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COM_PracticeProblems

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 h uh t x If incompressible: 0 h uh t x x y h ( x,t ) u ( x,t ) free surface liquid
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