Flow Meter

Overview

Flow measurement is fundamental to process control, custody transfer, and safety monitoring across industries from oil and gas to water treatment. While numerous technologies exist—including electromagnetic, ultrasonic, Coriolis, and turbine meters—differential pressure (DP) flow meters remain the most widely deployed in industrial applications due to their simplicity, robustness, standardization, and absence of moving parts.

Differential pressure flow meters operate on Bernoulli’s principle: a deliberate constriction in the flow path increases fluid velocity and creates a measurable pressure drop. Common DP meter types include orifice plates, venturi tubes, and flow nozzles, with orifice plates being the most prevalent due to their low cost and ease of installation. The fundamental relationship between flow rate Q and pressure drop \Delta P is:

Q = C_d A_t \sqrt{\frac{2 \Delta P}{\rho (1 - \beta^4)}}

where C_d is the discharge coefficient, A_t is the throat area, \rho is fluid density, and \beta is the beta ratio (throat diameter divided by pipe diameter). For compressible flows, an additional expansibility factor \varepsilon accounts for density changes across the meter.

These calculations are implemented using standard Python libraries including NumPy for numerical operations and fluids, a specialized library for fluid dynamics that provides ISO 5167-compliant correlations for discharge coefficients and pressure drop calculations.

Beta ratio (\beta = d/D) is a critical design parameter that affects meter sensitivity and permanent pressure loss. Typical values range from 0.2 to 0.75, with lower values providing higher differential pressure (better sensitivity) but greater non-recoverable pressure loss. The DIFF_PRESS_BETA tool helps engineers select the optimal beta ratio for their application, balancing measurement accuracy against energy costs.

Discharge coefficient (C_d) corrects the theoretical flow equation for real-world viscous, turbulent, and geometric effects. For orifice plates, the Reader-Harris-Gallagher correlation from ISO 5167 is the industry standard, accounting for Reynolds number, beta ratio, pipe diameter, and tap locations. The ORIFICE_DISCHARGE_C tool implements this correlation with uncertainty bands. For more general DP meters, DIFF_PRESS_C_EPS calculates both the discharge coefficient and expansibility factor.

Expansibility factor (\varepsilon) is essential for gas and steam applications where density changes significantly across the meter. It varies with pressure ratio, beta ratio, and isentropic exponent. The ORIFICE_EXPAND tool provides ISO-compliant calculations for compressible flows through orifice plates.

Pressure drop has two components: the differential pressure used for flow measurement (recoverable) and the permanent pressure loss (non-recoverable) due to turbulence and mixing downstream of the constriction. Non-recoverable pressure drop represents lost energy and operating cost. Tools like DIFF_PRESS_DP and ORIFICE_PRESS_DROP quantify this permanent loss for different meter geometries.

Flow rate calculation is the primary objective, converting measured differential pressure into mass or volumetric flow. The FLOW_METER_DISCH tool performs this calculation using measured upstream and downstream pressures along with meter geometry and fluid properties, providing the mass flow rate with appropriate corrections for real gas behavior and compressibility.

When designing a new DP meter installation, start with DIFF_PRESS_BETA to select an appropriate beta ratio, then use DIFF_PRESS_C_EPS or ORIFICE_DISCHARGE_C to determine the discharge coefficient. For operational calculations, use FLOW_METER_DISCH to convert field measurements into flow rates. Always evaluate permanent pressure loss using DIFF_PRESS_DP or ORIFICE_PRESS_DROP to understand the operating cost implications of your meter selection.

Tools

Tool	Description
DIFF_PRESS_BETA	Calculate the beta ratio (diameter ratio) for a differential pressure flow meter.
DIFF_PRESS_C_EPS	Calculate discharge coefficient and expansibility factor for differential pressure flow meters.
DIFF_PRESS_DP	Calculate non-recoverable pressure drop across a differential pressure flow meter.
FLOW_METER_DISCH	Calculate mass flow rate through a differential pressure flow meter based on measured pressures and meter geometry.
ORIFICE_DISCHARGE_C	Calculate the discharge coefficient for an orifice plate using the Reader-Harris-Gallagher correlation (ISO 5167 standard).
ORIFICE_EXPAND	Calculate the expansibility factor for an orifice plate based on geometry and pressure conditions.
ORIFICE_PRESS_DROP	Calculate non-recoverable pressure drop across an orifice plate based on geometry and discharge coefficient.