Question

Poiseuille's law is about factors that control the flow rate of fluid through pipe. Explain all the factors involved?

Answer 1

The length and radius of the pipe, as well as the viscosity of the fluid and the flow rate of the fluid all play a role in the required pressure difference across the pipe to maintain flow rate.

Explanation:

Suppose that fluid of viscosity `eta`, flows at a flow rate Q (where Q = volume of fluid flow per second), through a pipe of length L and cross-sectional radius R. Then the pressure difference `DeltaP` required across the ends of the pipe to maintain this flow rate may be given by Pouseuille's Law as flows :

`DeltaP=(8QetaL)/(piR^4)`

Important note:
This Law only holds for laminar flow, ie. flow in which the Reynolds number is less than 1000, ie
`R_e=(vrhod)/eta<1000`,
where `rho` is the density of the fluid flowing, v is the velocity of fluid flow (critical velocity) and d is the diameter of the pipe.
If the Reynold's number is greater than 1000, then unstable turbulent flow occurs and Poiseulle's Law is no longer valid.