Pipe Flow Calculator
Bernoulli's acceleration line: velocity from the pressure that drives it, then the discharge the bore carries — ideal, friction not yet invited.
Pipe Flow Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Ideal incompressible flow; no friction share
- Steady state, full-bore flow
In short: A 20 kPa drop across a pipe accelerates water to 6.324555 m/s — v = √(2Δp/ρ) = √40 — and a 50 mm bore then carries 12.418235 L/s of it. This is the ideal line: Bernoulli converting pressure into velocity with no tolls yet taken. Friction's share lives on the pressure drop page; the orifice page adds the contraction tax. Together the three price every metre of pipe honestly.
Formula
v = √(2Δp/ρ) ··· A = πd²/4 ··· Q = v·A
Pressure is stored push; the square root converts it to speed by equating flow work with kinetic energy — the same √ that prices falling objects prices accelerating fluids. The bore then turns speed into volume: quarter the diameter, sixteenth the area, and the discharge falls with it at any given velocity.
Worked Example
- Enter the driving pressure drop.
- Enter the fluid density.
- Enter the pipe bore.
- Read velocity, then the discharge it carries.
Defaults: 20 kPa, water, 50 mm → 6.324555 m/s, 12.418235 L/s. The quarter-area check: halve the bore to 25 mm and the same velocity carries only 3.104559 L/s — area is geometric and unappeasable.
Strengths & Limits Of This Model
Where this engine is strong
- Velocity and discharge in one read
- The ideal ceiling stated honestly
Where it stops
- No friction factor
- No fittings or minor losses
Practical Use Cases
Pipe sizing
velocity from available pressure
Gravity mains
head converted to speed
Teaching
Bernoulli's bargain
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Pipe Flow Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why the square root?
Because kinetic energy grows with velocity SQUARED, so solving energy = energy for velocity unearths a root: doubling the pressure multiplies the speed by only √2 ≈ 1.414. It is the same root that prices a falling body, for the identical reason — nature books kinetic energy, not velocity, and this page is just reading her ledger.
Where did friction go?
Deliberately absent — this is the IDEAL line: the velocity a pressure difference would produce with no viscosity in the world. Real pipes tax the flow on the way (the pressure drop page owns that bill), so treat this figure as the ceiling and the supply pressure's promise, not the delivery guarantee. Design splits the budget: acceleration here, friction tax there.
How is this different from the orifice page?
The orifice multiplies the SAME square root by a discharge coefficient Cd ≈ 0.62 to price the vena contracta — the jet's shrinkage through a hole in a wall. This page prices the full-bore case with no contraction: the pipe IS the flow area. Same Bernoulli heart; one page trusts the geometry, the other audits it.
What velocity should a pipe carry?
Water systems typically design for 1–3 m/s: below about 0.6 m/s sediment settles, above roughly 3 m/s wear and noise grow and the friction tax compounds quadratically. The page's default lands mid-band at 6.324555 m/s — vigorous, which is honest for a 20 kPa drive and a hint that real design would spend some of that pressure on a bigger bore instead.
Does this work for gases?
The algebra runs, but the ideal-incompressible assumption starts lying: gases change density as pressure converts to speed, and above roughly a tenth of the speed of sound the compressibility correction is no longer optional. For air at modest Δp the page's answer is a fair first cut; for serious pressure ratios, compressible flow owns the problem.
Why does halving the bore cut the discharge to a sixteenth at fixed velocity?
Because area scales with diameter SQUARED: A = πd²/4, so half the bore is a quarter the area, carrying a quarter the volume at the same speed. The fourfold drop in the worked example (12.418235 to 3.104559 L/s) is exactly that quarter. Velocity is per-square-metre truth; the bore decides how many square metres show up.
Is the velocity head on the pump page the same v?
It can be — if the pipe's velocity came from this page's acceleration, then v²/2g equals Δp/(ρg) by construction: the two pages are the same arithmetic read in metres instead of pascals. That identity is worth checking once by hand and trusting forever: 20 kPa is 2.038741 m of head, and the velocity head at 6.324555 m/s is 2.038741 m. The books balance.
When is the ideal answer close enough to use alone?
For short, smooth runs — a nozzle, a tank outlet, a downtube — where friction length is trivial and the geometry, not the viscosity, sets the flow. The moment a run grows pipe-length, the friction share outgrows the simplification and the honest answer is the pair: this page for the promise, the pressure drop page for the toll. The ceiling and the tax, together, bracket reality.