Calculating the Flow Rate of a Water Feature

by Tyler McBee

Submitted : Fall 2013

In order to find the flow rate of the pump that is pumping water into the 6in header, the flow rates of the spouts need to be found and added together since liquids are non-compressible and the input is equal to the output. Flow rate is a product of a fluid’s velocity and the cross sectional area of the container, in this case, the spouts. The areas are given in the problem statement, but the velocities for each spout are not, so, to find those missing velocities, the height of the water columns shooting out of the spouts need to be used. Knowing that the acceleration due to gravity on Earth is 32.2ft/s², simple integration calculus can be used to create an equation for velocity and another integration may be done for the position equation. With the velocity of only one spout, multiplied by that spout’s area, the flow rate can be found for the pump since, due to the header being oversized, the pressure loss between spouts in negligible and can be ignored and the flow rates for the spouts are all equal.

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