According To Torricelli’s Law, The Height Of Flu

Anonymous

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According to Torricelli’s Law, the height of fluid in a container above a hole (through which the fluid is escaping) is governed by a differential equation: dh/dt= -k(h)^(1/2) where k >= 0 is a constant. Suppose the height of the fluid is initially h(0) = h0. How long does it take for the fluid to drain to the level of the hole? Thanks a lot!

 

Answer No.1

SuperHead

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First, set up your diff equation. dh/dt = -k(h)^(1/2) Now, is this equation separable or do you need to use integrating factor? In this instance, it's separable.... dh/h^(1/2) = -k dt Now take the integral of both sides... 2h^(1/2) = -k*t + C Now you need to solve for C using your initial condition... h(0) = h0 Once you solve for C you have your equation as a function of height vs time. Solve to get t on one side of the equation and you will have the time it takes for the fluid to drain.

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