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8.1: Are You At a Loss?

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    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.


    Figure \(\PageIndex{1}\)

    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


    Solve the following pressure and force related problems.

    This page titled 8.1: Are You At a Loss? is shared under a CC BY license and was authored, remixed, and/or curated by Mike Alvord (ZTC Textbooks) .

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