Fluid Mechanics seventh edition by Frank M. White · Problem P3.26

Integral Relations for a Control Volume — Frank M. White

Physics — Fluid Mechanics · continuity-equation-control-volume

Problem

A thin layer of liquid, draining from an inclined plane, as in Fig. P3.26, will have a laminar velocity profile u≈U0(2y/h−y2/h2)u \approx U_0(2y/h - y^2/h^2), where U0U_0 is the surface velocity. If the plane has width bb into the paper, determine the volume rate of flow in the film. Suppose that h=0.5h = 0.5 in and the flow rate per foot of channel width is 1.25 gal/min. Estimate U0U_0 in ft/s.

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