Water Tower Specifications

by Andrew Tamasy

Submitted : Fall 2014

Specifications are needed the begin construction on a new water tower. It is to be erected 140 ft high (From the base to the top of the tank). The tank is a horizontally oriented ellipsoid and with a diameter of 40ft and a height of 30ft. The specs. needed are:

1.  How many gallons of water can this tank hold at full capacity?

2.  How many gallons of paint are required to cover the tank?

3.  How much water pressure is exerted on the valve when the tank is at full capacity? When it is at half capacity?

            This problem is focused on a hypothetical water tower. The questions build off of one another. First we must find the amount of water contained in the tank. The first step is to derive an equation for our elliptical cross section. Once this is known the first question can be answered using integral calculus. “The disk method” can provide the volume in cubic feet which can be converted to gallons of water.

The second question can be computed with the surface area formula. We must find the length of the arc between one of the sections.  This arc will then be rotated to find the total surface area. We can then estimate the amount of paint required assuming one gallon can cover approximately 400 square feet of material.

Finally the last question involves the use of a physics equation of hydrostatic pressure. This physical property of any fluid says that its standing pressure is solely based on the density of the fluid and the height of the column. This has nothing to do with how the shape or how wide the tank is. The overall height determines the pressure. 

                Using these methods we find that this hypothetical water tower can hold 188005.95 gallons of water, approximately 11 gallons of paint are required to cover the surface of the tank, and at its full capacity this tank has a pressure reading of 38.7 PSI.

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