A tank of volume Vo is filled initially with air at atmospheric density Par. Beginning at...

 

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A tank of volume Vo is filled initially with air at atmospheric density Par. Beginning at t = 0, a pump delivers to the tank a mixture of air and water. The volumetric inflow rate to the pump is Q, half of which is water having a density pw and the other half is air at the density Pat. Once inside the tank, the water falls to the bottom, occupying a volume V {1} that increases with time (see figure P3.14). The air rises to the top of the tank, forming a volume with uniform density Pa{t}. (a) In terms of the known quantities Vo, Pa, Q and pw, derive expressions for V{1} and pa {1} as functions of time t. (b) The pressure p of the air in the tank is related to its density P. and the atmospheric pressure par by: Pa P = Par Calculate the ratio p/Pa for the time when the tank is half full of water. Figure P3.14 air water e A tank of volume Vo is filled initially with air at atmospheric density Par. Beginning at t = 0, a pump delivers to the tank a mixture of air and water. The volumetric inflow rate to the pump is Q, half of which is water having a density pw and the other half is air at the density Pat. Once inside the tank, the water falls to the bottom, occupying a volume V {1} that increases with time (see figure P3.14). The air rises to the top of the tank, forming a volume with uniform density Pa{t}. (a) In terms of the known quantities Vo, Pa, Q and pw, derive expressions for V{1} and pa {1} as functions of time t. (b) The pressure p of the air in the tank is related to its density P. and the atmospheric pressure par by: Pa P = Par Calculate the ratio p/Pa for the time when the tank is half full of water. Figure P3.14 air water e

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a Volume of water Vwt w Qt2 Volume of air V0 Vwt Mass flow rate of air into tank Q2 ... View the full answer