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3.2: Calculating Pressure

  • Page ID
    11933
  • Pressure is critical because it is what moves water from one point to another. A common constraint when designing a rainwater harvesting system is providing enough pressure for the end use. For systems with low roofs or challenging topography (e.g. the catchment area is in a depression), sometimes sufficient pressure can only be obtained with a pump. Pressure from the vertical height of water, also called head, can be found from the following equation:

    \[Pressure=\frac{Force}{Area}\]

    The weight density of water is \(62.4 \frac{lb}{ft^3}\) , which is force/volume. Knowing that Volume is equal to \(Area * height (V=A*h)\), we can convert that weight density into the head by multiplying it by the vertical height of the water.

    \[Water Pressure\;(P)=\frac{Force}{Area}=62.4\frac{lb}{ft^3}*height\;of\;water\]

    Example \(\PageIndex{1}\)

    Find the water pressure from water that is 1 foot high:

    Solution

    \[P=62.4\frac{lb}{ft^3}*1\;ft=62.4\frac{lb}{ft^2}\]

    Therefore, the pressure from 1 foot of water is \(62.4 \frac{lb}{ft^2}\). Unfortunately, you won’t usually find pressure measured in these units. To convert \(\frac{lb}{ft^2}\) into the more conventional psi (pounds per square inch), use the fact that 1 foot is equal to 12 inches:

    \[P=62.4\frac{lb}{ft^2}*\frac{1\;ft}{12\;in}*\frac{1\;ft}{12\;in}=0.433\frac{lb}{in^2}=0.433\;psi\]

    This shows that the pressure from 1 foot of water is 0.433 psi, which is the basis of the commonly used conversion:

    \[0.433\; psi\; for\; every\; vertical \;foot \;of \;water\]

     

    You can use either process to find the pressure that is due to the vertical height of water.

    Example \(\PageIndex{2}\)

    Solve for the pressure exerted by 20 feet of water (e.g., at the bottom of a full 20-ft-tall tank): 

    Solution

    \[P=62.4\frac{lb}{ft^2}*20\;ft = 1,248\frac{lb}{ft^2}*\frac{1\;ft}{12\;in}*\frac{1\;ft}{12\;in}=8.67\frac{lb}{in^2}=8.67\;psi\]

    Or

    \[P=\frac{0.433\;psi}{ft\;of\;water}*20\;ft=8.66\;psi\]

    Therefore, 20 vertical feet of water exerts a pressure of 8.66 psi. That pressure is sufficient for hand washing, watering, and most drip irrigation lines.

     

    In addition, keep in mind the differences between static pressure and dynamic pressure. Static pressure refers to the pressure when the water is not flowing. Dynamic pressure refers to the pressure when the water is flowing. Static pressure is always higher than dynamic pressure because friction on the moving water reduces the pressure available at the bottom of the system. If you determine the static pressure to be just enough to get from one point to another, there actually might not be enough to get there because of dynamic pressure loss when the water is moving. The longer the pipe and the smaller the diameter, the more loss there will be.