An open-topped tank completely filled with water has a release valve near its bo

Question

An open-topped tank completely filled with water has a release valve near its bottom. The valve is 1.55 m below the water surface. Water is released from the valve to power a turbine, which generates electricity. The area of the top of the tank, AT, is a = 10.3 times the cross-sectional area, AV, of the valve opening.

a) Calculate the speed of the water as it exits the valve. Neglect friction and viscosity.

b) In addition, calculate the speed of a drop of water released from rest at h = 1.55 m when it reaches the elevation of the valve.

Explanation / Answer

Part b is asking for the speed of a water drop of mass m which has fallen height h from rest. By conservation of total mechanical energy, mgh + 0 = 0 + 1/2mv^2. Thus v = sqrt(2gh) = 5.5 m/s. The point is to see why this is the same as your answer to part a.

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