Consider a fully developed Couette flow, i.e. flow between two infinite parallel plates separated by distance h with the top plate moving with velocity V and the bottom stationary, as illustrated in figure Q3a below. The flow is steady, incompressible, and two dimensional in the x-y plane.
ryˆˆ The velocity field is given by V =V h i + 0j.
i. Is this flow rotational or irrotational? If it is rotational calculate the vorticity component in the z-direction. Do fluid particles rotate clockwise or counter clockwise?
ii. Generate an expression for the stream function along the vertical dashed line. For convenience let ?=0 along the bottom wall of the
channel. What is the value of ? along the top wall?
iii. Calculate the volume flow rate per unit width from first principles (integration of the velocity profile) and compare your result to that
obtained directly from the stream function.
iv. What is the shape of the streamlines for this flow? Do you expect them to be equally spaced? Explain.