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Volumetric flow rate  Help needed 
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#1
Feb1012, 10:02 AM

P: 4

I posted this in the DE forum as well since it is related.
 Hi all, I've got a fairly straight forward problem to solve here regarding flow rate out of a tank with uniform crosssectional area. I am treating this is a volumetric flow problem since there is assumed to be volume flow out of the tank, and volume flow into the tank. I have two Qout terms (one out of a hole in the bottom of the tank, and one from fluid consumed by an engine), as well as one Qin term (via a pump feeding fluid into the tank at a constant rate). Qouthole (Qh) = a*C*sqrt(2*g*z) Qoutengine (Qe) = constant Qin (Qi) = constant NOTE: a = exit hole area C = energy loss coefficient g = gravity z = head height in tank My DE looks like: A*(dh/dt) = Qh  Qi + Qe Separating the terms and solving for time by integrating h from Hi to Hf and t from 0 to T, I get this... ((a*C)/A)*sqrt(2*g)*(2/3)*((Hf^(3/2))(Hi^(3/2))) = (1/A)q*t I combined the Qi and Qe terms early on since they are constants (easier to integrate), therefore, q in the above equation equals QiQf. The problem is, solving for t eliminates the tank crosssectional area (A) since it is divided out. I feel confident with my general equation, but may have made a mistake somewhere in solving for t. Any help would be GREATLY appreciated! Thank you 


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