Differential equations- Creating a differential equation(mathematical models)

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Water enters a cylindrical tank at a constant rate (volume per second). The tank has a small hole in the bottom and so water flows out through the hole. Let y be the depth of the water in the tank. In hydrodynamics, it can be determined that the square of the rate of water leaving the tank is proportional to Ao2 (2gy) where Ao is the cross sectional area of the hole at the bottom of the tank and g(gravity) is 32
ft / s2.

1. Suppose that the hole at the bottom of the tank has a radius of 3 inches. Write a first order differential equation to model the depth of the water,y (Assume that we are ignoring any frication at the hole). Can the differential equation be classified as linear? Explain.

Answers (1)

  • Anonymous
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