Venturi Flow Meter Calculator

A Venturi meter measures flow rate by constricting a pipe and measuring the pressure drop across the constriction. As fluid speeds up through the narrow throat, pressure drops. The Bernoulli equation relates that pressure difference to velocity.

The derivation. Continuity: A1 v1 = A2 v2. Bernoulli: P1 + 0.5 rho v1^2 = P2 + 0.5 rho v2^2.

Combining and solving for the volumetric flow rate Q:

Q = Cd x A2 x sqrt( 2 x dP / (rho x (1 - (A2/A1)^2)) )

where:

• Cd is the discharge coefficient (typically 0.98-0.99 for well-machined Venturi meters)
• A1 and A2 are the pipe and throat cross-sectional areas
• dP is the differential pressure (P1 - P2)
• rho is the fluid density

The discharge coefficient Cd accounts for viscous friction and flow profile imperfections not captured by ideal Bernoulli theory. A standard Venturi (ISO 5167) has Cd = 0.984 at Re > 200,000.

Advantages over orifice plates. The Venturi has a gradual converging and diverging section, so most of the pressure drop is recovered. A Venturi loses about 10-25% of differential pressure as permanent loss; an orifice plate loses 50-80%. For large flow applications (natural gas pipelines, water treatment), the energy savings justify the higher initial cost.

Beta ratio limits. ISO 5167 keeps a classical Venturi between beta = 0.4 and 0.75, and the 0.984 discharge coefficient is only certified inside that band. Go narrower and you burn pressure for nothing. Go wider and the differential shrinks until your transmitter cannot resolve it.

Cavitation limit. If throat pressure drops below the fluid vapor pressure, cavitation occurs: bubbles form in the throat and collapse violently in the diverging cone, which pits the metal and ruins the calibration. The check is simple, because the throat sits exactly dP below the upstream line. The upstream absolute pressure must exceed dP plus the fluid’s vapour pressure, which for water at 20 °C is 2.34 kPa and climbs steeply with temperature: 7.4 kPa at 40 °C, 47.4 kPa at 80 °C. Hot water is far easier to cavitate than cold, which is why the same meter can work for years on a chilled line and destroy itself on a hot one. The calculator reports the minimum upstream pressure for cold water with every result.

Turndown. The differential falls with the square of the flow rate, so a meter reading 20 kPa at full flow sees only 0.2 kPa at a tenth of it. That square-law relationship is the reason differential-pressure meters rarely manage better than about 4:1 turndown without switching transmitters, and it is the single biggest argument for magnetic or Coriolis meters where the flow range is wide.