How Fast can a Liquid Flow from a Hole?

The kinetic energy of a mass of liquid = while the potential energy of this mass raised to a height, h, against the gravitational attraction, g, is: potential energy = mgh. These two are equal

= mgh

and thus the velocity of the mass of water is

The area of the hole the mass of water passes through is A_1 and so the volume of fluid per second, Q, is

As it leaves the orifice, the fluid narrows and the mass spreads out over a different area due to this affect. The factor representing this is given by the coefficient, c, in the following equation. Furthermore, there may be a reservoir whose area is A_2 above the orifice of area A_1. The flow through the orifice will be weighted by the ratio A_1/A_2 as well as by the factor 1/c^2 and the fluid flow in volume per second becomes

Which Way Will Water Flow Down the Bathtub Drain?


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