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Venturi Meter Calculator

Find flow rate Q from throat/inlet areas and pressure difference

Parameters

m²ⓘ
m²ⓘ
Paⓘ
kg/m³ⓘ
Show Trail

Controls

xⓘ

Calculated Values

Throat Velocity:
5.66;m/s5.66;m/s
Volume Flow Rate:
0.01;m3/s0.01;m³/s

Examples

Water line

ΔP=20 kPa, D₁=10 cm D₂=5 cm.

    Small throat

    Higher β ratio.

      Visualization

      Venturi Meter — Flow from Pressure Difference

      A Venturi meter is a flow-measurement device with a converging inlet, narrow throat, and diverging recovery section. By Bernoulli's principle, pressure falls where velocity rises — the throat has the highest speed and lowest pressure. Combining Bernoulli with continuity gives the theoretical volume flow rate through the throat.

      For horizontal flow (no elevation change), P₁ + ½ρv₁² = P₂ + ½ρv₂² and A₁v₁ = A₂v₂. Eliminating velocities yields v₂ = √[2ΔP / (ρ(1 − (A₂/A₁)²))] where ΔP = P₁ − P₂. Then Q = A₂v₂. The denominator shows why a significant area reduction is needed for measurable ΔP.

      Diameter ratio β = D₂/D₁ (or √(A₂/A₁)) is a key design parameter. As β → 1, ΔP → 0 for fixed Q — the meter becomes insensitive. Typical β ≈ 0.4–0.75. Real devices use Q = C_d A₂√[2ΔP/(ρ(1−β⁴))] with discharge coefficient C_d ≈ 0.95–0.99 accounting for losses and vena contracta.

      Venturi advantages over sharp orifice plates: gradual contraction and diffusion cause lower permanent pressure loss and less erosion/clogging. Used in municipal water, wastewater, oil pipelines, and HVAC when accurate, low-loss measurement is needed.

      Installation notes: straight pipe upstream (10–20 diameters) for developed flow; manometer or differential pressure transducer across inlet and throat; ΔP often read as ρ_manometer g Δh and converted to Pa.

      The same physics appears in carburetors (low throat pressure draws fuel), atomizers, and the Venturi effect in open channels. Cavitation occurs if throat pressure drops below vapor pressure — limits maximum ΔP.

      Key Concepts

      • Throat: maximum v, minimum P
      • v₂ = √[2ΔP/(ρ(1−β²))] horizontally
      • Q = C_d A₂v₂; β = D₂/D₁
      • ΔP ∝ Q² (square-root calibration)
      • Lower head loss than orifice plate
      • Bernoulli + continuity combined

      Real-World Applications

      • Municipal water and industrial flow metering
      • HVAC main duct airflow measurement
      • Oil, gas, and chemical pipeline monitoring
      • Class 12 Venturi derivation and lab
      • Carburetor and fuel injection venturi
      • Calibration reference for other flow meters

      Explore Further

      More fluid mechanics tools

      Physics Equations

      Throat Velocity:
      v2=2ΔPρ(1−(A2/A1)2)v_2 = \sqrt{\frac{2\Delta P}{\rho(1-(A_2/A_1)^2)}}
      Flow Rate:
      Q=A2v2Q = A_2 v_2

      Step-by-Step Solution

      See how the main results are calculated.

      1

      Step 1: Bernoulli (Horizontal Venturi)

      Equation:

      P1+12ρv12=P2+12ρv22P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2

      Explanation:

      Throat has lower pressure, higher velocity.

      2

      Step 2: With Continuity

      Equation:

      v2=2ΔPρ(1−(A2/A1)2)v_2 = \sqrt{\frac{2\Delta P}{\rho(1-(A_2/A_1)^2)}}

      Explanation:

      ΔP = P₁ − P₂ (Pa).

      3

      Step 3: Area Ratio

      Calculation:

      A2/A1=0.2497A_2/A_1 = 0.2497

      Explanation:

      Throat smaller ⇒ higher v₂.

      4

      Step 4: Throat Velocity

      Calculation:

      v2=5.6564 m/sv_2 = 5.6564 \text{ m/s}

      Result:

      v2=5.6564m/sv₂ = 5.6564 m/s
      5

      Step 5: Flow Rate

      Calculation:

      Q=A2v2=1.1086e−2 m3/sQ = A_2 v_2 = 1.1086e-2 \text{ m}^3\text{/s}

      Result:

      Q=1.1086e−2m3/sQ = 1.1086e-2 m³/s
      6

      Step 6: Measurement Use

      Venturi meters measure Q from ΔP.

      Explanation:

      Apply discharge coefficient C_d for real devices.

      Frequently Asked Questions (FAQ)

      Why square root in Q?

      Bernoulli gives ΔP ∝ v², so v ∝ √ΔP.

      Gas flow?

      Compressibility corrections if ΔP large.

      Vertical Venturi?

      Add ρg(z₁−z₂) to Bernoulli.

      Cavitation in throat?

      If P₂ below vapor pressure — limit operation.

      Manometer reading?

      Convert Δh to ΔP = ρ_manometer g Δh.

      Practice MCQs

      1. In Venturi throat, pressure is:
      2. Larger ΔP means:
      3. Venturi uses which equations?
      4. If A₂ approaches A₁, ΔP for given Q:
      5. β = D₂/D₁ is called:
      6. Venturi vs orifice:

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