# Williams Hazens Pressure Drop Equation

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

### Hazen-Williams Formula in Imperial Units

The Hazen-Williams equation 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 (inches)

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

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

*1.13 cSt.*For hot water with 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 (4 - 14 ^{o}C)*, the Darcy Weisbach equation should be used for other liquids or gases.

### Online Hazens-Williams Calculator - Imperial Units

The calculator below can used to calculate head loss in imperial units:

l- pipe or tube length (ft)

c- design coefficient determined for the type of pipe or tube

q- flow rate (gal/min)

d_{h}- hydraulic diameter (inch)

### 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}) (2)

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 in Pa can be calculated from the head loss by multiplying the 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}.