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Fluid mechanics

Flow rate in a circular pipe

Calculate flow area and volumetric flow rate from the pipe inside diameter and mean fluid velocity.

Created v1.0

By Thibaut Grzelak, Mechanical Analysis Engineer

Fluid mechanics
01Calculation inputsA = πD² / 4 ; Q = v · A
vDQ = vA
Input identificationD is the useful inside diameter and v is the mean velocity over area A.
mm
m/s
02

Results

SI
Flow area
—mm²

Inside pipe cross-sectional area.

Volumetric flow rate
—L/s

Volume crossing the section each second.

Hourly flow rate
—m³/h

Practical volumetric-flow conversion.

Primary relationA = πD² / 4 ; Q = v · A

Constant inside diameter and completely filled pipe. v is interpreted as the mean velocity over the section. Pressure drop, flow regime and pressure are not calculated.

01Formulas and symbols

Formulas used

AπD² / 4Inside area
Qv · AVolumetric flow rate
Qh3600 · QFlow rate in m³/h
02Assumptions and limits

Scope of validity

  • Constant inside diameter and completely filled pipe.
  • v is interpreted as the mean velocity over the section.
  • Pressure drop, flow regime and pressure are not calculated.
03Validation example

Reference numerical case

  1. D = 50 mm and v = 2 m/s.
  2. A = 1,963.495 mm².
  3. Q = 3.92699 L/s.
  4. Qh = 14.1372 m³/h.

Calculation path and sources

Flow rate sets mean velocity; losses then depend on flow regime and pipe friction.

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External technical sources

Pipe flow

Flow-rate calculation from pipe diameter and velocity

Use inside diameter and mean velocity. Outer diameter does not represent the flow area.

Flow area

Area is the internal circle.

A = πD² / 4

Volumetric flow rate

Flow rate is proportional to velocity and to diameter squared.

Q = v · A