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Venturi Meter Calculator

Flow rate through a classical venturi meter from the inlet and throat diameters and the measured differential — entered as head of the flowing fluid or as a manometer reading — with the beta ratio, velocity of approach factor and inlet and throat velocities.

in
in
—
ft
ft
—
—
——
——
—ft
—ft³/s
—gpm
—ft/s
—ft/s

In head mode only Δh is used; in manometer mode Δh = hm·(SGm/SGf − 1). Δh is the difference in piezometric head between the inlet and throat taps, so the meter may be horizontal, inclined or vertical. For a pressure transducer, Δh = Δp/(ρg).

$$ Q = C_d\,A_2\sqrt{\frac{2\,g\,\Delta h}{1-\beta^4}} \qquad \beta = \frac{D_2}{D_1} \qquad \Delta h = h_m\left(\frac{SG_m}{SG_f} - 1\right) $$
A₂ throat area · D₁, D₂ inlet and throat diameters · Cd discharge coefficient · Δh piezometric head difference in the flowing fluid · hm manometer deflection · SG specific gravity · g = 32.174 ft/s² or 9.80665 m/s².

Classical venturi discharge coefficients

ISO 5167-4 classical venturi tubes
Convergent sectionCd
As-cast0.984
Machined0.995
Rough-welded sheet iron0.985

Each value applies only within the diameter, β and Reynolds number limits in ISO 5167-4. Proprietary short-form and insert venturis have manufacturer-specific coefficients.

Worked examples

Example 1 — Water main venturi, head reading

Given: D₁ = 12 in, D₂ = 6 in, as-cast Cd = 0.984, Δh = 5.0 ft of water.
β = 6/12 = 0.5; 1 − β⁴ = 0.9375
A₂ = π × (0.5 ft)² / 4 = 0.19635 ft²
Q = 0.984 × 0.19635 × √(2 × 32.174 × 5.0 / 0.9375) = 3.579 ft³/s
Q = 3.58 cfs = 1,606 gpm · V₂ = 18.2 ft/s · V₁ = 4.56 ft/s

Example 2 — Mercury manometer

Same meter, differential read as 0.40 ft of mercury deflection under water.
Δh = 0.40 × (13.56/1.0 − 1) = 5.024 ft of water
Q = 3.59 cfs

Example 3 — SI, pressure transducer

Given: D₁ = 300 mm, D₂ = 150 mm, machined Cd = 0.995, Δp = 25 kPa, water ρ = 998 kg/m³.
Δh = Δp/(ρg) = 25,000 / (998 × 9.80665) = 2.554 m
Q = 0.995 × 0.017671 × √(2 × 9.80665 × 2.554 / 0.9375) = 0.1285 m³/s = 128.5 L/s

References: ISO 5167-4, Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full — Part 4: Venturi tubes. ASME MFC-3M, Measurement of Fluid Flow in Pipes Using Orifice, Nozzle, and Venturi. Streeter, V.L., Wylie, E.B. (1985). Fluid Mechanics, 8th ed.

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