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The steady incompressible flow in a shallow two-dimensional slot is driven by a constant free surface velocity U. Because of the ends, the flow has to turn around, setting up a pressure-gradient driven return flow opposite to the surface velocity-driven flow. While the flow near the ends is two-dimensional, the flow in the middle portion of the slot can be approximated as unidirectional, assuming L/d 1. The steady incompressible flow in a shallow two-dimensional slot is driven by a constant free surface velocity U. Because of the ends, the flow has to turn around, setting up a pressure-gradient driven return flow opposite to the surface velocity driven flow. While the flow near the ends is two-dimensional, the flow in the middle portion of the slot can be approximated as unidirectional, assuming L/d >> 1. Q1. The unidirectional flow in the middle portion is a superposition of a Couette flow and a Poisueille flow. Use conservation of mass to determine the pressure gradient and the velocity profile. Q2. compute the shear stress at the moving surface. Q3. find the depth at which the velocity becomes zero, which separates the research flow from the surface velocity-driven flow.