3-07 - Problem 3-7 solution According to the problem...

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Problem 3-7 solution According to the problem statement, the volume of the horizontal cylindrical tank is given by (1) V = p L R 2 - L R 2 ÅÅÅÅÅÅÅÅÅ 2 H a - sin a L where a is a function of time. From the geometry we can use trigonometry to relate h to a : (2) h = R + R cos I a ÅÅÅÅ 2 M It follows then that h=0 when a ê 2 = 180 ° . and h=2R when a /2=0° We select a moving control volume (t) that encloses the liquid in the tank at any given instant in time with a cut where the liquid enters the tank. The macroscopic mass balance for this moving control volume is (3) ÅÅÅÅÅÅÅ t H t L r „ V + H t L r H v - w L ÿ n A = 0 and the assumption that the density is constant leads to (4) ÅÅÅÅÅÅÅÅ t + H t L H v - w L ÿ n A = 0 The normal component of the relative velocity H v - w L is zero everywhere except at the entrance cut where the liquid flow into the control volume. Thus we have (5) ÅÅÅÅÅÅÅÅ t
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3-07 - Problem 3-7 solution According to the problem...

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