cm/ms	9.8(100cm)/ (1000ms^2) =9.8x10^-4 cm/ms^2
kg cm s	1kg/(100cm)^3 =0.000001 or 10^-6 kg/cm^3	210x10^9/ 100 cmx s^2 = 210x10^7 kg/m*s^2	(15.6x100cm)/s = 15.6 x10^3 cm/s	9.8(100cm)/ (s^2) = 9.8x10^2 cm/s^2
gm mm s	1000g/(1000mm)^3 =10^-6 g/mm^3	(210x10^9x1000g) /1000mmxs^2 = 210x10^9 g/mm*s^2	(15.6x1000mm)/s =15.6x10^4 mm/s	(9.8x1000mm)/s^2 = 9.8x10^3mm/s^2
g cm s	1000g/(100cm)^3 =10^-3 g/cm^3	(210x10^9x1000g)/ 100cmxs^2= 210x10^10 g/cm*s^2	(1.56x100cm)/s =15.6x10^2 cm/s	(9.8x100cm)/s^2 = 9.8x10^2 cm/s^2
g mm us	1000g/(1000mm)^3 =10^-6 g/mm^3	210x10^9x1000g /(10^-6us)^2=210x10^21 g/m*us^2	(15.6x1000mm)/ 10^-6 us = 15.6x10^9mm/us	(9.8x1000mm) /(10^-6us)^2 = 9.8x10^15mm/s^2
ton mm s	.001/(1000mm)^2 =10^-12 ton/mm^3	210x10^9x10^-3 ton/(1000mmxs^2) = 210x10^3 ton/mm*s^2	(15.6x1000mm)/s =15.6x10^3mm/s	(9.8x1000mm)/s^2 =9.8x10^3 mm/s^2
slug ft s	.068slug/(3.28ft)^3 = 1.92x10^-3 slug/ft^3	(210x10^9x0.068slug)/(3.28ftxs^2) =4.35x10^9 slug/ft*s^2	(15.6x3.28ft)/s = 51.168 ft/s	(9.8x3.28)/s^2 = 32.144 ft/s^2
kg mm s	1kg/(1000mm)^3 = 10^-9 kg/mm^3	(210x10^9kg)/(1000mmxs^2) = 210x10^6 kg/mm*s^2	(15.6x1000mm)/s =15.6x10^3mm/s	(9.8x1000mm)/s^2 =9.8x10^3 mm/s^2
g cm ms	1000g/(100cm^3) = 10^-3 g/cm^3	(210x10^9x1000g) / (100cmx (1000ms)^2)=210x10^4 g/cm*ms^2	(15.6x100cm)/ 1000ms = 15.6x10^-1 cm/ms	9.8(100cm)/ (1000ms^2) =9.8x10^-4 cm/ms^2
kg mm ms	1kg/(1000mm)^3 = 10^-9 kg/mm^3	210x10^9kg/(1000mmx(1000ms)^2) = 210 kg/mm*ms^2	(15.6x1000mm)/ 1000ms=15.6mm/ms	(9.8x1000mm)/ (1000ms)^2 = 9.8x10^-3 mm/ms^2

SI UNIT TO gm mm ms :

MEASUREMENT VALUES IN SI	IN gm mm ms
Mass = 1kg	1000 gm
Length = 1m	1000 mm
TIME 1s	1000 ms
FORCE 1N	= (kg*m)/s^2 = (1000gx1000mm)/(1000ms)^2 = 1 g*mm/ms
STRESS 1Pa	= kg/(m*s^2) = (1000g)/(1000mmx(1000ms)^2) = 10^-6 g/mm*ms^2
ENERGY 1N m	= (kgxm^2)/s^2 = (1000gx(1000mm)^2)/(1000ms)^2 = 10^3 g*mm^2/ms^2
DENSITY 1Kg/m3	= (kg/m^3) = (1000g)/(1000mm)^3 = 10^-6 g/mm^3
YOUNG'S Modulus 210GPa =210x10^9 N/m^2	= 210x10^9 kg/(m*s^2) = (210x10^9x1000g)/(1000mmx(1000ms)^2) = 210x10^3 g/mm*ms^2
Velocity 56.33 KMPH	= 56.33x(1000/3600) = 15.6 m/s = (15.6x1000mm)/1000ms =15.6 mm/ms
GRAVITY 9.8 m/s2	=(9.8x1000mm)/(1000ms)^2 = 9.8x10^-3 mm/ms^2

Unit Conversion factor :

FORCE 1 N

Kg cm ms - 10^-4

Kg cm s - 10^2

gm mm ms - 10^0

kg m s (SI) - 10^0

g cm s - 10^5

g cm us - 10^0

g mm s - 10^6

ton mm s - 10^0

slug ft s - 0.223

kg mm s - 10^3

g cm ms - 10^-1

kg mm ms - 10^-3

STRESS 1 Pa

Kg cm ms - 10^-8

Kg cm s - 10^-2

gm mm ms - 10^-6

kg m s (SI) - 10^0

g cm s - 10^1

g cm us - 10^12

g mm s - 10^0

ton mm s - 10^-6

slug ft s - 0.2

kg mm s - 10^3

g cm ms - 10^-5

kg mm ms - 10^-9

ENERGY 1Nm

Kg cm ms - 10^-2

Kg cm s - 10^4

gm mm ms - 10^3

kg m s (SI) - 10^0

g cm s - 10^7

g cm us - 10^20

g mm s - 10^9

ton mm s - 10^3

slug ft s - 0.731

kg mm s - 10^6

g cm ms - 10^1

kg mm ms - 10^0

DENSITY 1kg/m^3

Kg cm ms - 10^-6

Kg cm s - 10^-6

gm mm ms - 10^-6

kg m s (SI) - 10^0

g cm s - 10^-3

g cm us - 10^-6

g mm s - 10^-6

ton mm s - 10^-12

slug ft s - 1.92x10^-3

kg mm s - 10^-9

g cm ms - 10^-3

kg mm ms - 10^-9

YOUNG'S MODULUS 210GPa

Kg cm ms - 10^1

Kg cm s - 10^7

gm mm ms - 10^3

kg m s (SI) - 10^0

g cm s - 10^10

g cm us - 10^21

g mm s - 10^9

ton mm s - 10^3

slug ft s - 4.35x10^9

kg mm s - 10^6

g cm ms - 10^4

kg mm ms - 10^0

VELOCITY 56.33kmph

Kg cm ms - 10^-1

Kg cm s - 10^3

gm mm ms - 10^0

kg m s (SI) - 10^0

g cm s - 10^2

g cm us - 10^9

g mm s - 10^4

ton mm s - 10^3

slug ft s - 51.168

kg mm s - 10^3

g cm ms - 10^-1

kg mm ms - 10^0

GRAVITY 9.8m/s^2

Kg cm ms - 10^-4

Kg cm s - 10^2

gm mm ms - 10^-3

kg m s (SI) - 10^0

g cm s - 10^2

g cm us - 10^15

g mm s - 10^3

ton mm s - 10^3

slug ft s - 32.144

kg mm s - 10^3

g cm ms - 10^-4

kg mm ms - 10^-3

Conclusion :

1. The measurement values in SI unit system is converted to specified unit systems.

2. Detailed calculation of SI unit to gm mm ms is reported.

3. Unit conversion factors are specified for each parameters.