Derive an analytic formula for the water surface rise, Mechanical Engineering

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Derive an analytic formula for the water surface rise

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Q: Water enters the bottom of the cone in the figure at a uniformly increasing average velocity V = Kt. If d is very small, derive an analytic formula for the water surface rise h (t), assuming h = 0 at t = 0. You must provide a step by step solution to solve the question.

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