1. (a) Torricelli's law implies that the time rate of change (the rate of change with...

 

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1. (a) Torricelli's law implies that the time rate of change (the rate of change with respect to time, t) of the volume, V of water in a draining tank is proportional to the square root of the depth, y, of the water in the tank. Write down the associated differential equation. (b) Further, if the tank is a cylinder with vertical sides and cross-section area A then V = Ay. Use this substitution in part (a) to find the depth of water in the tank at any later time. 1. (a) Torricelli's law implies that the time rate of change (the rate of change with respect to time, t) of the volume, V of water in a draining tank is proportional to the square root of the depth, y, of the water in the tank. Write down the associated differential equation. (b) Further, if the tank is a cylinder with vertical sides and cross-section area A then V = Ay. Use this substitution in part (a) to find the depth of water in the tank at any later time.

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PART A If V be the volume of the tank and y be the depth of the water in the tank dV then the r... View the full answer