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Exam3_Solutions_Revised2007

# Exam3_Solutions_Revised2007 - Course Number SOLUTIONS...

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Course Number __ SOLUTIONS SOLUTIONS _________ NAME____ page 1 of 14 Fluid Mechanics Exam 3, Spring 2007 There are 7 problems on this exam for a total of 80 points Problem 1: 8 points Problem 2: 12 points Problem 3: 18 points Problem 4: 10 points Problem 5: 10 points Problem 6: 12 points Problem 7: 10 points By signing below I agree to abide by the following honor code: As a member of the Northwestern community, I will not take unfair advantage of any other member of the Northwestern community. I specifically agree not to reveal to any other student the contents of this exam. Signature: Date:

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Course Number __ SOLUTIONS SOLUTIONS _________ NAME____ page 2 of 14 Problem 1: 8 points One point each, no partial credit. Consider the vector field F and the scalar function Φ F = (x 2 + y 2 + z 2 ) (i + j + k). Φ = x 4 + y 3 + z 2 If it is possible, find the quantities requested below. If it is not possible to find the quantity, write “not possible” in the box. Be careful: each of these answers is worth one point each, and no partial credit will be given. 2(y-z) i + 2(z-x) j + 2(x-y) k (vector) x F not possible F 2(x + y + z) (scalar) • F zero • ( x F) not possible Φ 4x 3 i + 3y 2 j + 2z k (vector) ∇ Φ 12x 2 + 6y + 2 (scalar) 2 Φ not possible x Φ
Course Number __ SOLUTIONS SOLUTIONS _________ NAME____ page 3 of 14 You can use this page to work on problem 1 Be sure to write your final answers in the boxes provided on the previous page.

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Course Number __ SOLUTIONS SOLUTIONS _________ NAME____ page 4 of 14 Problem 2. A rectangular plate is fixed at the ground, and a second parallel plate with area 4 m 2 moves above it at a distance of 10 mm with a speed of 2 m/s. The shear stress developed is 40 N/m 2 . Assuming a Newtonian fluid, please do the following: (A) On the axes below, sketch a plot of velocity as a function of distance z between the plates. Indicate the origin, label the axes, and indicate the numerical value of the slope at each region of the curve you have sketched. 3 points – Zero credit if the graph is non-linear. Minus 2 if the graph is linear but the slope is wrong. Minus 1 if the origin is not indicated. Minus 1 if the axes are not labeled. We did not take off points for not showing units. We did not take off points if you did not simplify your answer. Note: You can get the identical answer by simply finding du/dz, without setting it equal to Tau over Mu. This solution simply shows you the “long way around” to make everything clear. Each of the following questions is worth one point, with no partial credit available: (B) What are the dimensions of pressure in terms of kilograms, meters, and seconds?
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Exam3_Solutions_Revised2007 - Course Number SOLUTIONS...

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