Exam10_Solutions2007

Exam10_Solutions2007 - ME or BME Class? _SOLUTIONS_...

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ME or BME Class? __ SOLUTIONS __ NAME_______ SOLUIONS ______________ Page 1 of 10 Fluid Mechanics Exam 10, Spring 2007 There are 5 problems on this exam for a total of 78 points Problem 1: 25 points Problem 2: 10 points Problem 3: 15 points Problem 4: 14 points Problem 5: 14 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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ME or BME Class? __ SOLUTIONS __ NAME_______ SOLUIONS ______________ Page 2 of 10 Problem 1 (22 points) A) In Cartesian coordinates, we can write that Write the velocity vector V in component form in cylindrical coordinates (analogous to the Cartesian form written above): B) Consider fluid flow in a pipe of circular cross-section (radius R) under the assumptions listed below. In the blanks next to each assumption, write down the mathematical expression that expresses that assumption (1) Newtonian fluid_________ mu = constant __________ (2) Constant density______ rho = constant ____________ (3) Steady flow _____partial(anything)/partial(t) = 0_________________ (4) Negligible elevation change across the diameter of the pipe ___ g = 0, or pressure gradient in the r direction = 0 ______ (5) Axisymmetric flow __________ partial(anything)/partial(theta) = 0 Note: Axisymmetric flow does NOT mean that V-theta equals 0. (6) Fully developed flow __ partial(anything)/partial(z) = 0 C) Use the continuity equation in cylindrical coordinates (provided below) to obtain an expression for the velocity in the radial direction. For full credit, you must clearly state all assumptions you are making in every step.
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ME or BME Class? __ SOLUTIONS
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This note was uploaded on 09/29/2008 for the course MECH 241 taught by Professor Hartmann during the Spring '08 term at Northwestern.

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Exam10_Solutions2007 - ME or BME Class? _SOLUTIONS_...

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