The rotating disk viscometer is a precise device for measuring the viscosity of fluids. In this type of viscometer, the flow develops in the gap (H) between the two parallel horizontal circular plates (disks) that have each a radius (R). The upper disk is rotated at a constant angular velocity (0) while the lower one is fixed. This results in a flow where only the angular component of the velocity vector (ve) is nonzero. It is possible to show that the flow velocity is: Ve(r,z)= 0.r.z/H. (a) Check that this velocity does indeed satisfy the continuity equation and the Navier-Stokes equation in the 0-direction, for steady, incompressible flow. Check that it also satisfies the boundary conditions at the lower and upper disks.

Problem 2 The apparatus sketched in the figure below serves as a viscometer i.e. it can be used to measure the viscosity of a liquid. In the drawing, D is a large reservoir containing a viscous liquid A and E is a cylindrical tube of radius R, open at both ends, surrounding and coaxial with B, which is a cylindrical "bob" of radius êR that is dragged up through the fluid by a frictionless pulley system (C) utilizing a weight W. Determine a design equation that relates the viscosity of the liquid to the geometry of the system and the weight W. Hint: you can assume that the length of the cylindrical tube is sufficiently long for the flow to reach steady state. W E D B

The fluid particles do not rotate about their own axis in an irrotational fluid flow. Select one: True False