How this calculator works
Volumetric flow is the integral of velocity over a cross section. With a known mean velocity, it reduces to area times velocity. The area is perpendicular to the motion and includes only liquid for a partly full pipe. A circular segment is computed from its central angle. Mass flow then multiplies volume flow by density. This page applies continuity and geometry, without predicting velocity from slope or pressure.
Formula
Q = Av; mass flow = rho Q. Circle: A = pi D^2/4. Rectangle: A = wh. Circular segment: theta = 2 acos(1 - 2h/D); A = D^2(theta - sin theta)/8, with theta in radians.
Worked example
A 2 m wide, 0.5 m deep rectangular stream at 3 m/s carries 3 m3/s. At 1000 kg/m3 its mass flow is 3000 kg/s. A half-full 2 m diameter pipe at 1 m/s carries pi/2 m3/s.
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Frequently asked questions
Can I use a point velocity measurement?
Only if it represents the area average. Real flow profiles usually require several measurements or a justified correction.
Is mass flow measured in CFM?
No. CFM is a volumetric rate. Mass flow additionally requires density at the actual flow conditions.
Does filling a pipe halfway halve the area?
At exactly half the diameter, yes. Other depth fractions do not correspond to the same area fractions.