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Dimensional Analysis - PowerPoint PPT Presentation


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Dimensional Analysis. Units and Types. Units are meters, seconds, feet, tons, etc. Types of units are length, mass, force, volume, etc. The type of unit of a value is called the dimension. A value in square meters has dimensions of an area.

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units and types
Units and Types
  • Units are meters, seconds, feet, tons, etc.
  • Types of units are length, mass, force, volume, etc.
  • The type of unit of a value is called the dimension.
    • A value in square meters has dimensions of an area.
    • A value in kilometers per hour has dimensions of a velocity.
powers of units
Powers of Units
  • It is useful to convert the dimensions of units into fundamental dimensions.
    • Length (L)
    • Time (T)
    • Mass (M)
  • Units can be raised to a power, and so can the fundamental dimensions.
    • Area (L2)
    • Volume (L3)
    • Force (M L / T2)
dimensional expressions
Dimensional Expressions
  • The speed of waves in shallow water depends only on the acceleration of gravity g, with dimensions L/T2, and on the water depth h. Which of the following formulas for the wave speed v could be correct?

a)

b)

base quantities
Acceleration g

dimensions: L/T2

length/time2

example: m/s2

Base Quantities

Height h

  • dimensions: L
  • length
  • example cm

Speed v

  • dimensions: L/T
  • length/time
  • example km/h
checking a result
Terms do not match

Terms match, this could be a valid formula.

Checking a Result
limitations
Limitations
  • Dimensional analysis only checks the units.
  • Numeric factors have no units and can’t be tested.
        • is also valid.
        • is not valid.

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