1. A boundary layer develops when water flows over a perforated flat plate. To control boundary layer groveth, water is sucked through the plate. Determine (a) the volume flow rate needed through the plate to maintain the streamline at the top of the boundary layer parallel to the plate, i.e., horizontal; (b) the drag force for this flow condition. There is no imposed pressure gradient. Note that the no-slip boundary condition for the tangential velocity component still applies.
2. A free vortex with a circulation C and a sink with a flow rate m are place at a height h above a solid plane. Assuming inviscid flow, determine a) the flow velocity at points A and B; b) the difference between the pressures at the points.
3. The thrust F of a propeller depends on its diameter, D, the angular velocity, to, the flight velocity, U, the air density, p, the air viscosity, p, and the speed of sound, a. Find a non-dimensional form of the dependence of F on the other parameters (with the Pi term containing F as the dependent variable).
4. A liquid with a viscosity g and a density p flows over a plane moving at velocities U. Starting from the Navier-Stokes equations, determine the velocity profile.
