Couette Flow

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The permanent laminar flow of an incompressible viscous fluid in the space between two parallel plates can be described by a linear ODE for :



where is the dynamic viscosity of the fluid and is the pressure gradient. The boundary conditions are:

(lower plate velocity),

(upper plate velocity).

This problem has an analytic solution:

that varies as a function of the pressure gradient and the upper plate velocity.


Contributed by: William C. Guttner (March 2011)
Open content licensed under CC BY-NC-SA



Snapshot 1: pressure induced parabolic flow (Poiseuille solution)

Snapshot 2: linear flow induced by the translation of the upper plate (without pressure gradient)

Snapshot 3: general solution

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