Venturi Effect

How a venturi works

A venturi is a length of pipe that narrows smoothly into a throat and then widens back out again. Three things happen in sequence as the fluid moves through it.

First, mass conservation applies. The mass flow rate ρvA must be the same at every cross-section, because no fluid is being created or destroyed inside the pipe. For an incompressible fluid (water, oil, or low-Mach air), that simplifies to v·A = const: shrink the area by 4× and the velocity must rise by 4×.

Second, that acceleration costs energy. Bernoulli's equation tracks the budget along a streamline:

P + ½ρv² + ρgh = constant

The kinetic-energy term ½ρv² grows in the throat because v grew. To keep the sum constant, the static pressure P has to drop by exactly the same amount. That low-pressure throat is the venturi's signature.

Third, in the diverging cone downstream, the area opens back up, the velocity slows, and the static pressure climbs again. A well-designed venturi recovers most — though never all — of the throat pressure drop. The unrecoverable bit becomes heat from viscous friction.

Flow through the device

          inlet              throat            outlet
          v₁, P₁              v₂, P₂            v₁, P₁'
         ────────╲          ┌──────┐          ╱────────
                  ╲         │      │         ╱
   →  →  →  →  →   ╲        │      │        ╱   →  →  →
                    ╲───────┘      └───────╱
   →  →  →  →  →   ╱                       ╲   →  →  →
                  ╱        ↓ low P          ╲
         ────────╱         ↑ high v          ╲────────
            21° converging cone     5–7° diverging cone

Static-pressure taps drilled at the inlet and throat let you read the differential. With the geometry fixed and the fluid density known, that single ΔP gives you the volumetric flow rate.

Worked example: water through a venturi meter

A pipeline carries water (ρ = 1000 kg/m³) through a 100 mm inlet that necks down to a 50 mm throat. A pressure gauge reads 25 kPa lower at the throat than at the inlet. What is the flow rate?

Continuity gives the velocity ratio. Areas go as the square of diameter, so A₁/A₂ = (100/50)² = 4. Therefore v₂ = 4·v₁.

Bernoulli (ignoring elevation, since the pipe is horizontal):

P₁ + ½ρv₁² = P₂ + ½ρv₂²
ΔP = ½ρ(v₂² − v₁²) = ½ρv₁²·(16 − 1) = 7.5·ρv₁²

Solve: v₁² = 25,000 / (7.5·1000) = 3.33 m²/s², so v₁ ≈ 1.83 m/s. The volumetric flow Q = v₁·A₁ = 1.83 · π·(0.05)² ≈ 0.0143 m³/s, or about 14 L/s. A real meter would multiply by C_d ≈ 0.97 to land near 13.9 L/s.

Venturi vs other differential-pressure flow meters

Device	Discharge C_d	Pressure recovery	Cost	Best for
Classical venturi	0.95–0.98	80–90%	High	Long pipelines, low pumping cost
Orifice plate	0.60–0.65	40–50%	Very low	Cheap retrofit, plant air/steam
Flow nozzle (ISA-1932)	0.94–0.99	50–70%	Medium	High-velocity steam, high temp
Pitot tube	0.98–1.00	≈100% (point velocity)	Low	Open ducts, aircraft airspeed
V-cone meter	0.78–0.85	60–75%	Medium	Low straight-run availability
Wedge meter	0.72–0.80	50–65%	Medium	Slurries, dirty fluids

The venturi wins on permanent pressure loss, which dominates pumping cost over a plant's life. The orifice plate wins on capital cost but bleeds energy continuously. Pick the meter that minimises lifetime cost, not purchase price.

Real-world venturis

• Carburetors. A car engine pulling air at 30–50 m/s through a 25 mm venturi throat drops the throat pressure by roughly 5–15 kPa below atmospheric. That suction lifts gasoline through a metering jet (~0.5 mm orifice) from the float bowl. Bigger throat → leaner mixture; that's why high-performance carbs use multiple venturis in parallel rather than one large bore.
• Aspirator pumps. Lab water aspirators run tap water through a small venturi throat at 3–6 m/s. The side-port suction reaches 20–30 mbar absolute — enough vacuum for filtration or rotary evaporation, with no moving parts.
• Spray guns and atomisers. Compressed air rushing past a paint pickup tube creates the suction that pulls and breaks paint into droplets. Same trick: low-pressure throat plus a side feed.
• Pitot-static aircraft instruments. A static port reads ambient pressure; a forward-facing Pitot tube reads stagnation. The difference, ½ρV², gives airspeed. The Pitot is the inverse of a venturi but uses identical Bernoulli reasoning.
• Natural-gas pipeline metering. Custody-transfer venturis on transmission lines size up to 1.2 m diameter with C_d certified to ±0.5%. Mis-readings of 1% over a year on a single 30-bcm/yr line equate to roughly $50M in mis-billed gas.
• Bunsen burners. Gas exits a small jet at 20–40 m/s through a venturi-shaped mixing tube. The throat suction pulls in primary combustion air at the air shutter holes. Adjust the shutter, the air-fuel ratio shifts.

Variants

• Cavitating venturi. Designed so the throat pressure drops below vapour pressure. Once vapour forms, the throat flow is choked and becomes a function of upstream conditions only — a passive flow limiter. Used in rocket propellant feed lines to decouple flow rate from chamber pressure fluctuations.
• Eductor (jet pump). A motive fluid through a venturi throat draws and entrains a second stream from the side port. Both streams mix and discharge through the diffuser. No moving parts; common in marine bilge pumps and chemical-plant transfer.
• Long-throat (Herschel) venturi. Adds a parallel-walled throat section between the converging and diverging cones to stabilise the boundary layer. Standard for water-utility metering at large diameters.
• Low-loss venturi (Dall tube). Replaces the throat with an annular gap; achieves higher signal at lower permanent loss. Trades calibration sensitivity for pumping cost.
• Critical-flow nozzle. A venturi for compressible flow operated at sonic throat conditions. Mass flow becomes proportional to upstream stagnation pressure alone — a calibration standard.

Common failure modes

• Cavitation in the throat. When system pressure or temperature pushes the throat below vapour pressure, vapour bubbles form, race into the recovery cone, and implode against the wall. Pitting, noise, and a measured flow that caps out regardless of downstream pressure are diagnostic. Fix by raising upstream pressure or enlarging the throat.
• Diverging-cone separation. If the diffuser angle exceeds about 7° total, the boundary layer detaches, recovery collapses to 30–40%, and the meter reads erratically. Detected by a noisy ΔP signal at high flow.
• Throat erosion. Slurries and high-velocity gas–particulate flows abrade the throat and increase its diameter, shifting C_d downward over months to years. Re-calibrate annually or use a hardened liner.
• Asymmetric inlet velocity profile. A venturi installed too close to an elbow, valve, or pump sees a swirling, distorted inlet — readings drift by 2–5%. ISO 5167 mandates 5–30 diameters of straight pipe upstream.
• Pressure-tap blockage. Particulates or bubbles collect in the small bore of a pressure tap and corrupt the differential reading. Periodic blow-down or annular piezometer rings mitigate.
• Low-Reynolds breakdown. Below Re ≈ 200,000 in the throat, the discharge coefficient becomes Reynolds-dependent and standard tables no longer apply. Use a Reynolds-corrected calibration or a different meter type.