ABSTRACT
Hagen-Poiseuille flow For a steady, incompressible fully developed flow in a straight pipe or duct section, the influx and outflux of momentum are equal. Thus, the flow is in equilibrium under the action of static pressure, gravity, and viscous stresses. For a Newtonian fluid and when the flow is laminar, the viscous stress is proportional to the velocity gradient du
dy . One
can, thus, use the equilibrium of forces to relate the velocity gradient to the pressure drop in the direction of the flow. For a circular pipe with radius ro, this relationship is given by:
−μdu dr
= − r 2
d
dx (p + ρgh) .
