Finding the Dimensionless Numbers

Suppose that our problem concerns a complicated fluid flow system in which we suspect that Bernoulli s equation, along with other equations, would apply. Then we can write Bernoulli s equation in differential form (without pump or compressor work) and integrate to find 

Let us assume that the term is. of the form given by the Poiseuille equation 

Each term in Eq. 13,1 has the same dimensions therefore, if we divide through by any one of them, the result. will be a dimensionless equation. 

The first term on the left is important enough to be given a name in fluid mechanics, the pressure coefficient it is also sometimes called 1/(Euler num-ber)l It appears in problems in which there are significant changes in velocity and pressure between different parts of the system. For example, Eq. 6.53 may 

SO this pressure coefficient is equivalent to the drag coefficient previously discussed. 

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Another systematic approach to finding the dimensionless numbers is the method of Buckingham [6], often referred to as the tt theorem or Buckingham s 7T theorem. It states that if there is some relationship where A (the... 

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