Orifice plate

By measuring the difference in fluid pressure across tappings upstream and downstream of the plate, the flow rate can be obtained from Bernoulli's equation using coefficients established from extensive research.

[4] Orifice plates are most commonly used to measure flow rates in pipes, when the fluid is single-phase (rather than being a mixture of gases and liquids, or of liquids and solids) and well-mixed, the flow is continuous rather than pulsating, the fluid occupies the entire pipe (precluding silt or trapped gas), the flow profile is even and well-developed and the fluid and flow rate meet certain other conditions.

Under these circumstances and when the orifice plate is constructed and installed according to appropriate standards, the flow rate can easily be determined using published formulae based on substantial research and published in industry, national and international standards.

Plates are commonly made with sharp-edged circular orifices and installed concentric with the pipe and with pressure tappings at one of three standard pairs of distances upstream and downstream of the plate; these types are covered by ISO 5167 and other major standards.

The edges may be rounded or conical, the plate may have an orifice the same size as the pipe except for a segment at top or bottom which is obstructed, the orifice may be installed eccentric to the pipe, and the pressure tappings may be at other positions.

[5] Once the orifice plate is designed and installed, the flow rate can often be indicated with an acceptably low uncertainty simply by taking the square root of the differential pressure across the orifice's pressure tappings and applying an appropriate constant.

Other types include The measured differential pressure differs for each combination and so the coefficient of discharge used in flow calculations depends partly on the tapping positions.

The simplest installations use single tappings upstream and downstream, but in some circumstances these may be unreliable; they might be blocked by solids or gas-bubbles, or the flow profile might be uneven so that the pressures at the tappings are higher or lower than the average in those planes.

In these situations multiple tappings can be used, arranged circumferentially around the pipe and joined by a piezometer ring, or (in the case of corner taps) annular slots running completely round the internal circumference of the orifice carrier.

In these, the leading edge is sharp and free of burrs and the cylindrical section of the orifice is short, either because the entire plate is thin or because the downstream edge of the plate is bevelled.

Exceptions include the quarter-circle or quadrant-edge orifice, which has a fully rounded leading edge and no cylindrical section, and the conical inlet or conical entrance plate which has a bevelled leading edge and a very short cylindrical section.

Standards and handbooks stipulate that the upstream surface of the plate is particularly flat and smooth.

Standards and handbooks stipulate a well-developed flow profile; velocities will be lower at the pipe wall than in the centre but not eccentric or jetting.

To achieve this, the pipe must be acceptably circular, smooth and straight for stipulated distances.

By assuming steady-state, incompressible (constant fluid density), inviscid, laminar flow in a horizontal pipe (no change in elevation) with negligible frictional losses, Bernoulli's equation (which expresses the conservation of energy of an incompressible fluid parcel as it moves between two points on the same streamline) can be rewritten without the gravitational potential energy term and reduced to:

to obtain the final equation for the volumetric flow of the fluid through the orifice which accounts for irreversible losses:

Multiplying by the density of the fluid to obtain the equation for the mass flow rate at any section in the pipe:[8][9][10][11]

In addition, frictional losses may not be negligible and viscosity and turbulence effects may be present.

Methods exist for determining the coefficient of discharge as a function of the Reynolds number.

An orifice only works well when supplied with a fully developed flow profile.

This is achieved by a long upstream length (20 to 40 pipe diameters, depending on Reynolds number) or the use of a flow conditioner.

Orifice plates are small and inexpensive but do not recover the pressure drop as well as a venturi, nozzle, or venturi-nozzle does.

A venturi meter is more efficient, but usually more expensive and less accurate (unless calibrated in a laboratory) than an orifice plate.

is 1.0 for incompressible fluids and it can be calculated for compressible gases[9] using empirically determined formulae as shown below in computation.

Flow rates through an orifice plate can be calculated without specifically calibrating the individual flowmeter so long as the construction and installation of the device complies with the stipulations of the relevant standard or handbook.

The calculation takes account of the fluid and fluid conditions, the pipe size, the orifice size and the measured differential pressure; it also takes account of the coefficient of discharge of the orifice plate, which depends upon the orifice type and the positions of the pressure tappings.

The equations provided in American and European national and industry standards and the various coefficients used to differ from each other even to the extent of using different combinations of correction factors, but many are now closely aligned and give identical results; in particular, they use the same Reader-Harris/Gallagher (1998) equation for the coefficient of discharge for sharp-edged orifice plates.

The equations below largely follow the notation of the international standard ISO 5167 and use SI units.

[3][16] Volume flow rate: Mass flow rate: Coefficient of discharge for sharp-edged orifice plates with corner, flange or D and D/2 tappings and no drain or vent hole (Reader-Harris/Gallagher equation): Expansibility factor, also called expansion factor, for sharp-edged orifice plates with corner, flange or D and D/2 tappings: The overall pressure loss caused by an orifice plate is less than the differential pressure measured across tappings near the plate.

For sharp-edged plates such as corner, flange or D and D/2 tappings, it can be approximated by the equation or