Engineering task and calculation objective
The RO module performs the orifice plate calculation using the differential pressure method: a measuring orifice constricts the pipe cross-section, and the flow rate is determined from the differential pressure dP between the pressure tappings upstream and downstream of the orifice plate. The basis is the standardised method for pressure differential devices (DIN EN ISO 5167, formerly DIN 1952), which specifies the discharge coefficient, the expansibility factor and the installation conditions.
The calculation links the geometry – pipe inside diameter D, orifice bore diameter d, from these the diameter ratio beta and the area ratio m, as well as the position of the pressure tappings via the distances l1 and l2′ – with the operating data of the medium: density, dynamic viscosity and, for gases, the isentropic exponent. As a result, the module delivers the mass flow rate qm, the Reynolds number, the discharge coefficient C, the flow coefficient alpha, the expansibility factor e, as well as the permanent pressure loss and the static pressure downstream of the orifice.
Anyone who wants to calculate an orifice plate or verify an existing flow measurement – for example to size a new metering point, to convert to changed operating conditions or to sanity-check plant measurement data – obtains here all characteristic quantities of the pressure differential device in a single calculation run.
Calculation workflow
- Define the medium and operating state: First, it is selected whether the medium is liquid or gaseous; then the density Rho, the dynamic viscosity Eta, for gases the isentropic exponent k, and the static pressure p1 upstream of the orifice and the differential pressure dP are entered.
- Describe the geometry of the metering run: The pipe inside diameter D and the orifice bore diameter d at operating conditions yield the diameter ratio beta and the area ratio m; the distances of the pressure tappings l1 and l2′, or the ratios L1 and L2′, define the tapping arrangement (corner, flange or D-D/2 tappings).
- Determine the discharge coefficient and expansibility factor: The discharge coefficient C is calculated per the standard equation as a function of beta, the Reynolds number Re and the tapping arrangement; for compressible media, the expansibility factor e accounts for the density change of the gas as it expands through the orifice bore.
- Calculate the flow rate iteratively: Since C depends on the Reynolds number, which in turn depends on the sought mass flow, the mass flow rate qm is determined iteratively until the flow equation and the Reynolds number are consistent; in addition, the flow velocity v in the pipe is reported.
- Determine the pressure loss and downstream pressure: Finally, the module calculates the permanent pressure loss dw of the orifice – considerably smaller than the differential pressure, since part of the pressure drop is recovered downstream – as well as the static pressure P2 downstream of the orifice.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Massenstrom | Massenstrom | kg/s |
| Rohres | Rohres | m |
| Blendendurchmesser | Blendendurchmesser | m |
| Viskosität | Viskosität | mPa·s |
| Dichte | Dichte | kg/m³ |
| Wirkdruck | Wirkdruck | Pa |
| Druckentnahme-Blendenstirns. | Druckentnahme-Blendenstirns. | m |
| Druckentnahme-Blendenrückseite | Druckentnahme-Blendenrückseite | m |
| l1/D | l1/D | – |
| l2'/D | l2'/D | – |
| Isentropenexponent | Isentropenexponent | – |
| _Blendenart | _Blendenart | – |
| Rohr | Rohr | m/s |
| 2 | 2 | – |
| Blende | Blende | Pa |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Durchmesserverhältnis | Durchmesserverhältnis | – |
| C | C | – |
| Blende | Blende | Pa |
| D) | D) | – |
| m | m | – |
| Expansionszahl | Expansionszahl | – |
| alpha | alpha | – |
| Blende | Blende | Pa |
Frequently asked questions
Within which range is the standardised orifice calculation valid?
The standard method applies to fully developed, swirl-free pipe flow of Newtonian fluids, typically for pipe inside diameters from about 50 mm, diameter ratios beta between 0.1 and 0.75 and Reynolds numbers above a minimum limit that depends on beta and the tapping arrangement. Outside these limits, the uncertainties of the discharge coefficient increase considerably; in addition, sufficient straight upstream and downstream lengths must be maintained.
What is the difference between differential pressure and permanent pressure loss?
The differential pressure dP is the pressure difference between the tapping points immediately at the orifice and serves as the measurement signal. Downstream, part of it is recovered as static pressure through the deceleration of the contracted jet; only the remainder persists as permanent pressure loss dw. The smaller beta, the larger the share of the permanent loss in the differential pressure – this must be considered in the hydraulic design of the piping.
What is the purpose of the expansibility factor for gases?
As the flow passes through the orifice, the pressure drops, a gas expands and its density decreases. The expansibility factor e corrects the flow equation, derived for incompressible media, for this effect; it depends on the pressure ratio dP/p1, the isentropic exponent k and beta. For liquids, e = 1. The method assumes moderate pressure ratios; for large expansions, the orifice is unsuitable as a metering device.
Which sources of error dominate in practice?
Edge wear and deposits on the orifice plate (the sharp inlet edge is a prerequisite for the standard discharge coefficient), too-short straightening lengths or swirl downstream of bends, incorrectly referenced density under fluctuating operating pressure, and confusion between the diameters at operating and reference temperature. The zero-point and characteristic-curve errors of the differential pressure transmitter also feed directly into the measured flow rate.