The flow of a fluid through a pipe is governed by the Hagen-Poiseuille equation:

Question

The flow of a fluid through a pipe is governed by the Hagen-Poiseuille equation: 

P = ZQ

where P represents a change in pressure and has the dimensions [P]=M/LT2, Q represents the volume flow and has dimensions [Q]=L3/T, and Z is the resistance of the pipe. 

We know that the resistance Z depends on only the following dimensioned parameters: 
the length of the pipe, (dimensions []=L),the radius of the pipe, R (dimensions [R]=L), andthe viscosity of the fluid, (dimensions []=M/LT).If we also know that Z is directly proportional to , how does Z depend on R?

Explanation / Answer

You can find it easily just by equating dimensions of the given equation i.e. P = ZQ.

Hence dimensions of Z becomes M/TL4.

Hence Z depends on R as R^-4.

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