Fluid Relation Cross Scans

Continuity Flow Rate Three-Row Scan

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