Question

Consider the following conical drainage collector of side angle α: You can assume that the liquid level is perfectly flat. All of the liquid in the tank is considered incompressible, and must satisfy Bernoulli's equation: PV2pgh -constant 2 You can assume that the height at the bottom is the baseline (h2 -0). the liquid line velocity is minimal (Vi 0). and that the pressure is equalized (Pi P2). The height of the liquid line being tracked is equal to the moving surface (h(t) -h1). a) Determine an expression for the Volume of liquid in the (right) conical tank as a function of the liquid height h(t) b) Determine an expression for the Volumetric rate of change of the tank as a function of the liquid height h(t). You can assume the drainage duct has an area of A. Hint: The mass loss can be found as pAV where A is the duct area and V is the velocity. c) Determine a differential equation for liquid volume based on your results from parts (a) and (b) d) Determine the solution to your differential equation from part (c)

Answer 1

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