Project: A Cylindrical Tank Problem
Consider an open cylindrical tank of height h0 meters and radius r meters that is filled with water. A circular hole of radius l meters in the bottom of the tank allows the water to flow out under the influence of gravity. According to Torricelli’s law, the water flows out with the same speed that it would acquire in falling freely from the water level in the tank to the hole.
Suppose now that starting at t = 0 chemical is added to the water in the tank at a rate of w grams/second. Derive the following differential equation governing the amount of chemical, A(t), in the tank at time t :
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