# 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:

Pd = 4.52  q1.85 / (c1.85 dh4.8655)                                 (1)

where

Pd = 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)

dh = 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 oF (15.6 oC) with kinematic viscosity 1.13 cSt. For hot water with lower kinematic viscosity (0.55 cSt at 130 oF (54.4 oC)) the error will be significant.

Since the Hazen Williams method is only valid for water flowing at ordinary temperatures between 40 to 75 oF (4 - 14 oC), 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)

dh - 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  q1.85 / (c1.85 dh4.8655)                                       (2)

where

h = head loss per unit pipe (mh2o/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 (m3/s)

dh = 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/m2, Pa)

γ = specific weight (N/m3)

Specific weight of water at 4oC is 9810 N/m3.

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