Pipe Flow (Continuity) Calculator
Solves the continuity equation Q = Vm·Af for a full, circular pipe: flow rate, mean velocity, or inside diameter — given the other two.
Calculator
Q = Vm × (π/4) × D²
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About this calculator
For a full, circular pipe flowing under pressure, the continuity equation relates flow rate (Q), mean velocity (Vm), and the pipe's cross-sectional flow area (Af):
Q = Vm × Af where Af = (π/4) × D²
Pick which quantity you want to solve for, enter the other two, and choose the unit you'd like the answer reported in. This is useful for sizing pipe (given a target flow and a maximum allowable velocity), checking whether an existing pipeline can carry a design flow, or converting a measured velocity to a flow rate.
Textbook Example 3.3: An 8-in ID pipeline has a mean velocity of
5 ft/s. Flow rate ≈ 785 gpm (the textbook rounds 1 cfs ≈ 450 gpm; this
calculator uses precise conversion factors, so it will show a very close value).
Click "Load textbook Example 3.3" above to see it worked through.