Hazen-Williams Equation: What is it?

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The Hazen-Williams equation is a formula for calculating how much the ambient pressure drops in a fluid as it flows through a pipe due to friction with the inside surface of the pipe, the inside diameter of the pipe, and the flow rate for the fluid . This flow reduction was commonly used by engineers in the past when fluid flow was turbulent, as it provided a good approximation of velocity loss. The formula is relatively simple, but has several factors limiting its effective use and the advent of personal computers has made it largely obsolete.

Fluid transfer water piping systems all have so-called pressure drop, which is a sum of the elevation, velocity and pressure loss of the fluid as it moves due to friction within the fluid , as it interacts with the pipe wall and other pipe obstructions and as a side effect of the turbulence these interactions cause. The pressure drop is also based on the friction factor present, which is calculated from the type of pipe material used and the flow rate of the fluid. Friction factors can range from 80 to 130 or more, and this variability makes the Hazen-Williams equation only a rough calculation for pressure drop.

Typical limiting factors in calculating volumetric flow using the Hazen-Williams equation are accepted by engineers. These factors include the limitation that the fluid must have a viscosity of at least 1.13 centistokes, which is what water exhibits at an ambient temperature of 60° Fahrenheit (15.5° Celsius). The pipe must also have a diameter greater than 2 inches (5.08 centimeters) and the flow rate cannot exceed 10 feet per second (3.05 meters per second).

There are two formulas typically used in the Hazen-Williams equation, one based on empirical or experimental data and imperial units, and one that uses standard international units. The imperial formula is written as hf = 0.002083 L (100/C)1.85 x (gpm1.85/d4.8655) where “hf” equals the pressure drop determined in feet, “L” represents the length of pipe measured from feet and “C” is the coefficient of friction for the type of pipe material. “Gpm” represents gallons per minute calculated as US gallons of flow through the pipe and “d” represents the initial inside diameter of the pipe before buildup or corrosion occurs on the pipe wall. Here, the value of 100 in the formula represents a dimensionless Hazen-Williams factor.

The standard international units formula is just another way to calculate pressure drop, also known as frictional pressure drop, in metric units. It is denoted as ΔP = 1.1101 x 1010 (Q/C) 1.85 1/D4.87 where “ΔP” is the pressure drop in kiloPascals per meter, “Q” is the fluid flow rate in cubic meters per hour, “D ” is the inside diameter of the pipe and “C” here is the dimensionless Hazen-Williams factor. While using the standard of 100 for the Hazen-Williams factor is routine, if the pipe is 10 to 15 years old, a value of 75 can often be substituted due to mineral deposits and corrosion in the pipe which increase the level of friction and turbulence.

The use of the Hazen-Williams equation in the absence of more accurate computer calculations is still possible for many types of liquid flow systems. It can be used for fire sprinkler systems for irrigation systems, or water supply networks for buildings or municipalities. This is because there are now several established friction factors for the types of pipe material that are entered into the formula, such as brass and copper pipe at 130, polyvinyl chloride (PVC) pipe at 150, steel pipe at 120, and more. Each value also has some leeway as it is an approximation based on the presence of deformations in the internal surface of the pipe which accumulate over time as the pipe ages. Where more accurate values ​​for pressure drop are needed or a fluid flow is being measured for a substance other than water, the Darcy-Weisbach equation is used, which uses a more accurately calculated coefficient of friction from a diagram Moody’s that incorporates Reynolds numbers.

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