Solved: Torricellis law An open cylindrical tank initially

Chapter , Problem 47

(choose chapter or problem)

Torricellis law An open cylindrical tank initially filled with water drains through a hole in the bottom of the tank according to Torricellis Law (see figure). If h1t2 is the depth of water in the tank, for t 0, then Torricellis Law implies h_1t2 = -2k1h, where k is a constant that includes g = 9.8 m>s2, the radius of the tank, and the radius of the drain. Assume that the initial depth of the water is h102 = H. a. Find the solution of the initial value problem. b. Find the solution in the case that k = 0.1 and H = 0.5 m. c. In part (b), how long does it take for the tank to drain? d. Graph the solution in part (b) and check that it is consistent with part (c). h(t) A a