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Venturi Meter Flow Rate Calculator

Calculate fluid flow rate through a Venturi meter from pipe and throat diameter, the measured pressure drop, and fluid density.

Flow rate
12.569 L/s
Flow rate (US gpm)
199.22 gpm
Flow rate (m³/s)
0.01257 m³/s
Throat velocity
6.401 m/s

How it works

A Venturi meter narrows a pipe to a smaller throat. By the continuity equation (A₁V₁ = A₂V₂), the fluid must speed up through the narrower throat, and by Bernoulli's equation (P₁ + ½ρV₁² = P₂ + ½ρV₂²) along the same streamline, that speed-up comes with a pressure drop — the pressure difference a Venturi meter actually measures to infer flow rate. Combining the two and solving for the throat velocity gives V₂ = √(2(P₁-P₂) ÷ (ρ(1-(A₂÷A₁)²))), and the ideal flow rate is Q = A₂ × V₂.

A discharge coefficient Cd scales that ideal result down to account for real-world friction and minor turbulence: Q = Cd × A₂ × √(2(P₁-P₂) ÷ (ρ(1-(A₂÷A₁)²))). A Venturi tube's smooth, gradual constriction loses far less energy than a sharp-edged orifice plate, so Cd typically runs 0.95-0.99 rather than the much lower values (around 0.6) a sharp orifice needs.

Pipe and throat diameter are converted to meters internally regardless of the unit toggle (producing the areas A₁ and A₂), and the pressure drop is converted to pascals, before the formula runs — fluid density is left in the universally-standard kg/m³ either way, the same convention this site's Hydrostatic Pressure calculator uses. The flow rate result is shown in liters per second, US gallons per minute, and m³/s together, since different fields default to different conventional units.

FAQ

Why must the throat be narrower than the pipe?

The entire effect depends on the fluid speeding up through a constriction — if the throat weren't narrower than the pipe, there would be no velocity increase, no pressure drop, and nothing for a Venturi meter to measure. This calculator requires the throat diameter to be smaller than the pipe diameter for exactly that reason.

What happens if the throat is almost as wide as the pipe?

The area ratio (A₂÷A₁) approaches 1, which drives the denominator 1-(A₂÷A₁)² toward zero and the computed velocity toward infinity for any nonzero pressure reading — in practice this means a very mild constriction produces too small a pressure drop to measure flow accurately, which is why real Venturi meters are deliberately designed with a meaningful throat-to-pipe ratio rather than the narrowest or widest ratio possible.

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