Challenge

Challenge: Can You Add Two Sprinkler Pressures?

An engineer adds the pressures of two parallel sprinklers to get 14 psi. Find the mistake and how flow and pressure behave at a junction.

Fire Protection · Last reviewed

Two identical sprinklers (K = 5.6 gpm/psi^½) are connected in parallel to one junction, and each needs 7.0 psi to discharge. An engineer calculates the supply requirement at the junction like this:

Pressure = 7.0 + 7.0 = 14.0 psi Flow = 5.6 × √14.0 = 21.0 gpm
  • Each sprinkler: K = 5.6 gpm/psi^½, needs 7.0 psi at its inlet.
  • The two sprinklers branch from the same junction through short pipes with negligible friction.

Your task: find the mistakes, calculate the correct pressure and total flow at the junction, and say what changes if each short pipe loses 0.5 psi to friction.

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There are two mistakes. Pressures do not add across parallel branches, and the flow was not found from the individual sprinklers.

Parallel branches from one junction share the same pressure, because the junction is a single point. Each sprinkler needs 7.0 psi, so the junction needs 7.0 psi, not 14.0 psi. It is the flows that add.

Each sprinkler: Q = 5.6 × √7.0 = 14.82 gpm | Total: 2 × 14.82 = 29.6 gpm at 7.0 psi

The engineer overstated the pressure (14.0 against 7.0 psi) and understated the flow (21.0 against 29.6 gpm), because the single-sprinkler formula was applied to the pair at the wrong pressure.

With 0.5 psi of friction in each short pipe, each sprinkler still needs 7.0 psi at its inlet, so the junction pressure is 7.0 + 0.5 = 7.5 psi. The flows stay 14.82 gpm each, so the total remains 29.6 gpm, now at 7.5 psi.

Pressure losses add along a path in series. Flows add where paths meet at a junction. If the two sprinklers were different, the one that needs the higher pressure would set the junction pressure, and the other would receive more than its minimum flow.

Check your reasoning: did you ask which quantity is shared at the junction (pressure) and which quantity is summed (flow)?

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Questions

Where do pressures add?

Along a single pipe path in series: the supply pressure must cover the pressure at the end plus the friction and elevation losses along the path.

What if the two sprinklers need different pressures?

The junction pressure must be at least the higher requirement. The sprinkler with the lower requirement then discharges more than its minimum flow.

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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