Orifice plate


An orifice plate is a device used for measuring flow rate, for reducing pressure or for restricting flow.

Description

An orifice plate is a thin plate with a hole in it, which is usually placed in a pipe. When a fluid passes through the orifice, its pressure builds up slightly upstream of the orifice but as the fluid is forced to converge to pass through the hole, the velocity increases and the fluid pressure decreases. A little downstream of the orifice the flow reaches its point of maximum convergence, the vena contracta where the velocity reaches its maximum and the pressure reaches its minimum. Beyond that, the flow expands, the velocity falls and the pressure increases. 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.
In general, the mass flow rate measured in kg/s across an orifice can be described as
The [|overall pressure loss] in the pipe due to an orifice plate is lower than the measured pressure, typically by a factor of.

Application

Orifice plates are most commonly used to measure flow rates in pipes, when the fluid is single-phase and well-mixed, the flow is continuous rather than pulsating, the fluid occupies the entire pipe, 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.
An orifice plate is called a calibrated orifice if it has been calibrated with an appropriate fluid flow and a traceable flow measurement device.
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. There are many other possibilities. 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. Variations on these possibilities are covered in various standards and handbooks. Each combination gives rise to different coefficients of discharge which can be predicted so long as various conditions are met, conditions which differ from one type to another.
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.
Orifice plates are also used to reduce pressure or restrict flow, in which case they are often called restriction plates.

Pressure tappings

There are three standard positions for pressure tappings, commonly named as follows:
These types are covered by ISO 5167 and other major standards. 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 annular slots running completely round the internal circumference of the orifice carrier.

Plate

Standards and handbooks are mainly concerned with ' plates. 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 ' or ' orifice, which has a fully rounded leading edge and no cylindrical section, and the ' or plate which has a bevelled leading edge and a very short cylindrical section. The orifices are normally concentric with the pipe and circular. Standards and handbooks stipulate that the upstream surface of the plate is particularly flat and smooth. Sometimes a small drain or vent hole is drilled through the plate where it meets the pipe, to allow condensate or gas bubbles to pass along the pipe.

Pipe

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. Similarly the flow downstream of the plate must be unobstructed, otherwise the downstream pressure will be affected. To achieve this, the pipe must be acceptably circular, smooth and straight for stipulated distances. Sometimes when it is impossible to provide enough straight pipe, flow conditioners such as tube bundles or plates with multiple holes are inserted into the pipe to straighten and develop the flow profile, but even these require a further length of straight pipe before the orifice itself. Some standards and handbooks also provide for flows from or into large spaces rather than pipes, stipulating that the region before or after the plate is free of obstruction and abnormalities in the flow.

Theory

Incompressible flow

By assuming steady-state, incompressible, inviscid, laminar flow in a horizontal pipe with negligible frictional losses, Bernoulli's equation reduces to an equation relating the conservation of energy between two points on the same streamline:
or:
By continuity equation:
or and :
Solving for :
and:
The above expression for gives the theoretical volume flow rate. Introducing the beta factor as well as the discharge coefficient :
And finally introducing the meter coefficient which is defined as 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:
Deriving the above equations used the cross-section of the orifice opening and is not as realistic as using the minimum cross-section at the vena contracta. In addition, frictional losses may not be negligible and viscosity and turbulence effects may be present. For that reason, the coefficient of discharge is introduced. Methods exist for determining the coefficient of discharge as a function of the Reynolds number.
The parameter is often referred to as the velocity of approach factor and multiplying the coefficient of discharge by that parameter produces the flow coefficient. Methods also exist for determining the flow coefficient as a function of the beta function and the location of the downstream pressure sensing tap. For rough approximations, the flow coefficient may be assumed to be between 0.60 and 0.75. For a first approximation, a flow coefficient of 0.62 can be used as this approximates to fully developed flow.
An orifice only works well when supplied with a fully developed flow profile. This is achieved by a long upstream length 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. Venturis also require much less straight pipe upstream. A venturi meter is more efficient, but usually more expensive and less accurate than an orifice plate.

Compressible flow

In general, equation is applicable only for incompressible flows. It can be modified by introducing the expansibility factor, to account for the compressibility of gasses.
is 1.0 for incompressible fluids and it can be calculated for compressible gases using empirically determined formulae as shown below in [|computation].
For smaller values of β, if the fluid is compressible, the rate of flow depends on whether the flow has become choked. If it is, then the flow may be calculated as shown at choked flow. By using a mechanical energy balance, compressible fluid flow in un-choked conditions may be calculated as:
or
Under choked flow conditions, the fluid flow rate becomes:
or

Computation according to ISO 5167

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. With local pressure tappings, sharp-edged orifices have coefficients around 0.6 to 0.63, while the coefficients for conical entrance plates are in the range 0.73 to 0.734 and for quarter-circle plates 0.77 to 0.85. The coefficients of sharp-edged orifices vary more with fluids and flow rates than the coefficients of conical-entrance and quarter-circle plates, especially at low flows and high viscosities.
For compressible flows such as flows of gases or steam, an expansibility factor or expansion factor is also calculated. This factor is primarily a function of the ratio of the measured differential pressure to the fluid pressure and so can vary significantly as the flow rate varies, especially at high differential pressures and low static pressures.
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 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.
Volume flow rate:

Mass flow rate:

Coefficient of discharge

Coefficient of discharge for sharp-edged orifice plates with corner, flange or D and D/2 tappings and no drain or vent hole :

Expansibility factor

Expansibility factor, also called expansion factor, for sharp-edged orifice plates with corner, flange or D and D/2 tappings:

Overall pressure loss

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