ORIFICE PLATE CONSTRUCTION AND COMPUTATION

ORIFICE PLATE 
CONSTRUCTION AND COMPUTATION

An orifice plate is a device used for measuring flow rate, for reducing pressure or for restricting flow (in the latter two cases it is often called a restriction plate). Either a volumetric or mass flow rate may be determined, depending on the calculation associated with the orifice plate. It uses the same principle as a Venturi nozzle, namely Bernoulli's principle which states that there is a relationship between the pressure of the fluid and the velocity of the fluid. When the velocity increases, the pressure decreases and vice versa.

Construction and General shape

An orifice plate consists of a circular, thin, flat plate with a hole (or orifice) machined through its centre to fine limits of accuracy. The orifice has a diameter less than the pipeline into which the plate is installed and a typical section of an installation is shown in Figure 1 (a). Orifice plates are manufactured in stainless steel, monel metal, polyester glass fibre, and for large pipes, such as

sewers or hot gas mains, in brick and concrete

Upstream face A

Care shall be taken in the design of the orifice plate and its installation to ensure that plastic
buckling and elastic deformation of the plate, due to the magnitude of the differential pressure or of any other stress, do not cause the slope of the straight line defined in figure 3 to exceed 1 % under working conditions.

The upstream face A of the plate shall be flat when the plate is installed in the pipe with zero
differential pressure across it. Provided that it can be shown that the method of mounting does not distort the plate, this flatness may be measured with the plate removed from the pipe. Under these circumstances, the plate may be considered to be flat when the maximum gap between the plate and a straight edge of length D laid across any diameter of the plate (see Figure 3) 
is less than 0,005(D – d)/2, i.e. the slope is less than 0,5 % when the orifice plate is examined prior to insertion into the meter line.
 As can be seen from Figure 3, the critical area is in the vicinity of the orifice bore. The uncertainty requirements for this dimension can be met using feeler gauges.

The upstream face of the orifice plate shall have a roughness criterion    within a circle
of diameter not less than D and which is concentric with the orifice. In all cases, the roughness of the
upstream face of the orifice plate shall not be such that it affects the edge sharpness measurement. If, under working conditions, the plate does not fulfil the specified conditions, it shall be repolished or cleaned to adiameter of at least D.
Downstream face B
The downstream face B shall be flat and parallel with the upstream face 
The flatness and surface condition of the downstream face may be judged by visual inspection
Thicknesses E and e
The thickness e of the orifice shall be between 0,005D and 0,02D.
The difference between the values of e measured at any point on the orifice shall not be greater than 0,001D.
The thickness E of the plate shall be between e and 0,05D. However, when 50 mm ≤ D ≤64 mm, a thickness E up to 3,2 mm is acceptable
If D W 200 mm, the difference between the values of E measured at any point of the plate shall
not be greater than 0,001D. If D < 200 mm, the difference between the values of E measured at any point ofthe plate shall not be greater than 0,2 mm.
Angle of bevel α
If the thickness E of the plate exceeds the thickness e of the orifice, the plate shall be bevelled on

the downstream side. The bevelled surface shall be well finished.
The angle of bevel α shall be 45° ± 15°.
Edges G, H and I
The upstream edge G shall be sharp. It is considered so if the edge radius is not greater than       0,000 4 d.
If d ≥ 25 mm, this requirement can generally be considered as satisfied by visual inspection, by checking that the edge does not reflect a beam of light when viewed with the naked eye. If d < 25 mm, visual inspection is not sufficient.
The upstream edge shall be square; it is considered to be so when the angle between the orifice
bore and the upstream face of the orifice plate is 90° ± 0,3°. The orifice bore is the region of the orifice plate between edges G and H.
The downstream edges H and I are within the separated flow region and hence the requirements
for their quality are less stringent than those for edge G. This being the case, small defects (for example, a single nick) are acceptable.
Diameter of orifice d

The diameter d shall in all cases be greater than or equal to 12,5 mm. The diameter ratio, β = d/D,

shall be always greater than or equal to 0,10 and less than or equal to 0,75.Within these limits, the value of β may be chosen by the user

The value d of the diameter of the orifice shall be taken as the mean of the measurements of at

least four diameters at approximately equal angles to each other. Care shall be taken that the edge and bore are not damaged when making these measurements

The orifice shall be cylindrical.

Principles of operation and pressure tappings 

When a fluid moves through a restriction in a pipe, the fluid accelerates and a reduction in pressure occurs, the magnitude of which is related to the flow rate of the fluid. The variation of pressure near an orifice plate is shown in Figure 1 (b). The position of minimum pressure is located downstream from the orifice plate where the flow stream is narrowest. This point of minimum cross-sectional area of the jet is called the ‘vena contracta’. Beyond this point the pressure rises but does not return to the original upstream value and there is a permanent pressure loss. This loss depends on the size and

type of orifice plate, the positions of the upstream and downstream pressure tappings and the change in fluid velocity between the pressure tappings that depends on the flow rate and the dimensions of the orifice plate. In Figure 1 (a) corner pressure tappings are shown at A and B. Alternatively, with an orifice plate inserted into a pipeline of diameter d, pressure tappings are often located at distances of D and D/2 from the plate respectively upstream and downstream. At distance D upstream the flow pattern is not influenced by the presence of the orifice plate, and distance D/2 coincides with the vena contracta.

There are three standard positions for pressure tappings (also called taps), commonly named as follows:

--Corner taps placed immediately upstream and downstream of the plate; convenient when the plate        is provided with an orifice carrier incorporating tappings 

--D and D/2 taps or radius taps placed one pipe diameter upstream and half a pipe diameter                 downstream of the plate; these can be installed by welding bosses to the pipe

--Flange taps placed 25.4 mm (1 inch) upstream and downstream of the plate, normally within               specialised pipe flanges.

These types are covered by ISO 5167 and other major standards. Other types include

---2½D and 8D taps or recovery taps placed 2.5 pipe diameters upstream and 8 diameters                      downstream, at which point the measured differential is equal to the unrecoverable pressure loss        caused by the orifice

---Vena contracta tappings placed one pipe diameter upstream and at a position 0.3 to 0.9 diameters     downstream, depending on the orifice type and size relative to the pipe, in the plane of minimum          fluid pressure.

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.

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. With local pressure tappings (corner, flange and D+D/2), 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 (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.

Volume flow rate:

Mass flow rate:

where

  = internal orifice diameter under operating conditions, m

 = volumetric flow rate (at any cross-section), m³/s

  = mass flow rate (at any cross-section), kg/s

   = orifice flow coefficient, dimensionless

    = ratio of orifice hole diameter to pipe diameter, dimensionless

   = diameter of the orifice hole, m

  = expansibility factor, 1 for incompressible gases and most liquids, and decreasing with pressure          ratio across the orifice, dimensionless

  = fluid density in plane of upstream tapping, kg/m³

  = differential pressure measured across the orifice, Pa

   = coefficient of discharge, dimensionless, typically between 0.6 and 0.85, depending on the orifice geometry and tappings

  = diameter ratio of orifice diameter to pipe diameter , dimensionless

Coefficient of discharge

YOU CAN FOLLOW THIS  IN ISO 5167

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):

The discharge coefficient - - varies considerably with changes in area ratio and the Reynolds number. A discharge coefficient  = 0.60 may be taken as standard, but the value varies noticeably at low values of the Reynolds number.

Discharge Coefficient - cd
Diameter Ratio d = D2 / D1	Reynolds Number - Re
	104	105	106	107
0.2	0.60	0.595	0.594	0.594
0.4	0.61	0.603	0.598	0.598
0.5	0.62	0.608	0.603	0.603
0.6	0.63	0.61	0.608	0.608
0.7	0.64	0.614	0.609	0.609

Limits of use
Standard orifice plates shall only be used in accordance with this part of ISO 5167 under the following conditions.

For orifice plates with corner or with D and D/2 pressure tappings:

- d ≥ 12,5 mm;

   50 mm ≤ D ≤1 000 mm;

  0,1 ≤ β ≤ 0,75;

 ReD ≥ 5 000 for 0,1 ≤ β ≤ 0,56;

 ReD ≥ 16 000 β² for β > 0,56.

For orifice plates with flange tappings:

-  d ≥ 12,5 mm;

 50 mm ≤ D ≤ 1 000 mm;

  0,1 ≤ β ≤ 0,75.

Both ReD ≥ 5 000 and ReD ≥ 170β²D
where D is expressed in millimetres

The pipe internal roughness shall satisfy the following specification if the uncertainty values in this part of  ISO 5167 are to be met, i.e. the value of the arithmetical mean deviation of the roughness profile, Ra, shall be such that 10⁴ Ra/D is less than the maximum value given in Table 1 and greater than the minimum value given in Table 2.

Expansibility factor 

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

but for incompressible fluids, including most liquids

${\displaystyle \epsilon =1}$

WHERE

    = pipe Reynolds number, , dimensionless

   = fluid absolute static pressure in plane of upstream tapping, Pa

   = fluid absolute static pressure in plane of downstream tapping, Pa

   = isentropic exponent, often approximated by specific heat ratio, dimensionless

   = dynamic viscosity of the fluid, Pa.s

   = fluid density in plane of upstream tapping, kg/m³

   = internal orifice diameter under operating conditions, m

  = internal pipe diameter under operating conditions, m

Values of the expansibility [expansion] factor as a function of the isentropic exponent, the pressure ratio and 

the diameter ratio are given for convenience in Table

Advantages of orifice plates

(i) They are relatively inexpensive.

(ii) They are usually thin enough to fit between an existing pair of pipe flanges.

Disadvantages of orifice plates

(i) The sharpness of the edge of the orifice can become worn with use, causing calibration errors.

(ii) The possible build-up of matter against the plate.

(iii) A considerable loss in the pumping efficiency due to the pressure loss downstream of the plate.

Applications

Orifice plates are usually used in medium and large pipes and are best suited to the indication and control of essentially constant flow rates. Several applications are found in the general process industries.