Question

A 10 cm jet of water issues from a 1 m diameter tank Assume that the velocity in the jet is /2gh m/s where h is the elevation of the water surface above the outlet jet. How long will it take for the water surface in the tank to drop from ho 2 m to h 0.50 m? Problem Definition Situation: Water draining by a 10 cm jet from 1 m diameter tank. Find: Time (in seconds) to drain from depth of 2 m to 0.5 m. Sketch: Air Water h /10 cm Control volume

Answer 1

discharge at out let Q_a = a.V v = squareroot 2gh = a squareroot 2gh a = pi/4 (10/100)^2 a = 7.85 times 10^-3 Q = dv/t dw = charge in volume of water = A dh A = pi/4 (1)^2 = 0.785 m^2 Rank area sv/t = a squareroot 2gh t = dv/a squareroot 2gh = > t = A.dh/a squareroot 2gh h_1 = dm h_2 = 0.5 m t = A/a squareroot 2gh (h^-1/2) dh Time to train from h_1 notequalto h_2 t = integral_h_2^h_1 A/a squareroot 2g (d^1/2)dh = A/a squareroot 2g (h^1/2/1/2)^h_1_h_2 t = 2A/a squareroot 2g [squareroot h_1 - squareroot h_2] t = 2 times 0.785/7.85 times 10^-3 times squareroot 2 times 9.81 [squareroot 2 - squareroot 0.5] t = 31.927 sec