Q1. Calculate the drag force on the slipper pad bearing discussed in Panton's section 22.4. Plot the drag force as a function of A, similar to Fig 22.4. Is there an optimal configuration (U, h0, h1, L, A, etc.) for such a slipper pad bearing?
Q2. Consider the problem of radial outflow between parallel disks at right. Solve for the velocity and pressure of the flow in the gap between the disks. Assume the flow has negligible inertia. Ignore the region near r = 0 where 3 dimensional effects dominate. Plot the velocity as a function of r and z and the pressure as a function of r.
Q3. Consider again the parallel disk geometry above. Now consider the steady creeping flow case where the lower disk is fixed and the upper disk is allowed to rotate at the constant rate ω and the inflow Q is zero. Find a solution of the form vθ = r f(z). Plot the velocity and pressure as functions of r and z.
Q4. What is the terminal velocity in still air of a water droplet 0.01 mm in diameter? What is the terminal velocity in still water of an air bubble 0.01 mm in diameter? In both situations, what is the maximum bubble/droplet size at which the flow can be considered low Reynolds number? Sketch the velocity fields both inside and outside the bubble/droplet as well as the shape of the bubble/droplet.
Q5. For the stagnation point flow F = U z2, find the streamlines, potential lines, and the equations for the velocity components u, v. What is the common name of this classical flow?
Q6. Consider two free vortices of identical circulation Γ separated by a distance h. Calculate and sketch the complex potential and velocity field for vortices of like sense as well as opposite sense. Calculate the pressure distribution on the line connecting the two vortices as well as on the line of symmetry between the two vortices. In each case what is the circulation of any closed curve surrounding the two vortices?
Q7. A line source (into the page) of strength m is parallel to a wall (extending infinitely into the page and in the horizontal direction) at a distance h. Sketch the streamlines and equipotential lines for the flow. Find the pressure distribution on the wall where p0 is the pressure at the stagnation point.
