Falling film flow

A steady film down a wall has a parabolic velocity profile set by gravity, ambient pressure gradient, and surface shear.

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- Inclined viscous film with opposing surface shear Falling film flow

Inclined viscous film with opposing surface shear

For a film of thickness

h

flowing down a slope of angle

α

, an upslope surface stress of magnitude

τ

gives

u (z) = \frac{ρ g s i n α}{μ} (h z - \frac{z ^{2}}{2}) - \frac{τ z}{μ} .

The surface velocity, total flux, and basal shear reverse at

τ = \frac{1}{2} ρ g h sin α, \frac{2}{3} ρ g h sin α, ρ g h sin α,

respectively.

 Ancestors (5)

 Incoming links (2)

Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 66 / 2 / Solution
Past exam of the mathematics course of the University of Cambridge / 2019 / ib / Paper 1 / 5C / Solution

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