Exam4_Solutions2007

# Exam4_Solutions2007 - Course Number SOLUTIONS...

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Course Number __ SOLUTIONS SOLUTIONS _________ NAME____ Page 1 of 11 Fluid Mechanics Exam 4, Spring 2007 There are 6 problems on this exam for a total of 55 points Problem 1: 5 points Problem 2: 13 points Problem 3: 12 points Problem 4: 9 points Problem 5: 9 points Problem 6: 7 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 11 Problem 1: 5 points Consider the vector field V and the scalar function Φ () ) k j i ( z y x V ˆ ˆ ˆ 4 3 2 + + + + = r Φ = x 2 + y 3 + z 4 If it is possible, find the quantities requested below. If it is not possible to find the quantity, write “not possible” in the box. 2 V ∇Φ 2 Φ If neither graphs had an x or y label you lost a total of one point. Sketch a vector field with zero divergence. Be sure to label your axes and be sure that your sketch has vectors in all four quadrants: Sketch a vector field with negative divergence Be sure to label your axes and be sure that your sketch has vectors in all four quadrants:
Course Number __ SOLUTIONS SOLUTIONS _________ NAME____ Page 3 of 11 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 11 Problem 2 (13 points): Each of the following questions is worth one point, with no partial credit available: (A) What are the dimensions of pressure in terms of kilograms, meters, and seconds? (kg) / (m s 2 ) (B) What are the dimensions of shearing stress in terms of kilograms, meters, and seconds? (kg) / (m s
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Exam4_Solutions2007 - Course Number SOLUTIONS...

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