Understanding Poiseuille Equation

[fog37]

Hello Forum,

The important Poiseuille equation tells us that there must be a pressure difference in an incompressible AND viscous Newtonian fluid in laminar flow flowing through a cylindrical pipe of constant cross section and radius R and length L. Viscosity hinders fluid motion.

But even in the case of a perfect fluid (zero viscosity) a pressure difference between the two ends of the tube is needed to set the fluid into motion. But the Poiseuille equation seems to tell us that no pressure is needed to maintain an inviscid fluid into motion...I am confused..

thanks,
fog37

 

[boneh3ad]

The Poiseuille equation has nothing to do with inviscid flow. You can't draw any conclusions about the inviscid case from that equation. And yes, a pressure difference would be required to start an inviscid pipe flow in motion, but not to maintain that motion. If you had a constant pressure difference in that case, then you would have a constantly accelerating flow. With no pressure difference, an inviscid flow just maintains a constant velocity.

When viscousity is included, you need a pressure difference to overcome the resistance of viscosity, thus the Poiseuille equation.