Venturi / Bernoulli

Change the diameters, mean inlet speed or absolute inlet pressure. Numbers and sliders control the same inputs. The tube, profiles and results all use the same cross-section. Examples compare a straight pipe with a half-diameter throat. Only the optional markers need an animation button.

Ideal flow

Water at about 20 °C: ρ = 998 kg/m³. Q = A₁v₁ = A₂v₂, with A = πd²/4. At equal height, p(x) + ρv(x)²/2 is constant. Halving the diameter quarters the area and multiplies speed by four. The outlet has the inlet diameter, so the ideal pressure recovers completely. This is not a permanent pressure-loss estimate.

Reading the diagram

Speed and absolute pressure have separate labelled vertical scales; x/L is a normalized position. The smooth tube is schematic. Marker travel uses integrated cross-sectional volume; a common slow-motion factor preserves relative speeds, not physical elapsed time. Equal diameters yield flat profiles; zero speed yields zero flow and pressure difference.

Limits

Steady, incompressible, inviscid, single-phase flow at equal height. No wall friction, separation or discharge coefficient. If the theoretical absolute throat pressure reaches approximately 2.34 kPa, water at 20 °C can cavitate. Results remain visible as ideal extrapolations and the single-phase animation stops. Negative absolute pressures are not physical predictions. This is an educational model, not a validated flow-meter calibration.

Only exact input text is retained, including empty or invalid drafts, in the displayed units. Results and marker positions are recalculated, not stored. Invalid entries remove the previous diagram until corrected. Reset restores the initial values.