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If the Reynold’s number is greater than 1000, then unstable turbulent flow occurs and Poiseulle’s Law is no longer valid.
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