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Flow Measurement by the Numbers
Volume, mass and standard flow, velocity profiles, orifice plates, magnetic, Coriolis, ultrasonic and vortex meters, uncertainty, totals and choosing a meter
How industrial flowmeters work and how to choose, install, read and trust them, from Reynolds number and orifice plates to magnetic, Coriolis, ultrasonic and vortex meters, worked with numbers.
Start readingAbout this book
Almost every process plant runs on flows it cannot see. Water arrives through a buried main, product moves between vessels in closed pipes, steam, compressed air and gases leave the utilities and disappear into machines. A flowmeter turns each of those flows into a number, and the numbers drive batches, bills, energy reports, mass balances, alarms and control loops. A meter that reads 3% high costs nothing visible on the day it is installed and a great deal over the years that its number is trusted.
This book shows how flowmeters work and how to use them with numbers. It starts with what a meter measures, volume, mass or standard volume, and with the velocity profile in the pipe, which every meter depends on. It then works through the main meter types: the orifice plate, the electromagnetic meter, whose principle is the electromotive force induced in a conductor moving through a magnetic field, the Coriolis mass meter, the ultrasonic transit-time meter and the vortex meter for gases. It finishes with uncertainty, totals and mass balances, and choosing a meter on accuracy, pressure loss and cost.
It is for process, mechanical, instrument and maintenance engineers, technicians, energy managers and production staff. It assumes engineering or trade training and comfort with basic fluid mechanics; the physics of each meter is explained as it is used. Each chapter works the running case with real numbers, includes a plausible mistake and how it was found, links the BIZOMAT tools that do the chapter’s calculations, and ends with an exercise and its worked answer.
The running case
Every chapter follows one plant. This is an illustration. A brewery in Bendigo, Victoria, brews about 2 million litres of beer a year and measures five flows:
- FT-101, mains water: an electromagnetic meter in the DN80 incoming water main, flows up to 30 m³/h.
- FT-201, wort: a Coriolis mass meter on the DN50 line carrying cooled wort from the brewhouse to the fermenters, at about 12 m³/h and a specific gravity of 1.048.
- FT-301, hot liquor: a legacy orifice plate in the DN65 hot water line at about 80 °C from the hot liquor tank to the brewhouse.
- FT-401, compressed air: a vortex meter in the DN50 compressed-air main at 7 bar gauge.
- FT-501, glycol: a clamp-on ultrasonic meter used to audit the DN100 glycol cooling loop to the fermenter jackets.
Pipe sizes, flows, properties, readings, prices and results are the brewery’s working figures or are calculated from stated assumptions. They do not describe BIZOMAT work or any real brewery, instrument maker or supplier. Fluid properties are typical values for illustration. Prices are in Australian dollars excluding GST.
How to use the book
Read Chapters 1 and 2 first: they define what is measured and explain the velocity profile and installation effects that every meter depends on. Chapters 3 to 7 cover the meter types and can be read in any order. Chapters 8 to 10 bring uncertainty, totals and the choice of meter together.
Every calculation in the book was checked by running it, and the BIZOMAT tools linked from each chapter were checked against the calculations they perform. Where a tool was built for a different purpose but does one step of a chapter’s calculation, such as the orifice flow tool’s discharge equation, the chapter says which output is used.
Source limits and professional responsibility
This book is educational. Meters used for trade, custody transfer, billing or regulatory reporting are subject to legal metrology requirements, in Australia administered by the National Measurement Institute, and to the standards and contracts that apply to them. Meters in hazardous areas, food contact service and safety functions have their own requirements. The book names standards by number and scope only; they must be read in full before use, and decisions about real installations remain with the competent people responsible for them.
Who this book is for
Process, mechanical, instrument and maintenance engineers, technicians, energy managers and production staff who specify, install, calibrate, read or act on flowmeters for water, product, utilities and gases.
What you will learn
- Distinguish volume, mass and standard volume flow, and work out velocity and Reynolds number to judge how a flow will behave in a meter.
- Explain how differential pressure, electromagnetic, Coriolis, ultrasonic and vortex meters turn flow into a signal, and what each needs to read correctly.
- Install a meter so that its velocity profile, fill, conductivity, grounding and straight runs support its stated accuracy.
- Convert gas flows between actual and standard conditions and correct liquid volumes for temperature.
- Build an uncertainty for a flow reading and a total, use meters in mass balances and batching, and choose a meter on accuracy, pressure loss and cost.
Inside this book
Chapters
- 01What a flowmeter measuresVolume, mass and standard volume flow and how to convert between them, mean velocity and Reynolds number, why temperature changes a litre, and a hot water recipe that came out 2.6% short.
- 02Velocity profiles and installationHow speed varies across a pipe, laminar and turbulent profiles and the profile factor, what fittings do to the flow, straight runs and conditioners, and a meter after a throttling valve.
- 03Orifice plates and differential pressureHow an orifice plate turns flow into a pressure difference, the discharge coefficient, sizing a plate, the square-root law and turndown, permanent pressure loss, and a square root left out.
- 04Electromagnetic flowmetersHow a conducting liquid moving through a magnetic field generates a voltage, signal size, conductivity, pulsed excitation, electrodes, liners and grounding, and a plastic pipe without grounding rings.
- 05Coriolis mass flowmetersHow vibrating tubes measure mass flow by the Coriolis effect and density by their frequency, zero stability, pressure loss, checks in place, and gas bubbles that made the wort look weak.
- 06Ultrasonic transit-time metersHow sound travelling with and against the flow measures velocity, nanosecond time differences, path geometry and profile factors, clamp-on pipe data, and a glycol audit that read 5% high.
- 07Gas flow and vortex metersWhy a gas’s actual volume changes with pressure and temperature, free air and normal volumes, how a vortex meter counts eddies, its low-flow cutoff, and an air audit that understated demand eightfold.
- 08Uncertainty and calibrationReading an accuracy specification, percentage of reading against span, zero stability at low flow, an orifice uncertainty budget, calibration and in-place checks, and a meter quoted in full scale.
- 09Totals, batches and mass balancesTurning flows into totals, the uncertainty of a sum, building a site water balance, charting its residual to find a leak, night flows, product losses, and two totalisers read at different times.
- 10Choosing a meter and the cost of errorA selection method across fluid, range, accuracy, pressure loss, installation and cost, sizing for the range, valuing a meter’s error, and appraising a meter that reveals compressed-air leaks.
Apply This in Practice
Use these BIZOMAT tools to try the method from this reading with your own numbers.
Explained in this book
Measurement Uncertainty Budget (Combined, Expanded, Test Ratio)
Shows the root-sum-square uncertainty method for a gauge; the chapter applies the same steps in percentages to an orifice meter's coefficient, bore, differential and density.
Used in Uncertainty and calibration
Applies this method
Compressed Air Leak Cost
Values compressed-air leakage from a measured leak flow, compressor specific power, hours and electricity price: 10 L/s of free air costs about A$10,200 a year.
Applies this method
Density and Specific Gravity Converter
Converts a wort's specific gravity to density in kg/m³, the factor that turns a volume flow into the mass flow that extract and yield calculations need.
Used in What a flowmeter measures
Applies this method
Equipment Investment Appraisal (NPV, IRR, Payback, B/C, EUAC)
Appraises meter decisions from cost, yearly benefit, life and hurdle rate: replacing an orifice plate does not pay, while a low-flow meter that reveals air leaks pays back in under two years.
Applies this method
Gas Volume at Pressure and Temperature
Converts gas flows between pressures and temperatures, turning a compressor's free air rating into the actual volume a vortex meter senses at 7 bar gauge, and back.
Used in Gas flow and vortex meters
Applies this method
Individuals Control Chart Check (Moving Range, Control Limits, Points Out of Control)
Charts a daily water balance residual with moving-range control limits; two days outside the limits revealed a buried leak of about 2 m³ a day.
Applies this method
Liquid Pipe Velocity and Reynolds Number
Gives mean velocity and Reynolds number for a liquid in a full pipe, which decide the velocity profile a meter sees; used for mains water and for glycol in a clamp-on audit.
Used in What a flowmeter measures
Applies this method
Orifice and Restrictor Flow
Calculates flow through an orifice from its coefficient, bore, pressure drop and density; with the coefficient entered as C × E it checks a hot water orifice plate at 162 mbar and 15 m³/h.
Applies this method
Pipe Flow Velocity
Gives the mean velocity from a flow and the internal bore, the first check on any meter reading: 200 L/min of wort in a 47.8 mm bore moves at 1.858 m/s.
Used in What a flowmeter measures
References and source notes
The manuscript and worked examples are original BIZOMAT writing. References inform particular concepts; their authors do not endorse this book. Web references were consulted on 3 November 2026.
- R. Fitzpatrick, University of Texas at Austin, lecture notes. Introduction to Plasma Physics: A Graduate Level Course (2006). Copyright work, used only as a map of ideas: the electromotive force induced in a conductor moving through a magnetic field, as in the homopolar generator and magnetohydrodynamics, and the propagation of waves in moving media. No text, equations as set out there, figures or problems are reproduced, and all cases and calculations are BIZOMAT originals.
- R. W. Miller, McGraw-Hill. Flow Measurement Engineering Handbook (1996). Third edition. Background for flow fundamentals, velocity profiles and installation effects, differential pressure meters, and the principles of magnetic, vortex, ultrasonic and Coriolis meters used throughout.
- International Organization for Standardization. ISO 5167, Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full (2022). Named by number and scope only (parts 1 to 6; part 1 revised in 2022): orifice plates, nozzles, Venturi tubes and cone and wedge meters. Its coefficients, uncertainties and installation requirements are not reproduced and must be read in full.
- Australian Government, National Measurement Institute. National Measurement Institute, trade measurement for meters (2026). Background for the distinction between process meters and meters used for trade in Australia, which must be of an approved pattern and verified. Requirements for any particular meter must be checked with the Institute.
- National Institute of Standards and Technology. NIST/SEMATECH e-Handbook of Statistical Methods (2012). Background for the uncertainty and propagation methods used in Chapters 8 and 9.