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How does a venturi tube measure the discharge rate in a pipe?

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differential manometer, Torricellian barometer, and siphon — fluid mechanics Figure 1: Schematic representations of (A) a differential manometer, (B) a Torricellian barometer, and (C) a siphon.

A venturi tube measures the discharge rate of a fluid in a pipe by utilizing the relationship between fluid velocity and pressure, as described by Bernoulli’s theorem.

The device consists of a short pipe with a constricted section, or "throat." As fluid enters this narrow area, it must speed up to maintain a constant mass flow rate, which causes the fluid pressure to drop. This phenomenon is known as the Venturi effect.

To determine the discharge rate ( $Q$ ), engineers measure the pressure difference between the wider section of the pipe and the narrow throat, typically by observing the difference in fluid levels ( $h$ ) in side tubes connected to these points. According to the principle of continuity and Bernoulli’s law, this pressure drop is directly related to the velocity of the fluid. By calculating the velocity from the measured pressure differential, the discharge rate can be accurately determined. This method is most reliable when the flow is sufficiently fast to be turbulent.123