Mathematics, 12.02.2021 06:30 mooncake9090

Let h(t) and V(t) be the height and volume of water in a tank at time t. If water drains through a hole with area a at the bottom of the tank, then Torricelli’s Law says that
where g is the acceleration due to gravity. So the rate at which water flows from the tank is proportional to
the square root of the water height.
Part 1
Suppose the tank is cylindrical with height 6 feet and radius 2 feet and the hole is circular with radius 1 inch. If
we take , show that h satisfies the differential equation
You are going to want to start with the formula for volume of a cylinder then use the equation given above for
Torricelli’s Law to substitute in. Your work should start with the volume formula and end with the differential
equation above.

Let h(t) and V(t) be the height and volume of water in a tank at time t. If water drains through a

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Let h(t) and V(t) be the height and volume of water in a tank at time t. If water drains through a h...