A worked example: 50mm pipe, 2 m/s water flow
Water flowing at 2 m/s through a 50mm-diameter pipe moves at 235.62 liters per minute, with a Reynolds number of 100,000 — well into turbulent flow.
The formula: Q = A × V (continuity equation)
Flow rate is cross-sectional area times velocity — the pipe's circular cross-section (π × radius²) multiplied by how fast the fluid moves through it. This is the same principle behind why a narrower hose nozzle sprays water faster: the same volume per second has to pass through a smaller opening.
Reynolds number: Re = ρVD/μ
Combining fluid density, velocity, pipe diameter, and fluid viscosity into one dimensionless number predicts whether flow will be smooth (laminar) or chaotic (turbulent) — critical because friction losses and mixing behavior differ significantly between the two.
A laminar contrast: a narrower pipe, much slower flow
A 20mm pipe with water crawling at just 0.05 m/s has a Reynolds number of only 1,000 — laminar flow, moving in smooth parallel layers with almost no mixing, a world away from the turbulent 100,000 example above.
The three flow regimes
Re below 2,300 is laminar, 2,300 to 4,000 is transitional, and above 4,000 is turbulent — standard thresholds for flow in a circular pipe. Most everyday pipe flows, like household plumbing, land solidly in the turbulent range.