11.5 Derive Hagen-Poiseuille equation for a steady viscous flow in a horizontal pipe with a diameter of ro. The fluid is incompressible with a constant viscosity. Assume one dimensional flow and constant pressure gradient Hint: start with the continuity equation and the Navier-Stokes equation in the cylindrical coordinates, which is:

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11.5 Derive Hagen-Poiseuille equation for a
steady viscous flow in a horizontal pipe with a
diameter of ro. The fluid is incompressible with
a constant viscosity. Assume one dimensional
flow and constant pressure gradient
Hint: start with the continuity equation and the
Navier-Stokes equation in the cylindrical
coordinates, which is:
And
1 dp
μ dz
=
²uz 1 duz
r ər
+
ər²
²0
20²
+
1 0² uz
r² 00²
Y
0
O
X
Z
Transcribed Image Text:11.5 Derive Hagen-Poiseuille equation for a steady viscous flow in a horizontal pipe with a diameter of ro. The fluid is incompressible with a constant viscosity. Assume one dimensional flow and constant pressure gradient Hint: start with the continuity equation and the Navier-Stokes equation in the cylindrical coordinates, which is: And 1 dp μ dz = ²uz 1 duz r ər + ər² ²0 20² + 1 0² uz r² 00² Y 0 O X Z
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