Introduction to Fluid Mechanics

Dimensional Analysis and Scaling

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Nature does not know about man-made measurements, such as metres, seconds, and kilograms. For a natural description of a flow, we need to remove these man-made measurements. This is the basis of the Buckingham Pi law.

A mathematician would write the dimensional Navier-Stokes equation in dimensionless form, by defining the smallest possible number of reference scales at the start of the problem and then writing every term in the equation in terms of these reference scales. Non-dimensional numbers naturally drop out of this process.

The engineer's approach to dimensional analysis is firmly rooted in the philosopher's approach and the mathematician's approach. This clip shows a systematic way to determine the dimensionless numbers in a problem.

This clip shows examples of dimensional analysis applied to the total pressure drop across an orifice plate, the drag on an aeroplane, and the drag on a ship.

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