Flow Meter

Overview

Flow measurement is essential for process control, custody transfer, and safety. While there are many technologies (magnetic, ultrasonic, turbine), differential pressure (DP) flow meters remain the most common in industrial applications due to their robustness, standardization, and lack of moving parts.

DP meters work on Bernoulli’s principle: they introduce a constriction (reduction in area) that increases fluid velocity and creates a localized pressure drop. By measuring this pressure difference, the flow rate can be inferred.

Q = C_d A \sqrt{\frac{2 \Delta P}{\rho}}

where C_d is the discharge coefficient, which corrects for real-world viscous, turbulent, and geometric effects.

Types of Differential Pressure Meters

  • Orifice Plate: A plate with a hole. Simple, cheap, but creates high permanent pressure loss.
  • Venturi Tube: A gradually shaped constriction. Expensive, but offers excellent pressure recovery (low energy loss).
  • Flow Nozzle: A compromise, often used for steam or high-velocity flows.
Figure 1: Pressure Separation and Recovery: Conceptual pressure profiles through varying meter types. The Venture tube (Green) recovers most of the pressure drop, while the Orifice plate (Blue) results in significant permanent energy loss.

Python Libraries

These functions rely on the fluids library, which provides comprehensive implementations of differential pressure flow metering standards. This includes the rigorous ISO 5167 standard used globally for custody transfer, ensuring that calculations meet industrial regulatory requirements.

Standards and Calculations

Accurate metering requires rigorous standard correlations for the discharge coefficient C_d, which depends on the Reynolds number (Re) and the diameter ratio (\beta = d/D).

  • ORIFICE_DISCHARGE_C: Implements the ISO 5167 standard (Reader-Harris/Gallagher equation) for orifice plates. This is the global standard for custody transfer, accounting for tap placement, pipe roughness, and expansion effects.
  • FLOW_METER_DISCH: A generic utility to calculate discharge coefficients given diameters and tap locations for various meter styles.

Native Excel Capabilities

Excel has no native functions for flow meter calculations. Users typically implement simplified versions of the orifice equation, often: - Assuming a constant discharge coefficient (C_d \approx 0.6), which leads to significant errors at low Reynolds numbers. - Neglecting expansion factors for compressible gases. - Failing to account for the complex dependencies defined in ISO 5167 or ASME MFC-3M.

Implementing the full ISO 5167 Reader-Harris/Gallagher equation in Excel is extremely difficult due to its complexity and the need for iterative solutions (as C_d depends on Re, which depends on flow rate). The Python functions provided here handle these iterations and standards automatically, ensuring high-accuracy metering directly within the spreadsheet.

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.