Problem 4.21 - Problem 4.21 [Difficulty: 3] Given: Data on...

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Problem 4.21 [Difficulty: 3] Given: Data on flow into and out of tank Find: Time at which exit pump is switched on; time at which drain is opened; flow rate into drain Solution: Basic equation t M CV CS ρ V A () + 0 = Assumptions: 1) Uniform flow 2) Incompressible flow After inlet pump is on t M CV CS ρ V A + t M tank ρ V in A in = 0 = t M tank ρ A tank dh dt = ρ V in A in = dh dt V in A in A tank = V in D in D tank 2 = where h is the level of water in the tank Hence the time to reach h exit = 0.7 m is t exit h exit dh dt = h exit V in D tank D in 2 = t exit 0.7 m 1 5 × s m 3m 0.1 m 2 × = t exit 126 s = After exit pump is on t M CV CS ρ V A + t M tank ρ V in A in ρ V exit A exit + = 0 = A tank dh dt V in A in V exit A exit = dh dt V in A in A tank V exit A exit A tank = V in D in D tank 2 V exit D exit D tank 2 = Hence the time to reach h
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