Unformatted text preview: EMCH 560, Spring 2010, HW01 Problem 1: For a velocity profile, which is a function of r only, is given by = (/)( 2 - 2 ), where C is a constant and R is the pipe radius. Determine the expression of wall shear stress. U of S Carolina Problem 2: Shown as Figure 1. A disk rotates steadily inside a disk-shaped container filled with oil of viscosity . Assume linear velocity profiles with no slip and neglect stress on the outer edges of the disk. Find a formula for the torque M required to drive the disk. If = 0.3 kg/(m*s), h = 0.5 mm and R = 2 cm, computing M. Figure 1 Problem 3: For the velocity fields described below determine: 1) The rate-of-strain tensor 2) The rate of rotation tensor and the vorticity vector a. = , = -, = 0 b. = 2 + 2 , = - 2 + 2 c. = 2 + 2 , = 2 + 2
+ - vorticity field, i.e. the vortex lines. The vortex lines are defined by = = . = ( 2 + 2 ), v = 0, w = 0 Problem 4 (graduate students only): For the following velocity field, determine the ...
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This note was uploaded on 02/10/2010 for the course EMCH 566 taught by Professor Li during the Spring '10 term at University of South Carolina Beaufort.
- Spring '10