quiz_10A - dy dt =-1 72 y. Solve this equiation to nd the...

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Math 213 — Quiz 10 Name Solution 1. Let y ( t ) and V ( t ) be the height and volume of water in a tank at time t . If water leaks through a hole with area a at the bottom of the tank, then Torricelli’s Law says that dV dt = - a p 2 gy where g is the acceleration due to gravity. Suppose the tank is cylindrical with height 6 ft and radius 2 ft and the hole is circular with radius 1 in. If we take g = 32 ft / s 2 . then y satisfies the differential equation
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Unformatted text preview: dy dt =-1 72 y. Solve this equiation to nd the height of water at time t , assuming the tank is full at time t = 0. The equation is separable, we can rewrite it as dy y =-dt 72 . Integrating both sides, we nd 2 y =-t 72 + C. Since y (0) = 6 ft we nd that C = 2 6. Therefore, y = 6-t 144 2 ....
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This note was uploaded on 05/09/2008 for the course MATH 2130 taught by Professor Dorais during the Spring '08 term at Cornell University (Engineering School).

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