Hazen–Williams equation
Material C Factor low C Factor high
Asbestos-cement 140 140
Cast iron new 130 130
Cast iron 10 years 107 113
Cast iron 20 years 89 100
Cast iron 30 years 75 90
Cast iron 40 years 64 83
Cement-Mortar Lined Ductile Iron Pipe 140 140
Concrete 100 140
Copper 130 140
Steel 90 110
Galvanized iron 120 120
Polyethylene 140 140
Polyvinyl chloride ( PVC ) 150 150
Fibre-reinforced plastic ( FRP ) 150 150
General form
Henri Pitot discovered that the velocity of a fluid was proportional to the square root of its head in the early 18th century . It takes energy to push a fluid through a pipe , and Antoine de Chézy discovered that the hydraulic head loss was proportional to the velocity squared . [ 4 ] Consequently , the Chézy formula relates hydraulic slope S ( head loss per unit length ) to the fluid velocity V and hydraulic radius R : V = C R S = C R 0.5 S 0.5 { \displaystyle V=C { \sqrt { RS } } =C\ , R^ { 0.5 } \ , S^ { 0.5 } } The variable C expresses the proportionality , but the value of C is not a constant . In 1838 and 1839 , Gotthilf Hagen and Jean Léonard Marie Poiseuille independently determined a head loss equation for laminar flow , the Hagen–Poiseuille equation . Around 1845 , Julius Weisbach and Henry Darcy developed the Darcy–Weisbach equation . [ 5 ] The Darcy-Weisbach equation was difficult to use because the friction factor was difficult to estimate . [ 6 ] In 1906 , Hazen and Williams provided an empirical formula that was easy to use . The general form of the equation relates the mean velocity of water in a pipe with the geometric properties of the pipe and slope of the energy line . V = k C R 0.63 S 0.54 { \displaystyle V=k\ , C\ , R^ { 0.63 } \ , S^ { 0.54 } } where : V is velocity k is a conversion factor for the unit system ( k = 1.318 for US customary units , k = 0.849 for SI units ) C is a roughness coefficient R is the hydraulic radius S is the slope of the energy line ( head loss per length of pipe or hf/L ) The equation is similar to the Chézy formula but the exponents have been adjusted to better fit data from typical engineering situations . A result of adjusting the exponents is that the value of C appears more like a constant over a wide range of the other parameters . [ 7 ] The conversion factor k was chosen so that the values for C were the same as in the Chézy formula for the typical hydraulic slope of S=0.001 . [ 8 ] The value of k is 0.001−0.04 . [ 9 ] Typical C factors used in design , which take into account some increase in roughness as pipe ages are as follows : [ 10 ]
The Hazen-Williams equation is an empirical relationship which 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 such as fire sprinkler systems, water supply networks, and irrigation systems. It is named after Allen Hazen and Gardner Stewart Williams. 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.