For the Hazen–Williams equation, we need the values of conversion factor kkk, roughness coefficient CCC, hydraulic radius RRR, and the slope of the energy line SSS.

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🙋 In the Advanced mode of the pipe flow calculator, you can find or input other parameters such as area, perimeter, hydraulic radius, and the slope.

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To calculate the hydraulic radius RRR, divide the cross-sectional area (A=π⋅r2) (A = \pi \cdot r^2)(A=π⋅r2) of the pipe by the wetted perimeter (P=2⋅π⋅r)(P = 2 \cdot \pi \cdot r)(P=2⋅π⋅r):

Use our pipe flow calculator to determine the velocity and flow rate of water that flows by gravity. This tool employs the gravitational form of the Hazen–Williams equation to calculate velocity in a pipe.

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The pipe roughness coefficient (C) is dependent on the material. Below you can find the values for this coefficient for different materials:

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These same values are included in the pipe flow calculator. By changing the Material variable of the calculator, you can see different values for the pipe Roughness coefficient.

Notice that the Hazen–Williams equation has some constraints (besides water only), making the results relatively accurate only for:

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This empirical equation, exclusively applicable to water, allows calculating the velocity or the head loss of a gravity flow. If you'd like to learn more about the Hazen–Williams equation's parameters and how to calculate water flow rate and velocity for yourself, we invite you to continue reading.

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This equation only applies to water, and it calculates the velocity of the water by relating the geometric properties of the pipe and the slope of the energy line. The Hazen–Williams equation or pipe velocity equation is given by:

A numerical example is the best way to understand how to use the Hazen–Williams equation to determine the velocity and flow of water. Assume we need to calculate the velocity and flow rate in a system with the following characteristics:

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The Hazen–Williams equation is an empirical formula used to calculate water's velocity in a gravity-fed system. In contrast to Darcy–Weisbach's equation, Hazen–Williams has the advantage that it doesn't require an iterative calculation or guessing the friction factor or Reynolds' number.

A pipe made of steel, with a diameter of 2.5 inches, with a length of 18 feet, and a difference in heights of 3 feet. Let's do the math:

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In the case of gravity-fed systems, only gravity is used to transport water (or other fluid) from a source to a final application. The only energy available in these systems is supplied by the difference in heights between the source, usually an atmospheric tank placed at a higher altitude and the system's lowest altitude point. In these cases, the flow of a fluid is referred to as gravity flow.

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The flow in a piping system is largely determined by the available energy and the losses in the pipes. This energy could be provided by gravity or/and by a pump.

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