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I was just doing an experiment with relating the weight flow rate of water out of cylinder with a pin hole at the bottom. The equation that I put together was: $$\dot{W}=\rho g C_d A \sqrt{2gh}$$ ##\dot{W}## is the weight flow rate, ##\rho## is the density of water, ##g## is the acceleration due to gravity, ##C_d## is the coefficient of discharge of the orifice, ##A## is the area of the orifice, ##h## is the height of the water above the hole. The problem that I am facing is that the weight flow rate changes with time along with the height of the water. Thus, I thought that if I can find an equation for the height as it relates to time, I can plug it into the equation above, and my equation would be complete. I also need to see how you got to whatever equation makes sense. I am looking for something like: ##h = kt##. As in k can be any function including any variables that make sense. I believe this requires derivatives and integrals so don't be afraid to include and explain them.

Thank you very much for your help.

Jonathan

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# Height to time equation: water cylinder with pinhole

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