(Solved): Problem 4. (20 points) Consider fully-developed two-dimensional flow between two infinite parallel ...

Problem 4. (20 points) Consider fully-developed two-dimensional flow between two infinite parallel plates separated by distance h. In fully-developed flow, the only component of velocity is in the x-direction and it only varies across the channel height, in the y-direction. The top and bottom plates are stationary and the water flow is driven by the pressure gradient dP/dx. (dP/dx is uniform and negative.) u(y) 2 1 dp The x-component of velocity is u(y) = - (y²-hy). 2? dx a. Calculate the vorticity component in the z-direction. b. Is this flow rotational or irrotational? c. Do fluid particles in the top half of the channel rotate clockwise or counterclockwise? Show how you determined this from the vorticity calculation in part a. d. Do fluid particles in the lower half of the channel rotate clockwise or counterclockwise? Show how you determined this from the vorticity calculation in part a. e. In your discussion, explain physically why the flow rotates clockwise or counterclockwise in each region. (You can use an explanation similar to Figure 4-45 in the text.)