Past Exam 1Samples Protected ViewSaved to this PC w Help Te

Past Exam #1-Samples - Protected View-Saved to this PC w Help Tell me what you want to do r to stay in Protected View. Enable Editing DEPARTMENT OF CIMIL AND ENVIRONMENTAL ENGINEERING Dr. Tarek Merabtene Past Exam Fall 2013 -2014 Problem 1 (8 pts): (draw your own figure) A top plate is moving over a second fixed plate to the right with a constant velocity of U-3 m/s. The gap between the two plates is h-ómm and is filled with a fluid of dynamic viscosity u-6.5x10- Pa.s. 1) Assuming linear velocity distribution, calculate the shear stress on the upper and bottom plates. 2) Assume a nonlinear velocity of the form v 6.990.873 In y where y is the distance from the bottom fixed plate. Calculate the shear stress for y-3 mm I Problem 2 (7 pts):

Solution

Newtons law of viscosity, shear tress T= u^l (du/dy)

For linear velocity distribution T= (u^lU)/y

Here u^l= dynamic viscosity= 6.5x10^-4 Pa.s

y= distance between plates= 6 mm

U=velocity= 3 m/s

1) shear stress T= {6.5x10^-4 (Pa.s)x 3 (m/s)}/{6x10^-3 (m)} = 0.325 N/m²

2) here non-linear velocity distribution T= u^l(dU/dy)

Here U=v=(6.99+.873 ln(y)); y=3 mm= 3x10^-3 m

T={6.5x10^-4 (Pa.s) x (0.873/y)} = 0.283 N/m²