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Unformatted text preview: z and using the z component of Eulers equation, we find p z = f I ( z ) = g cos = f ( z ) = C gz cos 494 CHAPTER 5. CONSERVATION OF MASS AND MOMENTUM where C is a constant. Thus, the pressure throughout the fluid in the car is p ( x, y, z ) = C gz cos On the free surface, p = p a . Also, at x = 0 , inspection of Figure 5.13 shows that z = h , wherefore C = p a + gh cos Therefore, the pressure at any point in the fluid is p ( x, y, z ) = p a + g ( h z ) cos On the free surface, p = p a . Thus, the equation of the free surface is p a = p a + g ( h z ) cos = z = h This means the free surface is parallel to the inclined plane, so that =...
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This note was uploaded on 10/12/2009 for the course AME 309 at USC.