Pipe Flow Velocity
Mean velocity in a round pipe from volumetric flow and diameter.
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The engineering
Continuity in its simplest suit: whatever volume goes in per second must cross every section, so velocity is just flow over area. The practical use runs backwards — pick a target velocity (roughly 1–3 m/s for water in commercial pipe, faster erodes, slower silts and costs metal) and size the pipe to hit it.
Remember the area goes with diameter *squared*: a 100 mm line carries four times what a 50 mm line does at the same velocity. That square is why pipe-sizing mistakes are rarely subtle.
Where this math comes from
Leonardo da Vinci sketched the principle around 1500 — narrow the channel, quicken the water — but Benedetto Castelli, Galileo's student, stated Q = A·V as a law in his 1628 treatise on running waters, written to referee Italian irrigation disputes. It is arguably hydraulics' first equation.
Euler folded continuity into the general equations of fluid motion in 1757, and it has been the first line of every flow calculation since — the conservation law so reliable that when it seems violated, you've found a leak.
- 1500Leonardo da VinciObserves the area–velocity trade in channels (circa).
- 1628Benedetto CastelliStates Q = A·V — continuity as a law.
- 1757Leonhard EulerContinuity embedded in the general flow equations.
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