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Flowmetry Analysis (relating height to flow rate)

Hello!

1. Homework Statement

I need to find the instantaneous height of a liquid during the simultaneous filling and emptying (through a hole) of a cylinder. I have varying Qin at incremental time of 1 sec. with cylinder area=5 cm and orifice area=0.5 cm.

2. Homework Equations
Torricelli's theorem
Continuity equation



3. The Attempt at a Solution
1) Used V=Qt to find volume for each flow rate.
2) Calculated H=V/A.
3) Used torricelli's theorem to calculate Qout.

But this doesn't seem to me like the correct modeling of the problem and am stuck on how to go about it.
 
Help anyone??
 

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