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# 3-09 - 3-9 In Figure 3.9 we have shown a tank into which...

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3-9. In Figure 3.9 we have shown a tank into which water enters at a volumetric rate and leaves at a rate that is given by 1 Q o Q o o 0.6 Q A = gh Here o A is the area of the orifice in the bottom of the tank. If the tank is initially empty when Figure 3.9 . Tank filling process water begins to flow into the tank, we have an initial condition of the form I.C. 0 , 0 h t = = In this problem you are asked to derive an equation that can be used to predict the height of the water at any time. For the special case given by 4 3 1 10 m /s Q = 2 o 0.5 cm A = 1.5 m D = = 2.78 m H you are asked to determine if the water will overflow the tank. 3-9. The control volume used to analyze this process is illustrated in Figure 3.9a where we have shown a moving control volume with “cuts” at the entrance and exit which are

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Figure 3.9a . Tank filling and overflow process joined by a surface at which ( ) v w n , is zero. When the water overflows, a second exit will be created; however, we are only concerned with the process that occurs prior to overflow.
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