Worked problem

Sprinkler Flow from K-Factor and Pressure

Use Q = K × √P to find the flow from a K-5.6 sprinkler at 7 psi and the density it delivers over a 130 ft² coverage area.

Fire Protection · Last reviewed

Given

A standard-response pendent sprinkler with K-factor 5.6 (GPM per √psi) operates at a residual pressure of 7 psi. Its assigned coverage area is 130 ft².

Find

The discharge in GPM and the resulting density in GPM per square foot.

Solution

Q = K × √P
  1. Q = 5.6 × √7 = 5.6 × 2.646 = 14.8 GPM.
  2. Density = Q ÷ coverage area = 14.8 ÷ 130 = 0.114 GPM/ft².
  3. Check the other direction: the pressure needed for 15 GPM is P = (15 ÷ 5.6)² = 7.2 psi.

Answer

14.8 GPM | 0.114 GPM/ft²

Common mistakes

  • Taking the square root of the wrong quantity or forgetting it. Flow rises with the square root of pressure, not in proportion to it.
  • Using the minimum pressure from a table for the remote sprinkler but not carrying that pressure through the pipe network. A hydraulic calculation adds friction loss and elevation along the pipe for each sprinkler in the design area.
  • Treating the design density as a single-sprinkler result. The design criteria set a density over a design area, and the standard governs the minimum.

Try three variations

  1. K = 8.0 at 12 psi: Q = 8.0 × √12 = 27.7 GPM.
  2. K = 11.2 at 7 psi: Q = 11.2 × √7 = 29.6 GPM.
  3. The pressure needed for 20 GPM from a K-5.6 sprinkler: P = (20 ÷ 5.6)² = 12.8 psi.

A larger K-factor gives more flow at low pressure, which is why it is used where the available pressure is limited. A K-11.2 sprinkler at 7 psi delivers about as much as a K-5.6 sprinkler at 28 psi.

Related tools and labs

Calculators, labs and simulators are part of the All-Access Pass.

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Questions

What does the K-factor represent?

It is the discharge coefficient of the sprinkler orifice. A larger K gives more flow at the same pressure.

Which standard governs sprinkler design?

NFPA 13 in the United States, which sets design densities, areas, spacing and the hydraulic calculation method. Local authorities may add requirements.

Is there a minimum operating pressure?

The sprinkler listing and the installation standard set a minimum. Many designs use 7 psi or more at the most remote sprinkler.

What is the difference between standard-response and quick-response sprinklers?

Quick-response sprinklers have a thermal element that reacts faster, so they open sooner in a fire. The standard says where each type is required or allowed.

How does a hydraulic calculation continue past the first sprinkler?

The flow from each sprinkler, and the friction and elevation losses in each pipe section, are added back toward the water supply, to find the total flow and pressure the system demands.

Educational material. Examples use simplified, hypothetical inputs and are not a design, a construction document or professional engineering advice. Confirm requirements with the codes and standards adopted where the work is built and with a licensed engineer.

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