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The Hazen–Williams equation has the advantage that the coefficient C is not a function of the Reynolds number, but it has the disadvantage that it is only valid for water. Also, it does not account for the temperature or viscosity of the water, [ 3 ] and therefore is only valid at room temperature and conventional velocities.
By setting the coefficient k to K, the flow rate Q to I and the exponent n to 1, the Hardy Cross method can be used to solve a simple circuit. However, because the relation between the voltage drop and current is linear, the Hardy Cross method is not necessary and the circuit can be solved using non-iterative methods.
The most common equation used to calculate major head losses is the Darcy–Weisbach equation. Older, more empirical approaches are the Hazen–Williams equation and the Prony equation. For relatively short pipe systems, with a relatively large number of bends and fittings, minor losses can easily exceed major losses.
Allen Hazen derived an empirical formula for approximating hydraulic conductivity from grain-size analyses: = where Hazen's empirical coefficient, which takes a value between 0.0 and 1.5 (depending on literature), with an average value of 1.0. A.F. Salarashayeri & M. Siosemarde indicate C is usually between 1.0 and 1.5, with D in mm and K in cm/s.
This can be used to calculate mean values (expectations) of the flow rates, head losses or any other variables of interest in the pipe network. This analysis has been extended using a reduced-parameter entropic formulation, which ensures consistency of the analysis regardless of the graphical representation of the network. [ 3 ]
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c = discharge coefficient (unitless). This is usually 1.0 if using a diffuser. If using a wand to measure the stagnation pressure, the coefficient value depends on the shape of the flow hydrant orifice. A smooth and rounded outlet has c=0.9, a square and sharp outlet has c=0.8, and a square outlet which projects into the barrel has c=0.7.
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