Engineering task and calculation objective
The DROS module designs differential pressure devices for flow measurement to ISO 5167-1 (including Amendment A1): standard orifice plates with corner, D-D/2 and flange tappings, ISA 1932 and long-radius nozzles, as well as classical Venturi tubes and Venturi nozzles. From the measured differential pressure, the mass or volume flow rate can be calculated — and conversely, for a required flow rate, the associated differential pressure or the required throat diameter can be determined.
This calculation is needed in practically every process plant: when designing new measuring points for liquids, gases and steam, when reassessing existing orifice measurements after a change in operating point, or when evaluating measurement uncertainty. The core of the standard comprises the discharge coefficient C (for orifice plates from the Reader-Harris/Gallagher equation), the expansibility factor ε for compressible fluids, and the geometry and installation requirements (diameter ratio β, Reynolds number limits, required straight upstream and downstream lengths).
The advantage of the standardized method: a differential pressure device manufactured and installed in accordance with ISO 5167 measures without individual calibration, with a known, documented uncertainty.
Standard and calculation basis: ISO 5167-1 inkl. Änderung A1
Calculation workflow
- Define device type and fluid: First, the device type is selected (orifice plate, nozzle, Venturi tube or Venturi nozzle) and the fluid is described with density, viscosity and — for gases and steam — the isentropic exponent at the operating point.
- Check geometry and validity limits: Pipe inside diameter D, throat diameter d and diameter ratio β = d/D must lie within the type-specific limits of ISO 5167-1; the same applies to the Reynolds number and the requirements for pipe roughness and undisturbed upstream/downstream lengths.
- Determine discharge coefficient and expansibility factor: The discharge coefficient C is determined depending on the device type — for orifice plates from the Reader-Harris/Gallagher equation as a function of β, Reynolds number and tapping arrangement; for Venturi tubes as a fixed value per method of manufacture. For compressible fluids, the expansibility factor ε is calculated from the pressure ratio, β and the isentropic exponent.
- Calculate flow rate or differential pressure: Using the basic equation of the standard, the mass flow rate qm is calculated from the differential pressure Δp — or, inversely, the differential pressure for a given flow rate, or iteratively the required throat diameter. Since C depends on the Reynolds number, the flow calculation for orifice plates is a short iteration process.
- Evaluate pressure loss and measurement uncertainty: Finally, the permanent pressure loss of the device (significantly lower for Venturis than for orifice plates) and the combined measurement uncertainty according to the uncertainty data of the standard are reported.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Entrainment coefficient | C | – |
| Inside diameter of the tube | 50 mm ≤ D ≤ 500 mm D | m |
| Diameter of the throttle hole | d | m |
| Max. permissible equiv. tube roughness | k | m |
| Pressure at plus-pressure-sampling | p1 | Pa |
| Pressure at minor-pressure-sampling | p2 | Pa |
| Mass flow | qm | kg/s |
| Volume flow before throttle | qv | m³/s |
| Reynolds number referring to D | ReD | – |
| Reynolds number referring to d | Red | – |
| Temperature before throttle | T | °C |
| Mean velocity before throttle | U | m/s |
| Diameter ratio β = d/D | 0.3 ≤ β ≤ 0.8 β | – |
| Effective pressure over the throttle | Δp | Pa |
| Permanent pressure loss | Δϖ | Pa |
| Expansion number | ε1 | – |
| Isentropic exponent | κ | – |
| Dynamic viscosity of the fluid | η | mPa·s |
| Kinematic viscosity of the fluid | ν | m²/s |
| Density before throttle | ρ1 | kg/m³ |
| Pressure ratio τ = p2/p1 | p2/p1 ≥ 0.75 τ | – |
| Max. permissible relative tube roughness | kr,max | – |
| Physical state (liquid/gas) | Phasenzustand | – |
| Type of pressure-sampling | Druckentnahme | – |
Calculation options
Physical state (liquid/gas)
liquid · 1
Type of pressure-sampling
Corner tap · D-D/2 tap · Flange tap
Type of inlet cone
rough · processed · welded
Type
Orifices · ISA-1932 nozzles · Long radius nozzles · Venturi tubes · Venturi nozzles
Worked example
A classical Venturi tube with a machined convergent section measures the flow of water. The mass flow rate is to be determined from the measured differential pressure — a worked example of a flow measurement calculation to ISO 5167-1.
Given values
| Pipe inside diameter D | 100 mm |
| Throat diameter d | 60 mm |
| Differential pressure Δp | 200 mbar (20,000 Pa) |
| Density of water ρ | 998 kg/m³ |
| Discharge coefficient C (Venturi, machined convergent section) | 0.995 |
| Expansibility factor ε (incompressible) | 1.0 |
Solution
Diameter ratio and velocity of approach factor
β = d/D = 60/100 = 0.6
1/√(1 − β4) = 1/√(1 − 0.1296) = 1/0.9330 = 1.0719
Mass flow rate from the basic equation of ISO 5167-1
qm = C/√(1 − β4) · ε · (π/4) · d² · √(2 · Δp · ρ)
Throat cross-section: (π/4) · 0.060² = 0.002827 m²
√(2 · 20,000 · 998) = √(39,920,000) = 6,318 kg/(m²·s)... combined:
qm = 0.995 · 1.0719 · 1.0 · 0.002827 · 6,318 = 19.05 kg/s
Volume flow rate
qv = qm/ρ = 19.05/998 = 0.01909 m³/s ≈ 68.7 m³/h
Result
| Mass flow rate qm | 19.05 kg/s |
| Volume flow rate qv | 68.7 m³/h |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
Orifice plate, nozzle or Venturi tube — how do I choose the device type?
The standard orifice plate is cheapest to manufacture and install, but has the largest permanent pressure loss and is sensitive to edge wear. Nozzles tolerate higher velocities and dirty fluids better (typical for steam). Venturi tubes have the lowest permanent pressure loss thanks to their diffuser — important for large volume flows and expensive pumping energy — but cost the most and require the greatest installation length. The deciding factors are operating cost (pressure loss), fluid and available installation length.
Why is the flow calculation from the differential pressure iterative?
For orifice plates, the discharge coefficient C depends on the Reynolds number via the Reader-Harris/Gallagher equation — but the Reynolds number is only known once the flow rate is established. You therefore start with an estimate for C, calculate qm and the Reynolds number, update C and repeat until convergence; two to three iterations are usually sufficient.
What happens if the straight upstream and downstream lengths are not maintained?
Swirl and asymmetric velocity profiles downstream of elbows, valves or tees distort the discharge coefficient; the uncertainty guaranteed in the standard then no longer applies. ISO 5167 specifies minimum lengths depending on device type and type of disturbance; if these cannot be maintained, a flow conditioner must be installed or an additional uncertainty contribution applied.
Up to what pressure ratio may I measure with gases?
The expansibility factor equations of ISO 5167 are only valid for moderate expansion; the limit is p2/p1 ≥ 0.75. At larger differential pressures relative to the absolute pressure, the measurement becomes increasingly uncertain and the approximation for ε invalid — in that case a smaller orifice bore, a different measuring range or a different measuring principle must be chosen.