Comparison of Head Loss Computed by Hazen-Williams and Darcy-Weisbach Equations

How do the head loss computed by the Hazen-Williams equation compare to the head loss computed by the Darcy-Weisbach equation?

Is there a significant difference between the two calculations?

Answer:

The head loss computed by the Hazen-Williams equation is very close to the head loss computed by the Darcy-Weisbach equation for a 12-inch diameter cast iron pipe one mile in length with a flow rate of 1,200 gallons per minute.

Although there are no elevations or pressures given, these values are not needed to determine the head loss in the pipe. Setting up FlowMaster to solve for the "Elevation at 1" allows us to use zero elevation and zero pressure assumptions and fill in the rest of the pipe characteristics.

For the Hazen-Williams equation, a C coefficient of 130 is assumed, resulting in 18.8 ft of head loss. This value agrees with the computed 18.8-ft elevation at point 1. On the other hand, using Darcy-Weisbach, a roughness height of 0.00085 ft is assumed, which results in a head loss of 18.9 ft. The difference between the two calculations is only 0.1 ft.

Therefore, the head loss computed by the Hazen-Williams equation is very close to the head loss computed by the Darcy-Weisbach equation. This shows that both equations provide similar results for the given pipe characteristics and flow rate.