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The Hazen–Williams equation is an empirical relationship that relates the flow of water in a pipe with the physical properties of the pipe and the pressure drop caused by friction. It is used in the design of water pipe systems [ 1 ] such as fire sprinkler systems , [ 2 ] water supply networks , and irrigation systems.
where is the density of the fluid, is the average velocity in the pipe, is the friction factor from the Moody chart, is the length of the pipe and is the pipe diameter. The chart plots Darcy–Weisbach friction factor f D {\displaystyle f_{D}} against Reynolds number Re for a variety of relative roughnesses, the ratio of the mean height of ...
PO gpm = pump output in gpm (gallons per minute) 1 gallon = 0.0238095238 barrels; ID 2 = inside diameter of the wellbore or casing, squared; OD 2 = outside diameter of the drill pipe or tubing, squared; 1029.4 = A conversion factor constant used to calculate the volume between the outside of a tube within the inside of another tube, using barrels.
The flow rate can be converted to a mean flow velocity V by dividing by the wetted area of the flow (which equals the cross-sectional area of the pipe if the pipe is full of fluid). Pressure has dimensions of energy per unit volume, therefore the pressure drop between two points must be proportional to the dynamic pressure q.
r = radius of the pipe (for a pipe of circular section, the internal radius of the pipe). v = mean velocity of fluid flowing through the pipe. A = cross sectional area of the pipe. In long pipes, the loss in pressure (assuming the pipe is level) is proportional to the length of pipe involved.
Units of n are often omitted, however n is not dimensionless, having dimension of T/L 1/3 and units of s/m 1/3. R h is the hydraulic radius (L; ft, m); S is the stream slope or hydraulic gradient , the linear hydraulic head loss loss (dimension of L/L, units of m/m or ft/ft); it is the same as the channel bed slope when the water depth is constant.