The first step is to determine the friction factor (f). Darcy-Weisbach Friction Loss EquationĪpplying the Darcy-Weisbach equation is a little convoluted because it not only has multiple variables (as shown by Figure 2), but determining the value for some of these variables is not a simple matter. In medium and high pressure mist systems, where pressures can be anywhere from 175 psi to well in excess of 1,000 psi, the higher pressures and velocities can impact the physical properties of the water enough that the Darcy-Weisbach equation will need to be used. Regarding water mist systems, low pressure systems (up to 175 psi) can also still be calculated using the Hazen-Williams formula. Even in foam-water solutions as high as six percent AR-AFFF (alcohol resistant aqueous film-forming foam concentrates), the Hazen-Williams equation can still be used. In the case of foam systems, once the foam concentrate has been appropriately proportioned with water downstream of the foam proportioning device, it is not necessary to use the Darcy-Weisbach formula for hydraulic calculations. So, when friction loss needs to be calculated for other fire protection fluids such as foam concentrate, anti-freeze systems exceeding 40 gallons in capacity, or for certain high pressure mist systems, the Darcy-Weisbach formula should be applied instead. The main point to understand is that when the fire protection fluid’s properties are dissimilar to those of water the Hazen-Williams formula is no longer valid. ![]() Having said that, don’t leap to the false conclusion that for other temperatures, you should not use the Hazen-Williams equation. ![]() It is assumed when using the Hazen-Williams formula that the fluid is water at room temperature. However, the Hazen-Williams equation has its limits since it does not contain a variable for density, viscosity, or temperature. The Hazen-Williams formula (see Figure 1) is used when doing sprinkler calculations by hand, and it is used by computer-based hydraulic calculation software. ![]() It is the fundamental equation used in water-based fire protection for calculating the friction loss of water flowing through pipe. Any seasoned fire sprinkler designer or fire protection engineer should be familiar with the Hazen-Williams equation.
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