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.

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.

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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🙋 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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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.

Viscosity and density of water are affected by temperature. You can take a look at our density calculator to find out more.

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Fastwarm® 22mm 2 port motorised valves are used to zone your homes heating. Allowing independent control of your underfloor heating system and homes central heating. Fastwarm® 22mm Motorised valve, two port zone normally closed, 230 V AC operation with microswitch. Head assembly fixed. Industry standard synchronous motor. Is used for a 'S' plan valve to control your heating system independently using a 3 amp switch.

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Delivery outside the mainland UK may be arranged by prior agreement. You will be notified of the amount of the charge for this service and will at that point have to make a decision whether you wish to proceed wth your order.

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

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

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:

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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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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.

Fastwarm® 22mm 2 port motorised valves are used to zone your homes heating. Allowing independent control of your underfloor heating system and homes central heating.

Important: Our deliveries rely on third party couriers, so, whilst we make every effort to deliver your order on the specified date and time, unfortunately there may be occasions when this will not be possible due to external influences. Due to this we strongly recommend you ensure you have received your order before any tradespeople/builders are scheduled to commence work.

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.

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):

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.