Week - 1 - Consistency of Units

AIM :-

The aim of this challenge is to convert the given SI unit values of given quantities to all different parameters  & also to prepare consistent unit system table for different unit system.

 

OBJECTIVE :-

The objective of this challenge is to convert the given values of the quantity to different system of units. And also prepare a table so that in near future while performing the various challenges of LS dyna it can be used frequently and without any issues. As LS Dyna don’t have any default system of units, so by preparing this table we can use it frequently to solve the challenges.

 

PROCEDURE :-

Each and every measurement given in the input parametres are converted into respective system of units. The input measurement values are displayed below,

1 Kg = 1000 gm = 0.001 ton = 0.068 slug

1 m = 1000 mm = 100 cm = 3.28 ft

1 s = 1000 ms = 106 us

 

The parameters to which different units to be assigned are:

• Mass = 1kg
• Length = 1m
• Time = 1s
• Force = 1N
• Stress = 1 Pa
• Energy = 1 Nm
• Density = 1 Kg/m3
• Young’s Modulus = 210 GPa
• Velocity = 56.33 kmph
• Gravity = 9.88 m/s2

The units in which the different parameters are to be converted are as follows:

• 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

                                                  1.Conversion of SI unit to kg cm ms                                                          

• Mass = 1 kg

1 kg

 

• Length = 1m

100 cm

 

• Time = 1 sec

1000 ms

 

• Force = 1 N

F => mass* acceleration

=> 1 kg * 1m/s^2

=> (1 kg*100cm)/(1000ms)2

=> 10-4 (kg*cm)/ms2

 Conversion factor = 10-4

 

• Stress = 1 Pa

1 Pa => 1N/m^2

As from the above derived 1N = 10-1 (kg cm)/ms2

=> {10-1 (kg cm/ms2)} / (100 cm2)

=> 10-3 kg/cm ms2

Conversion factor = 10-3

 

• Energy = 1 Nm
• 1N *1 m
• {10-4 kg cm/ms2} * 100 cm
• 10 kg cm2/ms2
• 10-2  kg cm2/ms2

      Conversion factor = 10-2

 

• Density = 1Kg/m^3
• 1 kg / (100 cm)3
• 1 kg/1000000 cm3
• 10-6 kg/cm3

      Conversion factor = 10-6

 

• Young’s Modulus = 210 GPa

1 Pa = 10-3 kg/cm*ms2

1 GPa = 109 * 10-3 kg/cm*ms2

210 GPa = 210 * 106 kg/cm*ms2

Conversion factor = 106

 

• Velocity = 56.33 Kmph

Km/h

1Km = 10000 cm = 104 cm

1 hr = 60min*60sec*1000 = 3600000= 36*105 ms

1 kmph

=> (104 )/(36*105)

=> 0.00277 cm/ms

56.33 kmph =

=> 56.33 * 0.00277 cm/ms

=> 0.1560 cm/ms

Conversion factor =0.00277

 

• Gravity = 9.88 m/s2

 1 m/s2 = 100 cm/(1000ms)2 = 10 -4 cm/ms2

 9.8 m/s2 = 9.8*10-4 cm/ms2

 Conversion Factor = 10-4