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Water flows out of a wide vessel through...

Water flows out of a wide vessel through a small orifice. Express the flow velocity as a function of the height of the column of liquid. 

Text Solution

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The correct Answer is:
`v=sqrt(2gh)`
Suppose that the volume of fluid flowing out through an orifice during a short time interval is so small that the drop in its level in the wide section of the vessel can be neglected. Taking into account that in our case the pressure drop is determined entirely by the hydrostatic pressure, we  conclude that the Bernoulli equation assumes the form `rho gh = rho v^2//2` from which we get the Torricelli formula for the velocity of fluid flowing out through a small orifice.
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