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Pipe Flow Continuity Equation

Understand how volumetric flow rate, average velocity, and pipe area are related by Q = V A for full circular pipes.

Referencefluids & pipingLast reviewed: 2026-05-16

Use the continuity relationship when a flow rate must be turned into average pipe velocity for Reynolds number, pressure-loss, or pump-system checks.

What This Means

For a full circular pipe with steady flow, volumetric flow rate equals average velocity times cross-sectional area. A smaller diameter raises velocity for the same flow rate; a larger diameter lowers it.

This relationship is geometric and simple, but it is one of the most common places for pipe-flow mistakes because the diameter must be actual inside diameter.

Key Formula

Q = V A
A = pi D^2 / 4
V = 4 Q / (pi D^2)
  • Q is volumetric flow rate.
  • V is average pipe velocity.
  • A is cross-sectional flow area.
  • D is inside pipe diameter.

Use This When

  • A calculation needs average velocity but your source data gives flow rate.
  • You are converting gpm, L/s, m3/s, or cfm into velocity.
  • You need velocity before calculating Reynolds number.
  • You need velocity before using Darcy-Weisbach pressure loss.

Assumptions

  • The pipe is full and circular.
  • The diameter is uniform over the section being checked.
  • Flow rate is actual volumetric flow at the local condition.
  • Velocity means cross-sectional average velocity.

Limitations

  • Partially full pipes and open channels need a different flow-area model.
  • Noncircular passages require a hydraulic-diameter or flow-area method appropriate to the geometry.
  • Standard gas flow units such as SCFM must be converted to actual local volumetric flow before using this relationship.
  • The equation does not judge whether the resulting velocity is acceptable for erosion, noise, pressure loss, or process requirements.

Common Mistakes

  • Using nominal pipe size as if it were inside diameter.
  • Forgetting that velocity changes with the square of diameter.
  • Mixing standard gas flow and actual volumetric flow.
  • Treating average velocity as the same as centerline velocity.
  • Feeding inconsistent units into a spreadsheet calculation.

Sources

This reference is based on White's Fluid Mechanics for continuity and average-velocity relationships, with Crane TP-410 used for mean velocity in practical pipe-flow calculations.

  1. Frank M. White. Fluid Mechanics, 7th ed., McGraw-Hill, 2011. ISBN 978-0-07-352934-9.
  2. Crane Co.. Flow of Fluids Through Valves, Fittings, and Pipe (Crane TP-410), Technical Paper No. 410, Crane Co., 2009. TP-410.