How this instrument works
Flow rate says how much fluid a line carries. Velocity says how hard that line is working. Two steps get you across — square the internal bore into a cross-section, then divide throughput by it — and all of the sensitivity hides in that first step. Because D is squared, speed falls off as the inverse square of bore: a 25% wider pipe moves an identical duty 36% slower, while shaving 20% off bore lifts speed by more than half. Little else in pipework repays one size change so steeply.
Geometry this plain has no discoverer, yet velocity earned its own line in design codes for reasons worth knowing. Through 1897 and 1898 Nikolai Joukowsky ran tests on Moscow's water mains, shutting valves on long runs and recording what the pressure did. He found that the spike depends not on discharge but on speed destroyed — very roughly ten bar for every metre per second halted abruptly in water. Mains carrying their duty quite comfortably were splitting open because of how fast, never how much. Engineers have sized to a velocity ceiling ever since, letting throughput follow behind.
What returns here is bulk mean speed through a full, round bore — duty spread evenly across the whole circle. Three situations break that picture. A part-filled drain wets a segment rather than all of it, so its true area is smaller than π·D²⁄4. A gas expands as pressure drops along its run, so identical kilograms per second read faster and faster downstream. And in slurry or two-phase lines, carrier and cargo travel at different rates, leaving this figure an average of things that are not really doing the same thing.
- Enter Volumetric flow rate — the duty your pump, meter or fixture schedule has to deliver. Units of l/s, gpm, m³/h and l/min all convert.
- Enter Internal pipe diameter as measured bore, never nominal size and never outside diameter; mm, cm, m and inches all convert.
- Read Pipe cross-section to confirm the geometry, then Flow velocity — the figure your material limits are actually written against.
- Step one bore size up or down and watch that speed move by roughly a third. Sizing decisions get made in exactly that comparison.
Worked example — 10 l/s down a 100 mm main
A borehole pump rated at 10 litres per second feeds a 100 mm main. Put 0.01 into Volumetric flow rate and 0.1 into Internal pipe diameter. Pipe cross-section returns A = π × 0.1² ⁄ 4 = 0.00785398 m², and Flow velocity returns v = 0.01 ⁄ 0.00785398 = 1.2732 m/s.
That answer holds a small elegance. With Q and D² both landing on 0.01, everything cancels except 4 ⁄ π, so 1.2732 m/s is exact rather than rounded. It also sits comfortably inside the 1 to 2 m/s band plumbers design toward. Price the neighbours before ordering, though: 80 mm bore pushes it to 1.99 m/s, near where copper begins eroding and pipework begins singing, while 125 mm drops it to 0.81 m/s — quiet, cheap to pump, but slow enough that whatever settles out will stay settled.
Questions
Why does one pipe size up drop the velocity so much?
Because bore enters squared. Speed is 4Q ⁄ (π·D²), so it tracks the square of diameter rather than diameter itself. Moving from 100 mm to 125 mm widens the pipe by 25% but its hole by 56%, cutting speed by 36% at identical duty. Friction loss falls faster still, near the square of velocity, which is why one size up frequently repays its extra cost in pump energy inside a year. Read that sensitivity backwards and it explains why a guessed bore goes wrong so quickly.
What velocity should water in a pipe not exceed?
Material and duty decide, not physics. Copper is the fussy one: erosion-corrosion strips its protective oxide film above roughly 1.5 m/s in hot service and about 2.4 m/s cold, and damage concentrates at elbows, where flow already has to turn. Plastics tolerate more. Pump suction lines are usually held near 1 m/s so friction does not eat into available NPSH and invite cavitation. Foul drainage carries the opposite risk and wants 0.75 m/s or better to keep solids moving. Clean water inside a building typically lands between 1 and 2 m/s.
Should I enter nominal size or measured bore?
Measured internal bore, and getting it wrong costs more here than in a discharge calculation because D is squared. A 4-inch steel pipe in Schedule 40 has about 102.3 mm of bore; identical nominal size in Schedule 80 has roughly 97.2 mm. That is 5% narrower, but 11% faster at the same duty. Plastic pipe hides the same trap inside its SDR rating, where a heavier pressure class takes wall thickness from the inside while outside diameter stays put. Pull real dimensions off a manufacturer table.
Is this the velocity a Reynolds number wants?
Yes. This is bulk mean speed — duty spread across the full circle — and it is what Reynolds number, Darcy-Weisbach head loss and Joukowsky surge all expect to be given. A probe parked mid-stream reads something higher, since friction holds fluid back near the wall and pushes the profile into a dome. Insertion meters therefore carry a profile correction to get from what they see back to what this sheet reports.
Why do design codes cap velocity instead of flow rate?
Surge. Halt a moving column of water quickly and its momentum turns into pressure, following Joukowsky's Δp = ρ·a·Δv, where a is how fast a pressure wave travels in that particular pipe — near 1400 m/s in rigid metal, well under 500 m/s in flexible plastic. For water in ordinary pipework, reckon on about 10 bar of spike per metre per second stopped. Discharge appears nowhere in that expression. A 300 mm main and a 25 mm branch running at equal speed generate equal surge, which is precisely why limits are written against velocity.
Does this work for air, steam or a half-full drain?
For gases, at one station only. Area times speed still gives volume per second, but a gas expands as pressure falls along a duct, so unchanged kilograms per second read as a rising speed further downstream — quote your flow at local conditions rather than some standard reference state, or the answer drifts. Steam layers dryness fraction on top of that. A part-full drain fails differently: liquid occupies a segment of the circle, so substitute wetted area for Pipe cross-section and work from there.