vessel faucets
Flow rate physics problem please help. Points for the best answer to the first poster correctly.
A cylindrical vessel, open at the top is 20 cm high and 10 cm in diameter. A circular hole with a cross-sectional area of 1 cm ^ 2 is cut in the bottom of the tank. Water from a faucet left in the tank at a speed of 140 cm ^ 3/sec. A. Show that the water in the reservoir will rise beyond 10 cm. b. Also show that once the tap is turned off Drain the water tank in 11.2 sec. Work and an explanation would be much appreciated. Thanks in advance for looking!
The flow is Torricelli's theorem, a genius who was one of Galileo conteporary. Using energy conservation, the kinetic energy of water flowing out of the hole is equal to its potential (pressure) energy. KE = 1 / 2 mv ² = mgh PE = Solving for the speed, m cancel v = sqrt (2gh) first time derivative wrt * vol = area x is: volume / time = speed * Total 140 cm ³ / s = 1 cm ² * sqrt (2gh) Resolve, h = 10 cm is correct. B. You have the water flow, simply integrate from h = 10 h = 0. Suggestion, you need to integrate sqrt (h).
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