ME 4220: Viscous Flows, (Fall 2009) Professor M.S.Chandrasekhara Home Work No. 1, Due Date: October 29, 2008 ME 4220: Viscous Flows Home Work No. II: Due Date: October 29, 2008 1. Make necessary assumptions; but explain them 2. Show all work 3. Write name, problem number, and page number on each page 4. Can use electronic submissions, e-mail to [email protected] 1. Consider the creeping flow between two circular disks of radius r = R, separated by a distance L. The bottom disk (z = 0) is fixed and the upper disk (at z = L) rotates at a constant angular rate ?. Solve the problem, i.e. obtain an expression for the velocity and if possible, pressure. 2. A vertical shaft weighing w per unit length is sliding down concentrically inside a pipe as shown in the figure below. Oil separates the two members. Determine the terminal velocity V of the shaft by solving the T Navier-Stokes equations. 3. A layer of viscous fluid flows down a vertical plate under the action of gravity. The density of the fluid varies linearly from ? at the wall to ? < ? at y = b, the free 1 2 1 surface. Find the velocity distribution and the velocity at the free surface. 4. Find the flow of a layer of viscous fluid on an oscillating plate (U cos ?t)at y = 0. o The fluid is of constant thickness a; the surface at y = a is stress-free. (Note: This is nd Stokes’ 2 problem in a confined fluid space of height a). 5. Find the flow in a rotating pipe of radius a. A pressure gradient is present. Take the flow to be axially symmetric and steady.