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FLD-23

Venturi flowmeter

Q = A₂ √(2 Δp / ρ (1 − β⁴)), β = d/D. Bernoulli plus continuity.

Reading speed
FluidsVenturi

Governing equation

Q=A22Δpρ(1−β4)Q=A_2\sqrt{\dfrac{2\Delta p}{\rho(1-\beta^4)}}

where

D
Upstream diameter (mm)
d
Throat diameter (mm)
\Delta p
Pressure drop (kPa)
\rho
Density (kg/m³)
Q
Discharge (L/s)

Lecture brief

Historical brief

Bernoulli, Navier–Stokes, Reynolds (1883) and Stokes drag made continuum flow a dimensionless craft. The sheets compute head, drag, Re and a pedagogical NS snapshot. This sheet (FLD-23 — Venturi flowmeter) is the form associated with Venturi. Working symbols: DD, dd, Δp\Delta p, ρ\rho →\rightarrow QQ. A constriction drops static pressure. Discharge coefficient C ≈ 0.98 on a real Venturi.

Purpose

Purpose: compute QQ from DD, dd, Δp\Delta p, ρ\rho in Fluid physics via Q=A22Δpρ(1−β4)Q=A_2\sqrt{\dfrac{2\Delta p}{\rho(1-\beta^4)}} Q = A₂ √(2 Δp / ρ (1 − β⁴)), β = d/D. Bernoulli plus continuity. Use it when a real fluid physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given D=50.000 mmD = 50.000\,\mathrm{mm}, d=25.000 mmd = 25.000\,\mathrm{mm}, Δp=8.000 kPa\Delta p = 8.000\,\mathrm{kPa}, ρ=1000.000 kg/m3\rho = 1000.000\,\mathrm{kg/m^{3}}, the governing relation Q=A22Δpρ(1−β4)Q=A_2\sqrt{\dfrac{2\Delta p}{\rho(1-\beta^4)}} yields Q=2.028 L/sQ = 2.028\,\mathrm{L/s}. A throat, two pressure taps, a flow. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Outputs

  • Discharge Q2.028 L/s
Reading speed

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FLD-23 · pipe
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Narration of this film

A throat, two pressure taps, a flow.

A constriction drops static pressure. Discharge coefficient C ≈ 0.98 on a real Venturi.

Reading speed

Watch on YouTube