8.1: Are You At a Loss?

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Pressure

Pressure is the amount of force that is “pushing” on a specific unit area. Well, what does this mean? When you turn on your water faucet or shower you feel the water flowing out, but why is it flowing out? Water flows through pipes and out of faucets because it is under pressure. It could be that a pump is turned on in which case the pump and motor are providing the pressure. More commonly, the pressure is being provided by water being stored at a higher elevation. Pressures are usually expressed as pounds per square inch (psi), but they can be expressed as pounds per square foot or pounds per square yard as well. The key is that the force is expressed per unit area.

Typically, water operators will measure pressures with gauges and express the unit answer as psig. The “g” is this case represents gauge. However, it is also common to express pressure in feet. Feet represent the height of the water in relation to the location that the pressure is being measured.

There are two commonly used factors to convert from feet to psi and vice versa. For every foot in elevation change, there is a 0.433 change in psi. Conversely, for every one psi change, there is a 2.31 foot in elevation change.

1 foot = 0.433 psi

2.31 feet = 1 psi

As previously discussed, the density or weight of water is approximately 8.34 pounds per gallon. Using this conversion factor, the actual force exerted by the water can be calculated.

Example

The pressure at the bottom of both tanks in this example is the same. This is due to the fact that the heights are equivalent and pressures are based solely on elevation. However, the force exerted on the bottom of the tanks is dramatically different. The “force” is based on the actual weight of the water.

Pressure = 30 ft x 0.433 psi/ft = 13 psi or 30 ft ÷ 2.31 ft/psi = 13 psi
Force = the volume of water (in gallons) in each tank multiplied by 8.34 lb/gal
Left Tank = 0.785 x 10 ft x 10 ft x 30 ft x 7.48 = 17,615 gallons
- 17,615 gallons x 8.34 lb/gal = 146,912 pounds of force
Right Tank = 0.785 x 40 ft x 40 ft x 30 ft x 7.48 = 281,846 gallons
- 281,846 gallons x 8.34 lb/gal = 2,350,599 pounds of force

Exercises

Solve the following pressure and force related problems.

What is the pressure at the bottom of a 30 ft tank if the tank is half full?
A 28-foot tall tank sits on a 75-foot tall hill. Assuming the tank is full, what is the pressure at the bottom of the hill?
The opening of a 2 1/2” fire hydrant nozzle has a pressure of 135 psi. What is the corresponding force in pounds?
A home sits at an elevation of 1,301 ft above sea level. The base of a water tank that serves the home sits at an elevation of 1,475 ft above sea level. The tank is 35 feet tall and ¾ full. What is the pressure in psi at the home?
Two houses are served by a nearby water storage tank. House A is 55 ft above House B which sits at 725 ft above sea level. The base of the tank sits at 855 ft above sea level. The low water level in the tank is at 7.5 ft. At the low level, will House A meet the minimum pressure requirements of 35 psi?
House A sits at an elevation of 975 ft. Another house (B) needs to be built 75 ft below House A. At what elevation should the tank be built in order to give House B the maximum pressure of 130 psi?
A flowing pipeline has a pressure of 98 psi and a corresponding force of 4,924 pounds. What is the diameter of the pipe?