Continuity Conserves Flow - Biophysical Separation and Detection Step by Step

Continuity says that narrowing a channel speeds up the flow so that area times speed stays constant, conserving the volume rate. The upstream area 2 m^2 times speed 3 m/s equals 6 m^3/s, matching the downstream product exactly for the stated toy flow ledger; real microfluidic channels have geometry tolerances, viscosity variation, wall effects, and flow-rate calibration uncertainty.

A microfluidic constriction is checked by equal volumetric 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

Narrower channel carries faster flow

The upstream area is 2 square metres and the speed is 3 m/s.

A_{\text{up}}=2\ \text{m}^{2},\quad v_{\text{up}}=3\ \text{m}/\text{s}

Flow is area times speed on both sides

Both products give 6 cubic metres per second. The claim is continuity only, not pressure drop or viscosity.

A_{\text{up}}v_{\text{up}}=A_{\text{down}}v_{\text{down}}=6\ \text{m}^{3}/\text{s}