| name | flow-measurement |
| description | Flow measurement devices — orifice plate, venturi, nozzle, V-notch weir, Coriolis, magnetic, ultrasonic, rotameter. Discharge coefficients, ISO 5167, uncertainty. |
| metadata | {"priority":7,"promptSignals":{"phrases":["flow measurement","orifice","venturi","flow meter","discharge coefficient","ISO 5167","Coriolis","ultrasonic meter"],"minScore":3}} |
Flow Measurement — Complete Skill
Differential Pressure Devices (ISO 5167)
Orifice Plate
Q = C_d × A_orifice × √(2ΔP/ρ) / √(1 - β⁴)
β = d/D (diameter ratio, d = orifice, D = pipe)
A_orifice = π d²/4
Discharge coefficient (Reader-Harris/Gallagher, ISO 5167-2):
C_d = 0.5961 + 0.0261β² - 0.216β⁸ + 0.000521(10⁶β/Re_D)^0.7 + (0.0188 + 0.0063A)β^3.5(10⁶/Re_D)^0.3 + (0.043 + 0.080e^(-10L₁) - 0.123e^(-7L₁))(1-0.11A)β⁴/(1-β⁴) - 0.031(M₂' - 0.8M₂'^1.1)β^1.3
Simplified (turbulent, β=0.4-0.7): C_d ≈ 0.61-0.64
Pressure tappings: D-D/2, flange, or corner (different C_d)
β limits (ISO 5167): 0.1 ≤ β ≤ 0.75
Minimum Re_D: 5000 (corner/flange taps), variable with β for D-D/2 taps
Permanent pressure loss: ΔP_perm = ΔP × (1-β²) approximately
Venturi Meter
C_d = 0.984 (classical venturi, machined inlet), 0.985-0.995 (range)
Q = C_d × π/4 × d² × √(2ΔP / (ρ(1-β⁴)))
Lower permanent loss than orifice: ΔP_perm ≈ 0.1-0.25 × ΔP
Flow Nozzle (ISA 1932)
C_d ≈ 0.96-0.99 (higher than orifice)
Lower loss than orifice, higher than venturi
Good for: wet steam, dirty fluids (no sharp edge to damage)
Pitot Tube (Point Velocity)
V = C_p × √(2 × (P_total - P_static) / ρ)
C_p = 0.99-1.00 for standard pitot
Average velocity requires traverse (multiple points per ISO 3966)
Open Channel Flow Measurement
V-Notch Weir
Q = C_d × (8/15) × tan(θ/2) × √(2g) × H^(5/2)
θ = notch angle; H = head above notch crest [m]
C_d ≈ 0.58-0.62 (full contraction, standard design)
90° V-notch: Q ≈ 1.38 H^2.5 [Q in m³/s, H in m]
Rectangular Weir (Francis Formula)
Q = C_d × L × √(2g) × H^(3/2) × 2/3
C_d ≈ 0.61 (suppressed weir)
Francis: Q = 1.84(L - 0.1H) × H^1.5 [m³/s, corrections for contractions]
Parshall Flume
Used for: irrigation, wastewater — robust, self-cleaning
Q = C × W^n × H_a^u (coefficients from table per throat width W)
Electromagnetic Flowmeter (Mag Meter)
Based on Faraday's law: E = B × D × V (E = induced EMF, B = magnetic field, D = pipe diameter)
Full-bore, obstruction-free, bidirectional
Best for: conductive liquids (σ > 5 μS/cm), slurries, corrosive liquids
Accuracy: ±0.2-0.5% of reading
Not suitable: hydrocarbons, gases
Coriolis Flowmeter
Measures true mass flow rate directly: Q_m = k × f₀² × ΔT
ΔT = time difference in Coriolis twist of vibrating tubes
Simultaneously measures: mass flow, density (from resonant frequency), temperature, viscosity (some models)
Accuracy: ±0.1-0.2% of reading (best accuracy of any meter)
Applications: custody transfer, pharmaceuticals, expensive fluids
Limitation: expensive, pressure drop, not for large pipes (>200mm uneconomical)
Ultrasonic Flowmeter
Transit-time: Δt = 2L V_fluid cos θ / (c² - V² cos²θ) → V_fluid
c = speed of sound in fluid, L = path length, θ = beam angle
Clamp-on: external transducers, no intrusion (maintenance-friendly)
Accuracy: ±1-2% clamp-on; ±0.5-1% wetted transducers
Good for: clean liquids, gases; poor for: bubbly/slurry flows
Rotameter (Variable Area)
Float equilibrium: buoyancy + drag = gravity → V_annulus × Q relationship
Cheap, simple, visual indication; accuracy ±2-5%
Must be vertical; limited to clean, non-viscous fluids
Turndown Ratio Comparison
| Meter | Turndown | Accuracy |
|---|
| Orifice | 3:1 to 5:1 | ±0.5-1% |
| Venturi | 3:1 to 5:1 | ±0.5-1% |
| Coriolis | 100:1+ | ±0.1% |
| Mag meter | 30:1 | ±0.2-0.5% |
| Ultrasonic | 40:1 | ±0.5-1% |
| Rotameter | 10:1 | ±2-5% |
Output
Provide: Q [m³/s or kg/s], C_d value, β ratio, ΔP required [Pa], permanent pressure loss [Pa], required straight pipe lengths upstream/downstream, meter type recommendation for application.
