HW_SET_4.soln - Chapter 3 Integral Relations for a Control...

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Chapter 3 Integral Relations for a Control Volume 183 P3.13 The cylindrical container in Fig. P3.13 D Fig. P3.13 h ( t ) is 20 cm in diameter and has a conical contraction at the bottom with an exit hole 3 cm in diameter. The tank contains fresh water at standard sea-level conditions. If the water surface is falling at the nearly steady rate dh/dt 0.072 m/s, estimate the average velocity V from the bottom exit. V ? Solution : We could simply note that dh/dt is the same as the water velocity at the surface and use Q 1 = Q 2 , or, more instructive, approach it as a control volume problem. Let the control volume encompass the entire container. Then the mass relation is . )] 072 . 0 ( [ ) 3 20 ( : data the Introduce ) ( ) ( : 4 Cancel 0 4 4 : or , 4 | ) 4 ( ) ( 0 | 2 2 2 2 2 2 Ans s m cm cm V dt dh D D V V D dt dh D V D h D dt d m d dt d dt dm exit exit exit cone CV out system s m 3.2   P3.14 The open tank in the figure contains water at 20 C. For incompressible flow, (a) derive an analytic expression for dh / dt in terms of (Q1, Q2, Q3). (b) If h is constant, determine V2 for the given data if V1 3 m/s and Q3 0.01 m 3 /s. Solution: For a control volume enclosing the tank, 2 ) ,  213 () ( 4 CV dd d h dQ Q Q Q Q Q dt dt   
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Solutions Manual Fluid Mechanics, Fifth Edition 184 . (a) solve Ans 132 2 QQQ dh dt (d/ 4 ) If h is constant, then 22 213 2 0.01 (0.05) (3.0) 0.0159 (0.07) , 44 QQ Q V  2 . (b) solve Ans V4 . 1 3 m / s P3.15 Water flows steadily through the round pipe in the figure. The entrance velocity is Vo. The exit velocity approximates turbulent flow, u umax(1 r/R) 1/7 . Determine the ratio Uo/umax for this incompressible flow.
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HW_SET_4.soln - Chapter 3 Integral Relations for a Control...

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