Volumetric Flow Rate (Q = Av)

Picture a plane cut across the pipe. In one second, every particle within a distance $v$ upstream of that plane will have crossed it, so what passes is a cylinder of length $v$ and cross-section $A$. Volume per second is $Av$, and there is nothing more to the relation than that geometry. It is worth noticing that this is really the definition of the average velocity rather than a discovery about it: real flow moves at different speeds at different points across the bore, and $v = Q/A$ is how we agree to summarise that profile with one number.

A 100 mm pipe has a bore area of $\pi(0.05)^2 = 7.854\times10^{-3}$ m². At 1.5 m/s that carries $Q = 0.0118$ m³/s, which is 11.8 L/s or about 707 L/min. Those three numbers are the same quantity in the three units different trades habitually speak in, and being fluent in all three saves a great deal of grief on site.

Almost every other calculation in fluids takes its velocity from here. The Reynolds number needs $v$ to decide whether the flow is laminar or turbulent; the velocity head needs $v^2$; friction loss correlations are written in terms of $v$ or $Q$ throughout. It is also the relation behind the design velocities that govern piping layout — closed hydronic loops are usually kept between roughly 1 and 3 m/s, fast enough to carry air and dirt along and slow enough to stay quiet, with copper held lower still because erosion-corrosion begins to strip the protective oxide film somewhere above about 1.2 m/s in hot water.

The error that costs the most is using the nominal size as the bore. A pipe's name is not a dimension. Nominal 2 in. steel has an outside diameter of 60.3 mm and a Schedule 40 inside diameter of 52.5 mm — nowhere near 50.8. Type L copper described as 1 in. actually runs about 26.8 mm inside. Because area goes as the square of the diameter, a 5% error in bore becomes a 10% error in flow, and it compounds silently through everything downstream. Look up the schedule and the wall thickness; do not assume the label.

Two further cautions. $v$ is the average velocity across the section, not the reading at the centre. In fully turbulent pipe flow the centreline runs about 1.2 times the mean, and in laminar flow it is exactly twice the mean — so a pitot or an insertion probe held in the middle of the pipe overstates the flow unless it is corrected or traversed. And $A$ is the area actually available to flow, which is not the clean-bore area in a scaled or fouled line, and not the full section in a partly filled gravity drain.