Couette flow
In fluid dynamics, Couette flow is the laminar flow of a viscous fluid in the space between two parallel plates, one of which is moving relative to the other. The flow is driven by virtue of viscous drag force acting on the fluid and the applied pressure gradient parallel to the plates. This type of flow is named in honor of Maurice Marie Alfred Couette, a Professor of Physics at the French University of Angers in the late 19th century.
Couette flow is frequently used in undergraduate physics and engineering courses to illustrate shear-driven fluid motion. The simplest conceptual configuration finds two infinite, parallel plates separated by a distance h. One plate, say the top one, translates with a constant velocity u0 in its own plane. Neglecting pressure gradients, the Navier–Stokes equations simplify to
where y is a spatial coordinate normal to the plates and u(y) is the velocity distribution. This equation reflects the assumption that the flow is uni-directional. That is, only one of the three velocity components is non-trivial. If y originates at the lower plate, the boundary conditions are u(0) = 0 and u(h) = u0. The exact solution
can be found by integrating twice and solving for the constants using the boundary conditions.
A notable aspect of this model is that shear stress is constant throughout the flow domain. In particular, the first derivative of the velocity, u0/h, is constant. (This is implied by the straight-line profile in the figure.) According to Newton's Law of Viscosity (Newtonian fluid), the shear stress is the product of this expression and the (constant) fluid viscosity.
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