Multi-Hole Orifice Plate Research | Discharge Coefficient Study

Abstract

This study, conducted entirely at Krtyata Private Limited's in-house R&D flow calibration laboratory, characterises the discharge coefficient (C_d) and permanent pressure loss (PPL) of six orifice plate prototypes — including single-hole and multi-hole configurations — across beta ratios of 0.25 to 0.62 in a 2″ (DN50) pipe. Calibration was performed using the water comparison method against a reference standard meter. Results are benchmarked against ISO 5167-2 and RW Miller calculations to assess the suitability of multi-hole designs as low-loss, short-installation-length alternatives to standard orifice plates.

Background & Motivation

Orifice plates are among the most widely deployed primary flow elements due to their simplicity, low maintenance requirements, and long-term operational reliability. However, the standard single-hole concentric orifice carries two persistent limitations: a substantial permanent pressure loss — which translates directly into energy cost — and a demanding upstream straight-pipe length requirement that increases installation cost and plant footprint.

Multi-hole orifice plates address both of these limitations by distributing the single bore into multiple smaller openings spread across the pipe cross-section. Splitting the bore reduces the severity of the vena contracta, lowering permanent pressure loss. Distributing flow area across the pipe diameter also linearises the velocity profile, making the measurement less sensitive to upstream disturbances and reducing the required straight-pipe run.

While various commercial multi-hole conditioner-meter products exist, independent experimental characterisation of bare multi-hole orifice plates — particularly in the context of generating traceable discharge coefficient data — remains sparse in the open literature. This study was undertaken at Krtyata's R&D calibration laboratory to generate original prototype test data across a range of beta ratios and hole configurations.

Krtyata R&D Flow Calibration Laboratory

All prototype testing was carried out on Krtyata's water calibration rig using the comparison method, with a reference standard meter of known discharge coefficient placed in series with the device under test. The rig operates at controlled temperature (32 °C), pressure (1.2 bar), and flow rate conditions, with full traceability of all measurements.

Krtyata flow calibration rig — comparison method test bench

Krtyata water flow calibration rig — comparison method test section

Krtyata R&D laboratory — orifice plate prototype testing

Prototype orifice plate installed in 2″ test section at Krtyata R&D lab

Test Programme — Six Prototype Models

Six orifice plate prototypes were designed, machined, and tested at the Krtyata laboratory. The test matrix was structured to compare single-hole and multi-hole configurations at matched beta ratios, enabling direct assessment of the effect of bore distribution on both discharge coefficient and pressure loss.

Model	Type	Beta Ratio (β)	No. of Holes	Pipe Size	Test Fluid
Model 1	Single Hole	0.40	1	2″ DN50	Water
Model 2	Multi-Hole	0.40	9	2″ DN50	Water
Model 3	Single Hole	0.62	1	2″ DN50	Water
Model 4	Multi-Hole	0.62	5 (with centre)	2″ DN50	Water
Model 5	Multi-Hole	0.25	5	2″ DN50	Water
Model 6	Multi-Hole	0.62	4 (no centre)	2″ DN50	Water

Prototype Orifice Plate Drawings

Each model was precision-machined in-house. The drawings below show the bore configuration for all six prototypes as tested in the Krtyata calibration laboratory.

Model 1 — Single Hole β=0.40 orifice plate drawing

Model 1 β=0.40 · 1 Hole

Model 2 — Multi-Hole β=0.40 9-bore orifice plate drawing

Model 2 β=0.40 · 9 Holes

Model 3 — Single Hole β=0.62 orifice plate drawing

Model 3 β=0.62 · 1 Hole

Model 4 — Multi-Hole β=0.62 5-bore with centre orifice plate drawing

Model 4 β=0.62 · 5 Holes

Model 5 — Multi-Hole β=0.25 5-bore orifice plate drawing

Model 5 β=0.25 · 5 Holes

Model 6 — Multi-Hole β=0.62 4-bore no-centre orifice plate drawing

Model 6 β=0.62 · 4 Holes

C_d vs Reynolds Number — All Models

Each chart below presents the discharge coefficient (C_d) measured at Krtyata's laboratory against the pipe Reynolds number (Re_D) for each prototype. Calibration was performed at controlled water conditions (ρ = 995 kg/m³, μ = 0.7647 cP, T = 32°C, P = 1.2 bar). Points represent individual calibration runs using the comparison method.

Model 1 — Single Hole, β = 0.40

17 calibration points · Re_D: 19,456 – 60,383 · C_d avg ≈ 0.612

Model 2 — Multi-Hole (9 bores), β = 0.40

17 calibration points · Re_D: 27,256 – 63,714 · C_d avg ≈ 0.704

Model 3 — Single Hole, β = 0.62

6 calibration points · Re_D: 80,014 – 210,334 · C_d avg ≈ 0.641

Model 4 — Multi-Hole (5 bores, with centre), β = 0.62

17 calibration points · Re_D: 46,449 – 158,101 · C_d avg ≈ 0.708

Model 5 — Multi-Hole (5 bores), β = 0.25

6 calibration points · Re_D: 13,821 – 26,292 · C_d avg ≈ 0.768

Model 6 — Multi-Hole (4 bores, no centre), β = 0.62

10 calibration points · Re_D: 50,831 – 161,256 · C_d avg ≈ 0.632

Comparative: C_d vs Permanent Pressure Loss (PPL %) — β = 0.62 Models

Chart 7 — Direct comparison of Models 3, 4 & 6 at matched beta ratio of 0.62. Demonstrates the PPL reduction achieved by multi-hole configurations relative to the single-hole standard orifice at equivalent flow conditions.

Key Findings from the Krtyata Study

Average C_d Summary vs Reference Standards

Measured average discharge coefficients are compared against ISO 5167-2 and RW Miller predicted values. Difference percentages are computed relative to the respective standard's predicted value. * Model 3 — only higher Re_D points considered for the average due to scatter at low Reynolds number.

Model	Type	β	Holes	Measured C_d (avg-Throat)	ISO 5167 C_d	Diff. vs ISO	Measured C_d (avg-Downstream)	RW Miller PPL C_d	Diff. vs Miller
Model 1	Single Hole	0.40	1	0.6125	0.6088	−0.61%	0.6766	0.6651	−1.88%
Model 2	Multi-Hole	0.40	9	0.7048	0.6088	−15.77%	0.7439	0.6651	−11.86%
Model 3 *	Single Hole	0.62	1	0.6397	0.6163	−3.80%	0.7911	0.7829	−4.78%
Model 4	Multi-Hole (with centre)	0.62	5	0.7078	0.6163	−14.85%	0.8223	0.7829	−5.03%
Model 5	Multi-Hole	0.25	5	0.7685	0.6042	−27.20%	0.7865	0.6211	−26.64%
Model 6	Multi-Hole (no centre)	0.62	4	0.6327	0.6163	−2.66%	0.7885	0.7829	−0.72%

Multi-hole (no centre) matches standard orifice best

Model 6 (4 holes, no centre bore, β = 0.62) produced a measured C_d of 0.632, the closest result to the single-hole Model 3 (0.641) at the same beta. This model also produced C_d values closest to the RW Miller restriction orifice prediction among all multi-hole configurations tested.

Centre hole raises C_d significantly

Comparing Model 4 (with centre hole, β = 0.62) against Model 6 (no centre hole, β = 0.62) reveals that the presence of a centre bore raises the discharge coefficient from ~0.632 to ~0.708. This is consistent with the centre bore contributing a disproportionately higher velocity component at the pipe centreline.

C_d vs DP is nearly constant for β = 0.40–0.62

Across Models 1 through 6, the measured discharge coefficient referenced to differential pressure (DP) remains nearly constant over the beta range of 0.40 to 0.62 — analogous to the behaviour of the standard restriction orifice. This is a potentially useful design property for multi-hole plate metering applications.

C_d vs PPL is more beta-dependent

When C_d is calculated from permanent pressure loss (PPL) rather than differential pressure, the dependence on beta ratio becomes more pronounced — consistent with the behaviour observed in single-hole restriction orifice plates. Further prototyping across a wider beta range is required to establish a reliable PPL-based calibration equation.

ISO 5167-2 under-predicts multi-hole C_d

ISO 5167-2, which is derived for single-hole concentric orifices, consistently under-predicts the discharge coefficient for multi-hole configurations. This is expected — the multi-hole geometry generates a different vena contracta structure. A dedicated multi-hole correction factor or independent calibration equation will be required for traceable flow computation.

Further testing recommended at higher β

The current dataset covers beta ratios from 0.25 to 0.62. To fully characterise the C_d trend and confirm its behaviour with respect to both DP and PPL at higher beta ratios, additional prototype testing at β = 0.70 and beyond is recommended as the next phase of this ongoing R&D programme.

Conclusions

This experimental study, conducted entirely within Krtyata's R&D calibration laboratory, demonstrates that multi-hole orifice plates exhibit measurably different discharge coefficients from their single-hole counterparts at equivalent beta ratios, and that the configuration of the bore pattern — particularly the presence or absence of a centre hole — has a significant influence on the resulting C_d.

The 4-hole, no-centre-bore configuration (Model 6, β = 0.62) offers the most promising performance from a standardisation perspective: its discharge coefficient is closest to the single-hole standard orifice, and its C_d with respect to differential pressure shows good stability across the tested Reynolds number range. This configuration warrants further study at a wider range of beta ratios and pipe diameters to develop a robust, independently validated calibration equation suitable for industrial metering applications.

The results from this study will form part of Krtyata's ongoing flow element research programme and will be extended in subsequent phases with additional prototype geometries, gas flow testing, and CFD correlation studies.

Multi-Hole Orifice Plate — Discharge Coefficient & Pressure Loss Study

Background & Motivation

Krtyata R&D Flow Calibration Laboratory