Of many kinds of flow restriction devices, restriction orifices (“RO”) are frequently used, because they are simple and economical devices. RO is applied to regulate the flow rate or pressure. This article will provide the guidelines for sizing of RO. It should be noted that this standard practice is applicable to single-phase fluids only.

**Input to the Design: **

The following is a summary of input data to be prepared for the design of RO:

(1) Operating Conditions

- Flow rate
- Upstream & downstream pressure
- Temperature (for vapor)
- Line Size

(2) Physical properties

- For liquid service : density,vapor pressure
- For vapor service : molecular weight, Cp/Cv, Z-factor, viscosity

(3) Minimum allowable value of cavitation index for liquid service

**Output from the Design: **

(1) Single orifice

- Orifice diameter
- Pressure at vena contracta
- Velocity at orifice
- Calculated cavitation index (for liquid)
- Critical or non-critical (for vapor)

(2) Multi-stage orifice

- Required stage number
- Orifice diameter of each orifice
- Distance between adjacent orifice plates
- Inlet and outlet pressures of each orifice
- Pressure at vena contracta of each orifice
- Velocity at each orifice
- Calculated cavitation index of each orifice

**Principle of RO Calculation:**

**Gas Service:**

**Critical Pressure Ratio:**The critical pressure ratio, rc can be obtained from the following equation.

**Orifice Diameter: **

Equation for orifice diameter should be selected using equation (2), depending on whether the flow is critical or non-critical.

**(A) Critical flow (sonic region)- **When ratio of downstream pressure to upstream pressure, r4, is smaller than or equal to critical pressure ratio, rc , the following equation of orifice diameter for critical flow should be used.

**(B) Non-critical flow (subsonic region)- **The following equation of orifice diameter can be used for non-critical flow region.

**Liquid Service:**

**Orifice Diameter-**

**Cavitation Index: **

In order to avoid cavitation problem, minimum allowable value of cavitation index, Kd,should be selected based on the following:

(1) Cavitation index Kd=0.37 shall be used for usual case. At this critical cavitation condition, the noise is steady but still light. No erosion will occur. (Once the orifice chokes and super cavitation occurs, no damage by erosion will exist near the orifice. This is because the damage is caused by the collapse of the cavities and the collapse occurs far downstream during super cavitation)

(2) In some occasion such as the following cases, use Kd=0.93 as an incipient cavitation condition in order to avoid severe economical risk.

- Material is high grade such as stainless steel or higher and pipe size is larger than 12”.

**Interval of Orifices: **

In case of multi-stage orifice, the minimum distance, as shown below, should be provided between orifices, to avoid the reduction in RO performance.

- For concentric orifice : L ≥ 5.4*D*(1-β)
- For eccentric orifice : L ≥ D

**Deflection Ratio of Eccentric Orifice: **

The deflection ratio of the eccentric orifice “e” is 0.75.

e = 2δ /(D − d0 ) = 0.75 (14)

Where,

δ : Pipe center to orifice center length (m)

dO: Orifice hole diameter (m)

D: Pipe inside diameter (m)

**Calculation Procedure: **

**A. Single RO system- **

① Decide minimum allowable value of cavitation index to meet a given situation.

Kd = 0.37: for usual case

Kd = 0.93: for conservative case

② Assume dO and calculate β by equation (8).

③ Incompressible coefficient of contraction CCi shall be calculated by equation (7).

④ Orifice diameter (dO) shall be calculated by equation (13).

⑤ Compare the assumed d0 with the calculated dO in step ④.

⑥ Calculated dO shall be replaced with previous dO and repeat step ② to step ⑤ until the dO agrees with calculated dO.

Calculate cavitation index, Kd by equation (15), and compare with minimum allowable value.

If cavitation index ≥ 0.37 (or 0.93), then the orifice diameter is acceptable.

If cavitation index < 0.37 (or 0.93), then single orifice is unable to accommodate the required pressure drop. In that case, multi-stage orifice system should be applied.

**B. Multi-stage RO system- **

① Decide minimum allowable value of cavitation index to meet a given situation.

Kd = 0.37: for usual case

Kd = 0.93: for conservative case

**First stage orifice: located at outlet **

② Assume upstream pressure of the first stage orifice.

③ Assume dO and calculate β by equation (8) for the first stage orifice.

④ Incompressible coefficient of contraction CCi shall be calculated by equation (7).

⑤ Orifice diameter (dO) shall be calculated by equation (13) using assumed upstream pressure.

⑥ Compare the assumed d0 with the calculated dO in step ⑤.

⑦ Calculated dO shall be replaced with previous dO and repeat step ③ to step ⑥ until the dO agrees with calculated dO.

⑧ Calculate cavitation index, Kd, using Equation (15), and compare with minimum allowable value.

If cavitation index > 0.37 (or 0.93), increase the upstream pressure and repeat the steps from ③ to ⑧.

If cavitation index < 0.37 (or 0.93), decrease the upstream pressure and repeat the steps from ③ to ⑧.

If cavitation index equals to or slightly bigger than 0.37 (or 0.93), the design of first stage RO is completed and go to step ⑨.

**n-th stage orifice **

⑨ Set the upstream pressure of (n-1)-th stage orifice for the downstream pressure of n-th stage orifice.

⑩ Assume the upstream pressure of n-th stage orifice.

⑪ Repeat the steps from ③ to ⑧, until the cavitation index is equivalent to the minimum allowable value.

**Special Consideration of RO Design: **

(1) Minimum hole diameter of RO- To prevent plugging problem with RO caused by debris, the hole diameter should be greater than the following values:

- For the clean liquid service : 2mm
- For the clean Gas service : 1mm

When the diameter smaller than the above values is required, the strainer or filter to remove debris should be provided upstream of RO.

(2) Necessity of minimum straight run length- Basically, the objective of RO is rough control of flow rate and should not be used for strict control of flow rate. Therefore, it should not be necessary to take straight run of piping both upstream and downstream of RO to keep performance. However, for the erosional services such as slurry or flush services, countermeasures for erosion shall be considered.

(3) Calculated hole diameter of RO should be rounded to the conservative size for easy manufacturing.

I am a Mechanical Engineer turned into a Piping Engineer. Currently, I work in a reputed MNC as a Senior Piping Stress Engineer. I am very much passionate about blogging and always tried to do unique things. This website is my first venture into the world of blogging with the aim of connecting with other piping engineers around the world.