# Williams Hazens Equation of Pressure Drop

## The Hazen-Williams equation can be used to calculate pressure drop (psi) in pipes or tubes due to friction

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### Hazen-Williams Formula in Imperial Units

The Hazen-Williams formula for calculating head loss in pipes and tubes due to friction can be expressed as:

P_{d}= 4.52 q^{1.85 }/ (c^{1.85}d_{h}^{4.8655}) (1)

where

P_{d}= pressure drop (psi/ft pipe)

c= design coefficient determined for the type of pipe or tube - the higher the factor, the smoother the pipe or tube

q= flow rate (gpm)

d_{h}= inside hydraulic diameter (inch)

**Note!** The Hazen-Williams formula gives accurate head loss due to friction for fluids with kinematic viscosity of approximately 1.1 cSt. More about fluids and kinematic viscosity.

The results for the formula is acceptable for cold water at *60 ^{o}F (15.6 ^{o}C)* with kinematic viscosity

*1.13 cSt.*For hot water with a lower kinematic viscosity

*(0.55 cSt at 130*the error will be significant.

^{o}F (54.4^{o}C))Since the Hazen Williams method is only valid for water flowing at ordinary temperatures between *40 to 75 ^{o}F*, the Darcy Weisbach method should be used for other liquids or gases.

### Online Hazens-Williams Calculator - Imperial Units

The calculator below can used to calculate the head loss:

### The Design Factor - *c*

The design factor is determined for the type of pipe or tube used:

- The c-value for
**cast iron**and**wrought iron pipes or tubes**ranges from*80 to 150,*with average value*130*and design value*100*. - The c-value for
**copper, glass or brass****pipes or tubes**ranges from*120 to 150*, with average value*140*and design value*140*. - The c-value for
**cement lined steel or iron pipes**has average value of*150*and design value*140*. - The c-value for
**epoxy and vinyl ester**pipes can be set to*150*.

### Hazen-Williams Formula in Metric Units

h = 10.67 q^{1.85 }/ (c^{1.85}d_{h}^{4.8655}) (1)

where

_{h}= head loss per unit pipe (m_{h2o}/m pipe)

c= design coefficient determined for the type of pipe or tube - the higher the factor, the smoother the pipe or tube

q= flow rate (m^{3}/s)

d_{h}= inside hydraulic diameter (m)

Pressure drop can be calculated from the head loss by multiplying head loss with the specific weight of water:

*p = h γ*

*where *

*p = pressure loss (N/m ^{2}, Pa)*

*γ = specific weight (N/m ^{3})*

Specific weight of water at *4 ^{o}C* is

*9810 N/m*

^{3}.

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