COM_PracticeProblems - Practice Problems on Conservation of...

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Practice Problems on Conservation of Mass C. Wassgren, Purdue University Page 1 of 23 Last Updated: 2010 Sep 08 COM_01 Construct from first principles an equation for the conservation of mass governing the planar flow (in the xy plane) of a compressible liquid lying on a flat horizontal plane. The depth, h ( x , t ), is a function of position, x , and time, t . Assume that the velocity of the fluid in the positive x -direction, u ( x , t ), is independent of y . Also assume that the wavelength of the wave is much greater than the wave amplitude so that the horizontal velocities are much greater than the vertical velocities. Answer(s):  0 hu h tx    If incompressible: 0 h uh x y h ( x,t ) u ( x,t ) free surface liquid
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Practice Problems on Conservation of Mass C. Wassgren, Purdue University Page 2 of 23 Last Updated: 2010 Sep 08 COM_02 Consider the flow of an incompressible fluid between two parallel plates separated by a distance 2 H . If the velocity profile is given by: 2 2 1 H y u u c where u c is the centerline velocity, determine the average velocity of the flow, u . Assume the depth into the page is w. Answer(s) : 2 3 c uu  y H H u u
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Practice Problems on Conservation of Mass C. Wassgren, Purdue University Page 3 of 23 Last Updated: 2010 Sep 08 COM_03 An incompressible flow in a pipe has a velocity profile given by: 2 2 1 ) ( R r u r u c where u c is the centerline velocity and R is the pipe radius. Determine the average velocity in the pipe. Answer(s): 1 2 c uu  u r R
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Practice Problems on Conservation of Mass C. Wassgren, Purdue University Page 4 of 23 Last Updated: 2010 Sep 08 COM_04 Water enters a cylindrical tank through two pipes at volumetric flow rates of Q 1 and Q 2 . If the level in the tank remains constant, calculate the average velocity of the flow leaving the tank through a pipe with an area, A 3 . Answer(s): 12 3 3 QQ V A  h =constant Q 2 Q 1 ? 3 V A 3
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Practice Problems on Conservation of Mass C. Wassgren, Purdue University Page 5 of 23 Last Updated: 2010 Sep 08 COM_05 Water enters a cylindrical tank with diameter, D , through two pipes at volumetric flow rates of Q 1 and Q 2 and leaves through a pipe with area, A 3 , with an average velocity, 3 V . The level in the tank, h , does not remain constant. Determine the time rate of change of the level in the tank. Answer(s): 213 3 2 4 QQV A dh dt D  h constant Q 2 Q 1 3 V A 3 D
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Practice Problems on Conservation of Mass C. Wassgren, Purdue University Page 6 of 23 Last Updated: 2010 Sep 08 COM_06 A spherical balloon is filled through an area, A 1 , with air flowing at velocity, V 1 , and constant density, 1 . The radius of the balloon, R ( t ), can change with time, t . The average density within the balloon at any given time is b ( t ). Determine the relationship between the rate of change of the density within the balloon and the rest of the variables.
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This note was uploaded on 10/01/2011 for the course ME 509 taught by Professor Wereley during the Spring '11 term at Purdue University-West Lafayette.

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COM_PracticeProblems - Practice Problems on Conservation of...

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