Dimensional analysis

What is a dimension?

Measurable extent of any kind

Rayleigh’s principle

In any equation which represents a physically real event, the dimensions of the various terms of the equation must be the same

What are the base dimensions?

Length, Mass, Time, Temperature

What are the base units?

Meters, Kilogrammes, Seconds, Kelvin

What are dimensionless numbers?

The ratio of one quantity to another

What does ‘similar’ mean?

Of the same substance or structure throughout

Geometric similarity

Similar shape

Kinematic similarity

Similar flow field

Dynamic similarity

Similar force distributions

Buckingham’s pi theory

Pi=n-r

where n is the dimensional variables

and r is the number of independent dimensions

and Pi is the number of non dimensional groups§

What is an example of a variable?

Density, viscosity, length etc