FLD-23

Venturi flowmeter

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

Reading speed

FluidsVenturi

Governing equation

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

$\Delta p \in \left[0.1, 80\right]$

where

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

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

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

$\Delta p \in \left[0.1, 80\right]$

$\Delta p = 0.1$ $Q = 0.227$

Along the curve

②

Domain of the variable — blue

\Delta p_{\min} = 0.1,\quad \Delta p_{\max} = 80

$\Delta p \in \left[0.1, 80\right]$

$\Delta p = 0.1$ $\Delta p = 0.1$

Along the curve

③

Response curve — green

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

$\Delta p \in \left[0.1, 80\right]$

$\Delta p = 0.1$ $Q = 0.227$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}Q}{\mathrm{d}\Delta p}

$\Delta p \in \left[0.1, 80\right]$

$\Delta p = 0.603$ $Q^{\prime} = 0.524$

Along the curve

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: $D$ , $d$ , $\Delta p$ , $\rho$ $\rightarrow$ $Q$ . A constriction drops static pressure. Discharge coefficient C ≈ 0.98 on a real Venturi.

Purpose

Purpose: compute

Q

from

D

d

\Delta p

\rho

in Fluid physics via

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\,\mathrm{mm}

d = 25.000\,\mathrm{mm}

\Delta p = 8.000\,\mathrm{kPa}

\rho = 1000.000\,\mathrm{kg/m^{3}}

, the governing relation

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

yields

Q = 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

Upstream diameter D50 mmThroat diameter d25 mmPressure drop \Delta p8 kPaDensity \rho1000 kg/m³

Outputs

Discharge Q2.028 L/s

Reading speed

Watch on YouTube

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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