Week - 1 - Consistency of Units

AIM:- Consistency of Units

OBJECTIVE:- Different industries use different systems of units as per their convenience.

 The units for the basic measurement quantities, mass distance, and time - dictate how the other derived quantities will be expressed.

For example, automotive industries use kg, mm, and ms as their standard unit system.

Construction industries are likely to use tonne,m,s as their unit system. Similarly, PCB simulation in the electronic industry uses gm, micrometer, and ms as their system of units.

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 have to be conversant with converting quantities from one system of units to another.

Here's an example: Young's Modulus of steel is 210GPa which is input as 210e+9 in LS-DYNA as per SI unit system.

 However, if you use the kg/mm/ms unit system, the input quantity will be 210. Thus the conversion factor is 10^-9.

But, how?

That's for you to find out in this assignment.

The values of the following measurements are given as follows:

MASS 1kg

LENGTH 1m
TIME 1

FORCE 1N
STRESS 1Pa
ENERGY 1Nm
DENSITY 1Kg/m3
YOUNG'S Modulus  210GPa
Velocity 56.33KMPH
GRAVITY 9.8m/s2

Now, here are a few systems of units:

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

Write the given measurements in the above different system of units. Also, mention the conversion factors.

**The assignment should show detailed calculations for conversion from SI unit to gm/mm/ms unit system.

For others, only the answers in the form of a table are sufficient with the unit systems as rows and measured quantities as columns.**

Write your report here calculations written down on a piece of paper and uploaded as an Image will not be accepted.

All the answers should be in the form of a report. Only then it will be considered for Grading.

 Write a detailed report on unit conversion with calculations and their units.

1) Convert Kg cm ms

MASS 1kg = 1000gms.

LENGTH 1m = 100cm.

TIME 1s = 1000ms

FORCE = Force is an external agent capable of changing the state of rest or motion of a particular body. It has a magnitude and a direction.

unit = kg·m/s²

STRESS = It is defined as internal resistance offered by the body or force per unit area.

unit = N/m^2.

EXPLANATION 0F UNITS

• Units are the most basic aspects of any measurement.
• they are arbitrarily chosen and internationally accepted.

Categories of units

1. Fundamental units

• Some units are arbitrarily chosen to be fundamental.
• They become the foundation for the system.
• Every other unit is derivable from them.

1. Derived units

• Units derived from the fundamental units by multiplication and division are called derived units.

Example   LENGTH=SPEED*TIME

In this length is a derived unit

At different points in time, different systems of measurement were pervasive

1. CGS SYSTEM

• Centimeter for length
• gram for mass
• second for time

2. FPS SYSTEM

• Foot for length
• pound for mass
• second for time

3. MKS SYSTEM

• Meter for length
• kilogram for mass
• second for time

EXAMPLE FOR CGS, MKS, FPS SYSTEMS

FORCE=MASS*ACCERLATION

SI UNIT-NEWTON

• F=M*a          m=1kg  a=1m/sec^2

      =1kg*1m/s^2

        1N=1kg.m/s^2

CGS

1DYNE=1gm * 1cm/s^2

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

   =1000gm * 100 cm/s^2

    =10^5 gm cm/s^2

     1N   =10^5 dyne

MKS

1KGF=1kg * 9.81 kg.m/s^2

1kgf=9.81N

FPS

1LBF=1lb * 32.17 ft/s^2

g=9.81m/s^2

1m=3.28 ft

1N=9.81  *  3.28 ft/s^2

    =32.17 ft/s^2

Calculation for conversion from SI unit to gm/mm/ms unit

MASS 1 Kg = 1000 gm

LENGTH 1 m = 1000 mm

TIME 1 s = 1000 ms

1. FORCE 

• 1N = (1Kg * m)/s^2 

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

      = (1 gm * mm ) / ms^2

       Conversion factor=1

2. STRESS

• 1Pa  = N / m^2  =1 kg / m · s².

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

    =   10^-6 gm /mm*ms^2

        Conversion factor=10^-6

3. ENERGY

• 1Nm  = { (1Kg * m^2)/s^2 } 

      =1000gm*1000mm*1000mm/1000ms*1000ms

       = 10^3 gm*mm^2/ms^2

        Conversion factor=10^3

4. DENSITY

• 1Kg/m3  = 1000 gm /1000mm*1000mm*1000mm                                      

      = 10^3 gm/ 10^9 ms^3

        = 10^-6gm/ms^3

           Conversion factor=10^-6

5. YOUNG’S Modulus 

•  210GPa = 210 X  [10^9 X (N / m^2)]                  (1 GPa   = 10^9 X (N / m^2)

       = 210 X [10^9 X (10^-6 gm /mm*ms^2)]

       = 210 X 10^3 gm/mm*ms^2

       = 210000 gm/mm*ms^2

          Conversion factor=10^3

6. Velocity

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

      = 10/36 = 0.277 mm/ms                                                     ( 1hr = 3600 *1000 ms)

       = 56.33KMPH  = 56.33 x 0.277

        = 56.33KMPH   = 15.64 mm/ms

          Conversion factor=1

7. GRAVITY 9.8m/s

•  1 m/s2  = 1000 mm/(1000 ms X 1000 ms)

       = 10^-3 mm/ms^2

          9.8m/s2  = 9.8 X 10^-3 mm/ms^2

        Conversion factor=10^-3