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 difference across the pipe to maintain flow rate

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 difference across the pipe to maintain flow rate.

Suppose that fluid of viscosity ##eta##, flows at a flow rate Q (where Q = volume of 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 If the Reynold's number is greater than 1000, then unstable turbulent flow occurs and Poiseulle's Law is no longer valid.