Flow Measurement

Venturi Meter Flow Measurement

Design and size venturi meters per ISO 5167-4 for applications requiring low permanent pressure loss. Ideal for compressor surge control, high-flow gas measurement, and installations where operating cost matters.

Pressure recovery

Beta ratio range

β = 0.30–0.75

Per ISO 5167-4; optimal range 0.45-0.65 for accuracy and turndown.

Permanent ΔP loss

10–30%

vs 40-90% for orifice plate. Significant compression cost savings.

Discharge coefficient

C = 0.984–0.995

Higher and more stable than orifice (0.59-0.65). Less Re sensitivity.

Contents

Use this guide when you need to:

  • Size venturi meters for gas or liquid flow.
  • Calculate pressure recovery and permanent loss.
  • Decide between venturi and orifice meters.
  • Design for compressor surge control.

1. Overview & Principles

Venturi meters are differential pressure flow measurement devices that offer significantly lower permanent pressure loss than orifice plates. Invented by Giovanni Venturi in 1797 and refined by Clemens Herschel in 1888, they remain the preferred choice for applications where operating cost (compression energy) is critical.

Classical venturi tube showing convergent cone (21°), throat section (d), and divergent cone (7°-15°) with pressure tap locations P₁ and P₂
Classical (Herschel) venturi tube: Gradual contraction and expansion minimize turbulence and maximize pressure recovery.

Key advantage

Low permanent loss

10-30% of differential pressure vs 40-90% for orifice. Reduces compression costs.

Discharge coefficient

C = 0.984–0.995

Nearly ideal flow. Much higher than orifice (0.59-0.65).

Disadvantages

Higher cost & length

3-10× orifice cost. Requires more pipe length for installation.

Turndown

3:1 to 5:1

Similar to orifice. Limited by differential pressure transmitter range.

Bernoulli Principle

Like all differential pressure meters, venturis operate on Bernoulli's principle: flow acceleration through the throat creates a pressure drop proportional to velocity squared.

Venturi Flow Equation: Q = C × ε × (π/4) × d² × √(2 × ΔP / (ρ × (1 - β⁴))) Where: Q = Volumetric flow rate (ft³/s or m³/s) C = Discharge coefficient (0.984-0.995 for classical venturi) ε = Expansibility factor (gas only) d = Throat diameter ΔP = Differential pressure (P₁ - P₂) ρ = Fluid density at flowing conditions β = d/D = throat-to-pipe diameter ratio For incompressible flow (liquids), ε = 1. For compressible flow (gases), ε accounts for gas expansion.

How a Venturi Works

  1. Convergent section: Flow accelerates gradually (21° cone angle typical) from pipe diameter D to throat diameter d
  2. Throat section: Flow reaches maximum velocity at constant diameter (length = d)
  3. Divergent section: Flow decelerates gradually (7-15° cone angle) back to pipe diameter, recovering most pressure

The gradual transitions minimize flow separation and turbulence, allowing 70-90% of the differential pressure to be recovered—the key advantage over orifice plates.

Standards and Regulations

  • ISO 5167-4:2003 — Venturi tubes (international standard)
  • ASME MFC-3M — Measurement of Fluid Flow Using Orifice, Nozzle, and Venturi
  • ASME Fluid Meters, 6th Ed. — Comprehensive flow measurement reference
  • API MPMS Ch 14.3 — Natural gas flow measurement (accepts venturi meters)
When to choose venturi over orifice: Select venturi when (1) permanent pressure loss cost over meter lifetime exceeds 3-5× the additional capital cost, (2) application requires very low pressure loss (compressor suction), or (3) installation space allows the longer venturi length.

2. Pressure Recovery Advantage

The venturi's gradual divergent section allows controlled deceleration of flow, converting kinetic energy back to pressure energy. This is the fundamental advantage over orifice plates, where abrupt expansion causes turbulent energy dissipation.

Pressure Recovery vs Orifice

Meter Type Permanent Loss Pressure Recovery Typical Application
Orifice plate 40-90% of ΔP 10-60% General purpose, custody transfer
Venturi (7° divergent) 10-15% of ΔP 85-90% Compressor surge control
Venturi (15° divergent) 15-30% of ΔP 70-85% Space-limited installations
Venturi nozzle (ISA 1932) 30-50% of ΔP 50-70% High-velocity applications
Flow nozzle 30-80% of ΔP 20-70% Steam, high temperature

Permanent Pressure Loss Calculation

Permanent Pressure Loss (Classical Venturi): For 7° divergent angle: ΔP_perm = ΔP_measured × (0.218 - 0.420β + 0.380β²) For 15° divergent angle: ΔP_perm = ΔP_measured × (0.436 - 0.860β + 0.760β²) Example (β = 0.50, ΔP = 100 in H₂O): 7° divergent: ΔP_perm = 100 × (0.218 - 0.420×0.5 + 0.380×0.25) = 10.3 in H₂O Recovery = 89.7% 15° divergent: ΔP_perm = 100 × (0.436 - 0.860×0.5 + 0.760×0.25) = 19.6 in H₂O Recovery = 80.4% Compare to orifice at β = 0.50: ΔP_perm ≈ 68 in H₂O (68% loss, only 32% recovery)

Operating Cost Impact

For gas compression applications, permanent pressure loss directly increases compression horsepower:

Compression Cost of Permanent Pressure Loss: Additional HP = (Q × ΔP_perm) / (33,000 × η) Where: Q = Flow rate (ACFM) ΔP_perm = Permanent pressure loss (psi) η = Compressor efficiency (typically 0.75-0.85) Example: 50 MMSCFD at 500 psig, 80°F, SG = 0.65 ACFM = 50,000,000 / 1440 × (14.7/514.7) × (540/520) / 0.90 = 1,020 ACFM Orifice (β=0.5): ΔP_meas = 100 in H₂O, ΔP_perm = 68 in H₂O = 2.45 psi Additional HP = (1,020 × 2.45 × 144) / (33,000 × 0.80) = 13.6 HP Venturi (β=0.5, 7°): ΔP_meas = 100 in H₂O, ΔP_perm = 10.3 in H₂O = 0.37 psi Additional HP = (1,020 × 0.37 × 144) / (33,000 × 0.80) = 2.1 HP Savings = 11.5 HP continuous Annual cost savings at $0.10/kWh: = 11.5 × 0.746 × 8,760 × $0.10 = $7,500/year Over 20-year meter life: ~$150,000 savings

Divergent Angle Trade-offs

Divergent Angle Pressure Recovery Divergent Length Best Use
5-7° 85-90% Longest (4-8D) Maximum recovery, space available
10° 80-85% Medium (2-4D) Balanced recovery and length
15° 70-80% Shortest (1.5-2.5D) Space-constrained installations
>15° <70% Very short Not recommended (flow separation)
Rule of thumb: If the permanent pressure loss savings over the meter's 20-year life exceed 3-5× the additional capital cost of a venturi vs orifice, choose venturi. For high-pressure gas applications >500 psig, this breakeven point is typically reached at flows >10 MMSCFD.

3. Venturi Geometry & Types

ISO 5167-4 defines two primary venturi types: the Classical (Herschel) Venturi with truncated cone inlet, and the Venturi Nozzle with curved ISA 1932 profile inlet. Each has specific dimensional requirements for calibration validity.

Classical (Herschel) Venturi

Classical Venturi Dimensions (ISO 5167-4): Convergent Section: - Angle: 21° ± 1° (total included angle) - Length: L_conv = (D - d) / (2 × tan(10.5°)) ≈ 2.7 × (D - d) Throat Section: - Diameter: d (measured to ±0.1%) - Length: L_throat = d (one throat diameter) Divergent Section: - Angle: 7° to 15° (typically 7° for best recovery) - 7° angle: L_div = (D - d) / (2 × tan(3.5°)) ≈ 8.2 × (D - d) - 15° angle: L_div = (D - d) / (2 × tan(7.5°)) ≈ 3.8 × (D - d) Total Length (approximate): - 7° divergent: L_total ≈ 12 × (D - d) + d - 15° divergent: L_total ≈ 7 × (D - d) + d Example: D = 12", d = 6" (β = 0.5) - 7° version: L_total ≈ 12 × 6 + 6 = 78" = 6.5 ft - 15° version: L_total ≈ 7 × 6 + 6 = 48" = 4 ft

Venturi Nozzle (ISA 1932)

The venturi nozzle combines an ISA 1932 nozzle inlet with a divergent recovery cone. It has a higher pressure loss than the classical venturi but is shorter and has well-characterized performance at high velocities.

Venturi Nozzle Characteristics: Inlet: Curved ISA 1932 profile (elliptical contraction) Throat: Cylindrical section, length = 0.3d Divergent: 7° to 15° cone Permanent pressure loss: 30-50% (higher than classical) Discharge coefficient: C = 0.986 to 0.995 Best suited for: - High-velocity flow (throat velocity >300 ft/s) - Steam and high-temperature gas - Shorter installation length required

Discharge Coefficient

The venturi discharge coefficient is much higher and more stable than orifice plates:

Venturi Type Beta Range Discharge Coefficient C Re Minimum
Classical (as-cast) 0.30 - 0.75 0.984 ± 0.7% 2 × 10⁵
Classical (machined) 0.30 - 0.75 0.995 ± 0.5% 2 × 10⁵
Classical (rough-welded) 0.30 - 0.75 0.985 ± 1.5% 2 × 10⁵
Venturi nozzle 0.30 - 0.75 0.986 - 0.995 1.5 × 10⁵

Expansibility Factor

Expansibility Factor for Gas Flow (ISO 5167-4): ε = 1 - (0.649 + 0.696β⁴) × (ΔP / (κ × P₁)) Where: κ = Isentropic exponent (Cp/Cv) P₁ = Upstream absolute pressure ΔP = Differential pressure For natural gas: κ ≈ 1.27-1.31 For air: κ = 1.40 Validity limit: ΔP/P₁ ≤ 0.25 Example: β = 0.50, ΔP = 100 in H₂O = 3.6 psi, P₁ = 500 psia, κ = 1.30 ε = 1 - (0.649 + 0.696 × 0.0625) × (3.6 / (1.30 × 500)) ε = 1 - 0.692 × 0.0055 = 0.9962 For most gas applications, ε ≈ 0.99-1.00 (nearly incompressible behavior)

Pressure Tap Locations

  • Upstream tap (P₁): Located 0.5D to 1D upstream of convergent entrance
  • Throat tap (P₂): Located at mid-throat (0.5d from throat entrance)
  • Tap drilling: 0.25" to 0.50" diameter, perpendicular to wall, flush with inside surface
  • Multiple taps: 4 taps at 90° intervals, manifolded for averaging (recommended)
Construction quality matters: Machined venturis (C = 0.995) have 40% lower uncertainty than as-cast venturis (C = 0.984). For custody transfer applications, always specify machined or lab-calibrated venturis.

4. Sizing & Calculations

Venturi sizing involves selecting throat diameter to achieve desired differential pressure at design flow while maintaining beta ratio within ISO 5167-4 limits (0.30-0.75).

Sizing Procedure

Venturi Sizing Steps: Given: Q_design, P, T, gas properties, pipe diameter D Step 1: Calculate gas density at flowing conditions ρ = (P × MW) / (Z × R × T) Step 2: Convert design flow to actual conditions Q_actual = Q_std × (P_std/P) × (T/T_std) × (Z/Z_std) Step 3: Select target differential pressure Typical: 100-200 in H₂O for good accuracy and turndown Maximum: 400 in H₂O (limited by transmitter range) Step 4: Assume initial beta (0.50 recommended) Step 5: Calculate required throat area from flow equation A = Q / (C × ε × √(2 × ΔP / (ρ × (1 - β⁴)))) Step 6: Calculate throat diameter d = √(4 × A / π) Step 7: Calculate actual beta β = d / D Step 8: Check 0.30 ≤ β ≤ 0.75; if not, adjust ΔP and repeat Step 9: Verify Reynolds number Re_D = 4 × ṁ / (π × D × μ) > 2 × 10⁵ Step 10: Calculate physical dimensions

Example: Size Venturi for Compressor Suction

Given: Gas flow: 25 MMSCFD natural gas Suction pressure: 300 psig Temperature: 80°F Pipe: 16" Schedule 40 (ID = 15.0") Gas: SG = 0.65, MW = 18.8, Z = 0.92, κ = 1.28 Target ΔP: 150 in H₂O Step 1: Gas density P_abs = 300 + 14.7 = 314.7 psia T_R = 80 + 460 = 540°R ρ = (314.7 × 18.8) / (0.92 × 10.73 × 540) = 1.11 lb/ft³ Step 2: Actual flow rate Q_std = 25,000,000 scfd / 86,400 = 289.4 scfm Q_actual = 289.4 × (14.73/314.7) × (540/520) × (0.92/1.0) Q_actual = 289.4 × 0.0468 × 1.038 × 0.92 = 12.93 acfm = 0.216 acfs Step 3: Assume β = 0.50, C = 0.995, ε = 0.997 ΔP = 150 in H₂O = 5.42 psi = 780 lbf/ft² Step 4: Required throat area Velocity factor = √(2 × 780 / (1.11 × (1 - 0.0625))) = √1501 = 38.7 ft/s A = 0.216 / (0.995 × 0.997 × 38.7) = 0.00563 ft² = 0.810 in² Step 5: Throat diameter d = √(4 × 0.810 / π) = 1.015" → Use 1.0" throat? No, too small! Problem: β = 1.0/15.0 = 0.067 (below minimum 0.30) Iteration: Reduce ΔP to 50 in H₂O ... (calculations) Result: d = 7.5", β = 0.50 ✓ Final Design: Throat diameter: 7.5" Beta ratio: 0.50 ΔP at design: 50 in H₂O Permanent loss: 5-7 in H₂O (10-15%) Divergent angle: 7° (recommended) Total length: ~5 ft

Beta Ratio Selection Guide

Consideration Low Beta (0.30-0.45) Optimal Beta (0.45-0.60) High Beta (0.60-0.75)
Differential pressure High ΔP Moderate ΔP Low ΔP
Throat velocity Very high Moderate Low
Turndown ratio 4:1 to 5:1 3:1 to 4:1 2:1 to 3:1
Permanent loss Higher (15-20%) Low (10-15%) Lowest (8-12%)
Physical length Longest Medium Shortest
Cost Highest Moderate Lowest

Flow Rate Calculation

Venturi Flow Calculation (from measured ΔP): Q_MMSCFD = K × d² × √(h_w × P_f / (T_f × SG × Z)) Where: K = 16.33 × C × ε × F_pv (constant for given venturi) d = Throat diameter (inches) h_w = Differential pressure (inches H₂O) P_f = Flowing pressure (psia) T_f = Flowing temperature (°R) SG = Gas specific gravity Z = Compressibility factor Simplified (for C ≈ 0.995, ε ≈ 0.997): Q_MMSCFD ≈ 16.25 × d² × √(h_w × P_f / (T_f × SG × Z)) Example: d = 6", h_w = 100 in H₂O, P_f = 514.7 psia, T_f = 540°R, SG = 0.65, Z = 0.90 Q_MMSCFD = 16.25 × 36 × √(100 × 514.7 / (540 × 0.65 × 0.90)) Q_MMSCFD = 585 × √(51,470 / 315.9) = 585 × 12.77 = 7.47 MMSCFD
Sizing tip: For compressor surge control, size the venturi throat for 110-120% of maximum expected flow at 80% of transmitter range. This provides headroom for flow excursions while maintaining good accuracy in the normal operating range.

5. Applications & Selection

Venturi meters excel in specific applications where their higher capital cost is justified by operating cost savings or technical requirements.

Ideal Applications for Venturi Meters

  • Compressor suction/surge control: Low pressure loss critical to avoid compressor surge; real-time flow measurement for anti-surge control
  • High-pressure gas transmission: Permanent loss × pressure × flow = significant compression energy over 20+ year life
  • Large-diameter pipelines (>24"): Orifice permanent loss becomes prohibitive at high flows
  • Dirty/erosive fluids: No sharp edges to erode; less sensitive to buildup than orifice
  • Pulsating flow: More stable than orifice due to higher C and gradual transitions
  • Wet gas/two-phase: Better handling of liquid droplets due to smooth geometry

Venturi vs Orifice Selection Matrix

Factor Favor Venturi Favor Orifice
Permanent pressure loss cost High (>$50,000/year) Low (<$10,000/year)
Operating pressure >500 psig <200 psig
Flow rate >20 MMSCFD <5 MMSCFD
Pipeline diameter >16" <8"
Installation space Available (>10D) Limited
Fluid cleanliness Dirty, erosive, wet Clean, dry
Flow profile Disturbed, pulsating Steady, developed
Budget priority Operating cost Capital cost
Accuracy requirement ±0.5% (custody) ±1-2% (process)

Installation Requirements

Venturi Installation (ISO 5167-4): Upstream straight pipe: - After single 90° elbow: 4D minimum (vs 17D for orifice) - After two elbows in plane: 7D minimum (vs 34D for orifice) - After reducer: 4D minimum (vs 22D for orifice) - After expander: 3D minimum (vs 12D for orifice) Downstream straight pipe: 4D minimum Key advantage: Venturi requires only 20-30% of orifice straight pipe length due to: - Higher C value less sensitive to velocity profile - Convergent section acts as flow straightener Orientation: Horizontal preferred; vertical acceptable with proper draining Pressure taps: At horizontal plane (±15°) for gas; at bottom for liquid

Cost-Benefit Analysis Template

Venturi vs Orifice Economic Comparison: Capital Costs: - Orifice fitting + plate: $5,000 - $15,000 (size dependent) - Venturi meter: $15,000 - $75,000 (3-5× orifice cost) - Delta capital: $10,000 - $60,000 Operating Costs (annual compression energy): - Orifice permanent loss: ΔP_perm × Q × P × 8,760 × electricity_rate / η - Venturi permanent loss: typically 15-25% of orifice loss - Annual savings: 75-85% of orifice loss cost Breakeven calculation: Years to payback = Delta_capital / Annual_savings Example: 30 MMSCFD at 800 psig - Orifice ΔP_perm = 2.5 psi, energy cost = $18,500/year - Venturi ΔP_perm = 0.4 psi, energy cost = $2,960/year - Annual savings = $15,540 - Delta capital = $40,000 - Payback = 40,000 / 15,540 = 2.6 years For 20-year meter life: NPV savings = ~$200,000

Common Venturi Applications by Industry

  • Natural gas transmission: Main line flow measurement, compressor station metering
  • Gas processing plants: Inlet separator gas flow, compressor anti-surge control
  • LNG facilities: Send-out gas measurement, boil-off gas metering
  • Power generation: Natural gas fuel metering, combustion air measurement
  • Chemical plants: Process gas flows, reactor feed measurement
  • Water/wastewater: Large-diameter water mains, pump station monitoring
Bottom line: Choose venturi when permanent pressure loss cost over meter lifetime exceeds 3× the capital cost premium. For high-pressure gas (>500 psig) and large flows (>20 MMSCFD), venturi almost always wins the economic comparison. For low-pressure or small flows, orifice is typically more cost-effective.

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