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Fluid Mechanics

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Consider the 2D, incompressible, steady flow between parallel walls, the bottom wall is stationary and the top one is moving at a constant velocity Uw. The pressure is constant.
Assuming the flow is fully developed (i.e. independent of x), we can write ∂/∂x≡0. We will also assume that the flow has parallel streamlines so that the y-velocity component is zero. The x-component of the velocity field is then linear and given by

u(y)=Uw*(y/h)

Your answers to the questions below can only depend on x, y, h, Uw. In the answer box, use Uw to denote Uw.

1) Using the x- and y-momentum equations, derive the expression for the viscous term fτ.

fτ1=
fτ2=

3) Write the expression for the vorticity (ωz).

Is the flow rotational or irrotational?

4) Write the expressions for the strain rate components.

εxx=
εyy=
εxy=

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