A continuity flow-rate scan varies area across three rows while holding speed fixed (or vice versa), showing how Q = A * v moves through the ledger row by row. The arithmetic is exact only for the stated areas, speeds, and rows in the ideal steady incompressible model. Real flows add viscosity, turbulence, compressibility, pipe geometry, calibration, elevation reference, and measurement uncertainty.

Area and speed pairs close to the same steady flow. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Halving area doubles speed

Upstream 2 square metres times 2 metres per second gives flow 4. Downstream 1 times 4 gives the same flow.

2×2=41×4=42\times2=4\quad1\times4=4
Continuity scan rowBoth sides are checked against the same flow.areainflowareaoutflowA1=2 m^2v1=2 m/sA2=1 m^2v2=4 m/sQ=4 m^3/s

Three by three closes to nine

Upstream 3 square metres times 3 metres per second gives flow 9. Downstream 1 times 9 gives the same flow.

3×3=91×9=93\times3=9\quad1\times9=9
Continuity scan rowBoth sides are checked against the same flow.areainflowareaoutflowA1=3 m^2v1=3 m/sA2=1 m^2v2=9 m/sQ=9 m^3/s

A wider outlet halves the speed

Upstream 4 square metres times 1 metres per second gives flow 4. Downstream 2 times 2 gives the same flow.

4×1=42×2=44\times1=4\quad2\times2=4
Continuity scan rowBoth sides are checked against the same flow.areainflowareaoutflowA1=4 m^2v1=1 m/sA2=2 m^2v2=2 m/sQ=4 m^3/s