Week - 1 - Consistency of Units

AIM:- Conversion of given mesurements into different unit systems and to find their corresponding conversions.

EXPLANATION:-

Value of the measurements are given as follows-

1. MASS 1 KG
2. LENGTH 1 MTR.
3. TIME 1 SEC.
4. FORCR 1N
5. STRESS 1PA.
6. ENERGY 1Nm
7. DENSITY 1 KG/M^3
8. YOUNG'S MODULUS 210 GPa
9. VELOCITY 56.33 KMPH
10. GRAVITY 9.8 MTR./S^2

Above mentioned value of measurements are converted into the given systems of Unit.

Kg cm ms

Kg cm s

gm mm ms

Kg m s

g cm s

g cm us

g mm s

ton mm s

slug ft s

Kg mm s

g cm ms

Kg mm ms

CONVERSIONS:-

Mass- 1KG = 1000 gm =0.001 Tonne= 0.0685218 Slug

Length- 1 Mtr.= 100 cm = 1000 mm= 3.28084 Ft.

Time- 1 Sec.= 1000 ms = 1000000 us

Force Unit Conversion:-

Force 1N = (1kg*m)/s^2

= (1000 gm* 1000mm) / (1000 ms*1000 ms)

= (1 gm*mm)/ ms^2

Stress Unit Conversion:-

Stress 1Pa= N/m^2

= {(1 gm*mm)/s^2} / (1000 ms*1000 ms)

= 10^-6 gm/mm*ms^2

Energy Unit Conversion:-

Energy 1Nm= {(1 Kg* m)/s^2} * (1000 mm)

=10^3 gm *mm ^2 / ms^2

Density Unit Conversion:-

Density 1Kg/m^3= 1000 gm / {10^3 ms}^3

= 10^3 gm/ 10^9 ms^3

Youngs Modulus Unit Conversion:-

Youngs Modulus is given as 210 GPa

210 GPa= 210 * {10^9*(N/m^2)}

= 210 * {10^9*(10^-6 gm/mm*ms^2)}

= 210 *10^3 gm/mm * ms^2

= 210000 gm/mm*ms^2

Velocity Unit Conversion:-

Velocity= 56.33 KMPH

1 KMPH = 10^6 mm / (3600*1000 ms) {1 KM = 10^6mm}

= 10/36 = 0.277 mm/ms {1 hr = 3600*1000 ms}

Therefore,

56.33 KMPH = 56.33*0.277

= 15.603 mm/ms

Gravity Unit Conversion:-

Gravity- 9.81 m/s^2

1 mtr. / s^2 = 1000 mm / (1000 ms x 1000 ms)

= 10^-3 mm / ms^2

9.81 m/s^2= 9.81* 10^3 mm/ms^2

Unit System	Mass	Length	Time	Force	Stress	Energy	Density	Youngs Moduls	Velocity	Gravity
Kg cm ms	1 Kg	100 cm	1000 ms	10^-4 Kg*cm/ms^2	10^8 Kg*cm/ms^2	10^-2 Kg*cm^2/ms^2	10^-6 Kg/cm^3	210 Kg/cm*ms^2	156.4*10^-2 cm/ms	9.81 * 10^-4 cm/ms^2
Kg cm s	1 Kg	100 cm	1 s	10^2 kg*cm/s^2	10^-2 kg/cm*s^2	10^4 kg*cm^2/s	10^-6 kg/cm^2	210*10^7 kg/cm*s^2	15647.22 cm/s	980 cm/s^2
gm mm ms	1000 gm	1000 mm	1000 ms	1 gm*mm/ms^2	10^-6 gm/mm*ms^2	10^3 gm*mm^2/ms^2	10^-6 gm/mm^3	210000 gm/mm*ms^2	15.64 mm/ms	9.81*10^-3 mm/ms^2
Kg m s	1 Kg	1 Mtrs.	1 s	1 kg*m/s^2	1 kg/m*s^2	1 kg*m^2/s^2	1 kg/m^3	210 *10^9 kg/m*s^2	15.647 m/s	9.81 m/s^2
gm cm s	1000 gm	100 cm	1 s	10^5 g*cm/s^2	10 gm/cm*s^2	10^7 gm*cm^2/s^2	10^-3 gm/cm	210*10^10 gm/ cm*s^2	1564.7 cm/s	981 cm/s^2
gm cm us	1000 gm	100 cm	10^6 us	10^-7 gm*cm/us^2	10^-11 gm/cm*us^2	10^-5 gm*cm^2/us^2	10^-3 gm/cm	2.10 gm/cm*us^2	15.647*10^-4 cm/us^2	9.81 10^-10 cm/us^2
gm mm s	1000 gm	1000 mm	1 s	10^6 g*mm/s^2	1 gm/mm*s^2	10^9 g*mm^2/s^2	10^-6 gm/mm^3	2.10*10^11 gm/mm*s^2	15647 mm/s	9.81*10^3 m/s^2
ton mm s	0.001 ton	1000 mm	1 s	1 ton*mm/s^2	10^-6 ton/mm*s^2	10^3 ton*mm^2/s^2	10^-12 ton/mm^3	210^-12 ton/mm*s^2	15647 mm/s	9.81*10^3 mm/s^2
slug ft s	0.068 slug	3.28 Ft	1 s	0.2246 slug*ft/s^2	0.0208 slug/ft*s^2	0.736 slug*ft^2/s^2	1.93*10^-3 slug/ ft^3	4.368 *10^9 slug/ ft*s^2	51.322 ft/s	32.144 ft/s^2
Kg mm s	1 Kg	1000mm	1 s	1000 kg*mm/s^2	10^-3 kg/mm*s^2	10^6 Kg*mm^2/s^2	10^-9 kg/mm^3	210*10^6 kg/mm*s^2	15647 mm/s	9.81*10^3 mm/s^2
g cm ms	1000 gm	100 cm	1000 ms	0.1 gm*cm/ms^2	10^-5 gm/cm*ms^2	10 gm* cm^2/ms^2	10^-3 g/cm^3	210*10^4 gm/ cm*ms^2	1.5647 cm/ms	9.81*10^-4 cm/ms^2
Kg mm ms	1 Kg	1000 mm	1000 ms	10^-3 kg*mm/ms^2	10^-9 kg/ mm*ms^2	1 kg*mm^2/md^2	10^-9 kg/mm^3	210 kg/ mm*ms^2	15.647 mm/ms	9.81*10^3 mm/ms^2

CONCLUSION:-

Thus the given input measurements are converted into respective unit systems and this used in LS Dyna calculation.