What is the smooth bore flow formula?

GPM = 29.7 × d² × √NP, where d is tip diameter in inches and NP is nozzle pressure in psi. 29.7 is the discharge coefficient for a smooth bore tip.

What nozzle pressure do smooth bore nozzles use?

Handline smooth bore tips are rated at 50 psi nozzle pressure; master stream tips at 80 psi. Some departments flow handlines slightly lower for control.

Why does a small tip change make such a big flow difference?

Flow grows with the square of the tip diameter. Going from a 7/8″ to a 1″ tip at 50 psi raises flow from about 161 to 210 gpm — roughly a 30% increase from a 1/8″ change.

Does this work for fog nozzles?

No. Fog / combination nozzles have a rated flow set by the manufacturer at a given pressure (often 100 psi). This formula is specifically for smooth bore (solid stream) tips.

Smooth bore nozzle flow calculator

Find the smooth bore nozzle GPM — the flow a smooth bore nozzle delivers from its tip diameter and nozzle pressure — using the standard fire-service discharge formula used for handlines and master streams.

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Tip diameter (in)

Nozzle pressure (psi)

Flow rate — gpm

Flow = 29.7 × d² × √NP. The constant 29.7 is the smooth bore discharge coefficient for tip diameter in inches and pressure in psi.

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How smooth bore flow is calculated

A smooth bore (solid stream) nozzle delivers a flow set by the tip diameter and the nozzle pressure behind it:

GPM = 29.7 × d² × √NP

d is the tip diameter in inches and NP is the nozzle pressure in psi. Because flow scales with the square of the diameter, a small bump in tip size is a big jump in gallons.

Handline tips at 50 psi

Tip	Flow (gpm)
7/8″	161
15/16″	185
1″	210
1⅛″	266

Master stream tips at 80 psi

Tip	Flow (gpm)
1¼″	415
1⅜″	502
1½″	598
1¾″	814
2″	1063

Worked example

A 1″ smooth bore handline tip at 50 psi nozzle pressure:

GPM = 29.7 × 1.0² × √50
= 29.7 × 1 × 7.07 = 210 gpm

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Frequently asked questions

What is the smooth bore flow formula?: GPM = 29.7 × d² × √NP, where d is tip diameter in inches and NP is nozzle pressure in psi. 29.7 is the discharge coefficient for a smooth bore tip.
What nozzle pressure do smooth bore nozzles use?: Handline smooth bore tips are rated at 50 psi nozzle pressure; master stream tips at 80 psi. Some departments flow handlines slightly lower for control.
Why does a small tip change make such a big flow difference?: Flow grows with the square of the tip diameter. Going from a 7/8″ to a 1″ tip at 50 psi raises flow from about 161 to 210 gpm — roughly a 30% increase from a 1/8″ change.
Does this work for fog nozzles?: No. Fog / combination nozzles have a rated flow set by the manufacturer at a given pressure (often 100 psi). This formula is specifically for smooth bore (solid stream) tips.

Worked Example

1" tip at 50 PSI: GPM = 29.7 × d² × √NP = 29.7 × 1 × 7.07 ≈ 210 GPM.

Step up one tip size to 1⅛" at the same pressure: 29.7 × 1.266 × 7.07 ≈ 266 GPM — a 27% flow jump from an eighth of an inch, because diameter enters the formula squared.

This is why tip selection is a flow decision, not a detail: your pump operator's PDP, your water supply plan, and your nozzle crew's stamina all move with that d² term.

Knowing the flow is step one. Delivering it under pressure is the job.

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Coefficients per IFSTA / NFA. For training and estimation; always verify against your department SOPs and nozzle manufacturer ratings. Related tools: pump discharge pressure calculator, friction loss calculator, and nozzle reaction force calculator. How the nozzle type changes flow and reaction: smooth bore vs. fog nozzles. Producing effective streams is the first JPR in NFPA 1002.