How to Size an Orifice Plate
An orifice plate is a differential pressure flow measurement device installed between orifice flanges. Sizing determines the bore diameter (d) of the orifice plate based on the required flow rate, pipe diameter, fluid properties, and the desired differential pressure range. The calculation follows ISO 5167-2 (or AGA Report No. 3).
When This Calculation Is Used
Instrument engineers size orifice plates during the detailed engineering phase for each flow measurement point. The goal is to select a beta ratio (d/D) that produces a measurable differential pressure (typically 100-250 inches H2O at normal flow) while keeping permanent pressure loss within acceptable limits.
Orifice Plate Sizing Formula
The volumetric flow rate through a concentric, sharp-edged orifice plate is:
Q = Cd x E x (pi/4) x d2 x sqrt(2 x dP / rho)
Where:
| Symbol | Parameter | Unit |
|---|---|---|
| Q | Volumetric flow rate | m3/s |
| Cd | Discharge coefficient (function of Re and beta) | Dimensionless |
| E | Velocity of approach factor: 1 / sqrt(1 - beta4) | Dimensionless |
| d | Orifice bore diameter | m |
| D | Internal pipe diameter | m |
| beta | Diameter ratio: d / D | Dimensionless (0.20 to 0.75) |
| dP | Differential pressure across the orifice | Pa |
| rho | Fluid density at operating conditions | kg/m3 |
Beta Ratio Guidelines
| Beta Ratio (d/D) | Application | Permanent Pressure Loss |
|---|---|---|
| 0.20-0.40 | Low flow rates, high accuracy needed | High (70-90% of dP) |
| 0.40-0.55 | Standard flow measurement | Moderate (55-70% of dP) |
| 0.55-0.65 | Most common range for process piping | Moderate (40-55% of dP) |
| 0.65-0.75 | High flow rates, low available pressure drop | Low (25-40% of dP) |
ISO 5167 limits the beta ratio to 0.20-0.75 for concentric orifice plates with corner, flange, or D-D/2 taps.
Worked Example
Given: NPS 4, SCH 40 pipe (ID = 102.3 mm), water at 20 C, flow rate 50 m3/hr, target dP = 150 inches H2O (37.3 kPa).
| Step | Parameter | Value |
|---|---|---|
| Pipe ID (D) | From ASME B36.10 | 102.3 mm |
| Flow rate (Q) | 50 m3/hr | 0.01389 m3/s |
| Fluid density (rho) | Water at 20 C | 998.2 kg/m3 |
| Target dP | 150 in H2O | 37,300 Pa |
| Assumed Cd | Initial estimate | 0.605 |
| E x Cd (initial) | 0.605 x 1.05 | 0.635 |
| Calculated d | From rearranged formula | 62.8 mm |
| Beta ratio | 62.8 / 102.3 | 0.614 |
The beta ratio of 0.614 falls within the standard range. After iterating with the Reader-Harris/Gallagher equation for the exact Cd at this beta and Reynolds number, the final bore diameter is confirmed.
Key Design Considerations
- Straight pipe runs: ISO 5167 requires minimum upstream and downstream straight pipe lengths depending on the beta ratio and upstream disturbance type (typically 15D-44D upstream, 5D-8D downstream).
- Pressure taps: Flange taps (25.4 mm from orifice face) are the most common in the oil and gas industry. Corner taps and D-D/2 taps are alternatives.
- Material: Orifice plates are typically 316 stainless steel, with bore edges sharp and square per ISO 5167.
- Permanent pressure loss: A significant disadvantage of orifice plates compared to other flow meter types.
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