Hazen–Williams equation

  1. Pages with script errors
  2. All articles with dead external links
  3. Articles with dead external links from October 2010
  4. Articles with invalid date parameter in template
  5. Use dmy dates from September 2010
  6. Equations of fluid dynamics
  7. Piping
  8. Plumbing
  9. Hydraulics
  10. Irrigation


The Hazen–Williams equation is an empirical formula 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[1] such as fire sprinkler systems[2], 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.[3]

General form

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.

\[V = k\, C\, R^{0.63}\, S^{0.54}\]

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)

Typical C factors used in design, which take into account some increase in roughness as pipe ages are as follows:[4]

Material C Factor low C Factor high Reference
Asbestos-cement 140 140 -
Cast iron 100 140 -
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) 130 130 -
Fibre-reinforced plastic (FRP) 150 150 -

Pipe equation

The general form can be specialized for full pipe flows. Taking the general form \[V = k\, C\, R^{0.63}\, S^{0.54}\] and exponentiating each side by \(1/0.54\) gives (rounding exponents to 2 decimals) \[V^{1.85} = k^{1.85}\, C^{1.85}\, R^{1.17}\, S\] Rearranging gives \[S = {V^{1.85} \over k^{1.85}\, C^{1.85}\, R^{1.17}} \] The flow rate Q = V A, so \[S = {V^{1.85} A^{1.85}\over k^{1.85}\, C^{1.85}\, R^{1.17}\, A^{1.85}} = {Q^{1.85}\over k^{1.85}\, C^{1.85}\, R^{1.17}\, A^{1.85}} \] The hydraulic radius R (which is different from the geometric radius r) for a full pipe of geometric diameter d is d/4; the pipe's cross sectional area A is \(\pi d^2 / 4\), so \[S = {4^{1.17}\, 4^{1.85}\,Q^{1.85}\over \pi^{1.85}\,k^{1.85}\, C^{1.85}\, d^{1.17}\, d^{3.70}} = {4^{3.02}\,Q^{1.85}\over \pi^{1.85}\,k^{1.85}\, C^{1.85}\, d^{4.87}} = { 4^{3.02} \over \pi^{1.85}\,k^{1.85}} {Q^{1.85}\over C^{1.85}\, d^{4.87}} = { 7.916 \over k^{1.85}} {Q^{1.85}\over C^{1.85}\, d^{4.87}} \]

U.S. customary units (Imperial)

When used to calculate the pressure drop using the US customary units system, the equation is: \[P_d=\frac{4.52\quad L\quad Q^{1.85}}{C^{1.85}\quad d^{4.87}}\]

where:

Pd = pressure drop over a length of pipe, psig (pounds per square inch gauge pressure)

L = length of pipe, ft (feet)

Q = flow, gpm (gallons per minute)

d = inside pipe diameter, in (inches)

SI units

When used to calculate the pressure drop with the International System of Units, the equation becomes:[5]

\[h_f = \frac{10.67\quad L \quad Q^{1.85}}{C^{1.85}\quad d^{4.87}}\]

where:

  • hf = pressure loss over a length of pipe, m (head pressure)
  • L = length of pipe, m (meters)
  • Q = volumetric flow rate, m3/s (cubic meters per second)
  • d = inside pipe diameter, m (meters)

See also

References

  1. ↑ "Hazen–Williams Formula". http://docs.bentley.com/en/HMFlowMaster/FlowMasterHelp-06-05.html. Retrieved 2008-12-06.
  2. ↑ "Hazen–Williams equation in fire protection systems". Canute LLP. 27 January 2009. http://www.canutesoft.com/index.php/Basic-Hydraulics-for-fire-protection-engineers/Hazen-Williams-formula-for-use-in-fire-sprinkler-systems.html. Retrieved 2009-01-27.[dead link]
  3. ↑ Script error
  4. ↑ Engineering toolbox Hazen–Williams coefficients
  5. ↑ "Comparison of Pipe Flow Equations and Head Losses in Fittings" (PDF). http://rpitt.eng.ua.edu/Class/Water%20Resources%20Engineering/M3e%20Comparison%20of%20methods.pdf. Retrieved 2008-12-06.
  • Hazen, A.; Williams, G. S. (1920), Hydraulic Tables (3rd ed.), New York: John Wiley and Sons
  • Watkins, James A. (1987), Turf Irrigation Manual (5th ed.), Telsco
  • Finnemore, E. John; Franzini, Joseph B. (2002), Fluid Mechanics (10th ed.), McGraw Hill
  • Mays, Larry W. (1999), Hydraulic Design Handbook, McGraw Hill

External links

es:Ecuación de Hazen-Williams fa:معادله هیزن ویلیامز fr:Équation de Hazen-Williams he:משוואת היזן ויליאמס ja:ヘーゼン・ウィリアムスの式 ru:Формула Хазена — Вильямса


...