Consider a plane Couette flow of a viscous fluid confined
between two flat plates at a distance b...

Question

Consider a plane Couette flow of a viscous fluid confined
between two flat plates at a distance b apart (see Figure 9.4c). At steady
state the velocity distribution is

u = Uy/b v = w = 0,

where the upper plate at y = b is moving parallel to itself
at speed U, and the lower plate is held stationary. Find the rate of linear
strain, the rate of shear strain, and vorticity. Show that the streamfunction
is given by

Aditi · Accepted Answer

ANSWER
Here there is only one velocity component: u = Uy/b
The strain rate tensor is:
The linear strain rates are both zero.
Shear strain rate is U/2b.
The vorticity vector has one non – zero component:

Consider a plane Couette flow of a viscous fluid confined between two flat plates at a distance b apart (see Figure 9.4c). At steady state the velocity distribution is u = Uy/b v = w = 0, where the...

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