Fluid statics is the study of what happens in a fluid when it is not moving. One of the most basic elements of fluid statics is the pressure head in a fluid. Pressure head is the height within a specific fluid that yields a given pressure difference. Mathematically, it is h = (p2 - p1)/gamma, where the Greek letter "gamma" refers to the specific weight of the fluid, which is the density of the fluid multiplied by the acceleration of gravity.
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Decide on a pressure difference to use for your calculations. This value will either be given or it will be measured with a pressure gauge suitable for the fluid you are analysing. You may have to measure the pressure at one point and then measure at another point and calculate the difference. Example: p1 = 0.907 Kilogram per square inch (psi) p2 = 10 psi (p2-p1) = 8 psi
Calculate the specific weight (gamma) for your fluid. For some fluids, you will be able to look this value up on an engineering table of liquids or gases. If not, you will have to look up the density (rho) for the fluid and multiply by the acceleration of gravity. For water: rho = 1.94 slugs/ft^3 g = 32.2 slugs/ft^2 gamma = rho * g = 28.3kg/ft^3
Convert units as necessary to match. In this example, pressure is given in psi, but all the other values are in terms of feet. Here you would convert psi to pounds per square foot (psf). Example: 8 psi * 144 in^2/ft^2 = 1152 psf
Divide pressure difference by specific gravity to get pressure head. So in our example: 1152 psf / 28.3kg/ft^3 = 18.46ft
Tips and warnings
- This equation only works when you can consider density to be a constant. If you are using a highly compressible fluid or you are using distances in the hundreds or thousands of feet depending on the fluid, you must use a much more complicated equation to account for density changes.
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