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  1. Home/
  2. Prasanna Srinivasan/
  3. Week - 1 - Consistency of Units

Week - 1 - Consistency of Units

LS-Dyna Consistency of Units Aim: Value of the following measurements are given as follows: 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 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…

    • Prasanna Srinivasan

      updated on 24 Dec 2021

    LS-Dyna Consistency of Units

    Aim: Value of the following measurements are given as follows:

    • 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

    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 calculation 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. **

    Solution:

    • Fundamental Quantity: The Fundamental Quantity is independent Physical Quantity that is not possible to express in other Physical Quantity.
    • Derived Quantity: Derived quantities are quantities that are calculated from two or more measurements. Derived quantities cannot be measured directly. They can only be computed.
    • Below are the fundamental quantities that will be used in this task:
      • 1 kg = 1e3 g = 1e-3 tonne = 0.06852 slug
      • 1 m = 100 cm = 1e3 mm = 3.2808 ft
      • 1 s = 1e3 ms = 1e6 = µs

    Assuming the SI units for Length, Mass, and Time, we will proceed to convert kg/m/s system to g/mm/ms system.

    SI System (kg, m, s)

    (g, mm, ms) system

    MASS 1kg

    1000 g

    LENGTH 1m

    1000 mm

    TIME 1s

    1000 ms

    FORCE 1N

    1N = 1 kg m/s2
    = (1000 g * 1000 mm)/ (1000 ms)2
    = 1 g mm/ms2

    STRESS 1 Pa

    1Pa = 1 N/m2 = 1 kg/m s2
    = (1000 g) / (1000 mm * 1000 ms)2
    = 10-6 g/mm ms2

    ENERGY 1Nm

    1J = 1Nm = 1 kg m2/s2
    1 kg m2/s2 = [1000 g * (1000 mm)2]/ (1000 ms)2
    = 103 g mm2/ms2

    DENSITY 1kg/m3

    1 kg/m3
    = (1000 g)/ (1000 mm)3
    = 10-6 g/mm3

    YOUNG'S Modulus 210GPa

    210 GPa = 210e9 Pa = 210e9 kg/m s2
    = 210 x 103 g/mm ms2

    Velocity 56.33KMPH

    56.33 km/h = 15.647 m/s
    = 56.33 * [106 mm/ (3600*1000 ms)]
    = 15.647 mm/ms (Conversion Factor = 1)

    GRAVITY 9.8m/s2

    9.8 m/s2 = 9.8 * [1000 mm/ (1000 ms)2]
    = 9.8 x 10-3 mm/ms2

     

    Conversion Table

    Unit System

    Mass

    Length

    Time

    Force

    Stress

    Energy

    SI Unit (kg m s)

    1 kg

    1 m

    1 s

    1N = 1 kg m/s2

    1Pa = 1 N/m2 = 1 kg/m s2

    1J = 1Nm = 1 kg m2/s2

    kg cm ms

    1 kg

    102 cm

    103 ms

    10-4 kg cm/ms2

    10-8 kg/cm ms2

    10-2 kg cm2/ms2

    kg cm s

    1 kg

    102 cm

    1 s

    102 kg cm/s2

    10-2 kg/cm s2

    104 kg cm2/s2

    g mm ms

    103 g

    103 mm

    103 ms

    1 g mm/ms2

    10-6 g/mm ms2

    103 g mm2/ms2

    g cm s

    103 g

    102 cm

    1 s

    105 g cm/s2

    10 g/cm s2

    107 g cm2/s2

    g cm µs

    103 g

    102 cm

    106 µs

    10-7 g cm/µs2

    10-11 g/cm µs2

    10-5 g cm2/µs2

    g mm s

    103 g

    103 mm

    1 s

    106 g mm/s2

    1 g/mm s2

    109 g mm2/s2

    tonne mm s

    10-3 tonne

    103 mm

    1 s

    1 tonne mm/s2

    10-6 tonne/mm s2

    103 tonne mm2/s2

    slug ft s

    0.068 slug

    3.28 ft

    1 s

    0.2246 slug ft/s2

    0.0208 slug/ft s2

    0.7366 slug ft2/s2

    kg mm s

    1 kg

    103 mm

    1 s

    103 kg mm/s2

    10-3 kg/mm s2

    106 kg mm2/s2

    g cm ms

    103 g

    102 cm

    103 ms

    10-1 g cm/ms2

    10-5 g/cm ms2

    10 g cm2/ms2

    kg mm ms

    1 kg

    103 mm

    103 ms

    10-3 kg mm/ms2

    10-9 kg/mm ms2

    1 kg mm2/ms2

     

    Unit System

    Density

    Young's Modulus 210GPa

    Velocity = 56.33 km/h

    Gravity = 9.8 m/s2

    SI Unit ( kg m s)

    1 kg/m3

    210 Gpa = 210e9 kg/m s2

    56.33 km/h = 15.647 m/s

    9.8 m/s2

    kg cm ms

    10-6 kg/cm3

    2100 kg/cm ms2

    1.5647 cm/ms

    9.8 x 10-4 cm/ms2

    kg cm s

    10-6 kg/cm3

    210e7 kg/cm s2

    1564.7 cm/s

    9.8 x 102 cm/s2

    g mm ms

    10-6 g/mm3

    210e3 g/mm ms2

    15.647 mm/ms

    9.8 x 10-3 mm/ms2

    g cm s

    10-3 g/cm3

    210e10 g/cm s2

    1564.7 cm/s

    9.8 x 102 cm/s2

    g cm µs

    10-3 g/cm3

    2.10 g/cm µs2

    15.647 x 10-4 cm/µs

    9.8 x 10-10 cm/µs2

    g mm s

    10-6 g/mm3

    2.10e11 g/mm s2

    15647 mm/s

    9.8 x 103 mm/s2

    tonne mm s

    10-12 tonne/mm3

    210e3 tonne/mm s2

    15647 mm/s

    9.8 x 103 mm/s2

    slug ft s

    1.93 x 10-3 slug/ft3

    4.368e9 slug/ft s2

    51.322 ft/s

    32.144 ft/s2

    kg mm s

    10-9 kg/mm3

    210e6 kg/mm s2

    15647 mm/s

    9.8 x 103 mm/s2

    g cm ms

    10-3 g/cm3

    210e4 g/cm ms2

    1.5647 cm/ms

    9.8 x 10-4 cm/ms2

    kg mm ms

    10-9 kg/mm3

    210 kg/mm ms2

    15.647 mm/ms

    9.8 x 10-3 mm/ms2

     

    Note: Conversion factors are highlighted in Bold.

     

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