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Thermal Expansion by the Numbers

Growth, measurement, thermal stress, pipe loops, shrink fits, closed-system liquids and gases and machine design, worked through one factory hot water system

Calculate how parts, pipes, liquids and gases change with temperature: growth, measuring at 20 °C, thermal stress, pipe loops, shrink fits, expansion vessels, gas pressure and machine design.

8 chapters · About 80 minutes · Free to read · Intermediate engineering physics and mechanical design

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KEVOS® LibraryENGINEERINGMODELThermalExpansion by theNumbersKEVOS® ORIGINAL BOOK8 CHAPTERS

About this book

Almost everything grows when it warms and shrinks when it cools. The amounts are small, a fraction of a millimetre per metre for every few degrees, and that smallness is the trap. A 60 m hot water pipe grows by more than 70 mm when it warms up. A precision part measured warm can be rejected for an error that is only its temperature. A pipe held rigidly between two anchors can push on them with tens of kilonewtons. A closed tank of water heated without room to expand can burst. And a machine whose shaft and housing grow differently can bind its own bearings. Each of these has a short calculation that predicts it and a design habit that prevents it.

This book works through thermal expansion by numbers. It covers how solids, liquids and gases grow with temperature; measuring parts at the right temperature; the stress and force when growth is prevented; pipe anchors, guides and loops; shrink and expansion fits; expansion of water in closed systems and the vessels that absorb it; gas pressure and temperature; and designing machines for movement. Each chapter works one problem through the running case, shows an error and how it is caught, and ends with an exercise and its worked answer.

The running case

The book follows HW-60, the wash-down hot water system of a fictional food factory, also used in Heat Transfer by the Numbers. Its 60 m stainless steel hot water pipe, 60.3 mm in outside diameter with a 2.0 mm wall, carries 85 °C water and is installed at about 15 °C. A closed primary loop of about 400 L carries heat from a boiler to a plate heat exchanger. The system’s pump has a coupling hub shrunk onto its shaft, and an aluminium flowmeter body is machined and inspected in the factory’s workshop.

All dimensions, temperatures, pressures, costs and results are invented for teaching. This is an illustration. None of it describes a KEVOS® client, supplier or project. Money is in Australian dollars, excluding GST.

How to use the book

Chapters 1 and 2 cover growth and its effect on measurement. Chapters 3 to 5 deal with solids that are restrained or fitted together. Chapters 6 and 7 cover liquids and gases in closed systems, and Chapter 8 machines. KEVOS® calculators for several steps include thermal growth, thermal stress, pipe expansion loop and shrink fit design.

Source limits and professional responsibility

The supplied 1925 textbook informed the range of subjects. The methods here are standard physics and mechanics with sources for material data. Allowable stresses, pressure ratings and relief settings in the case are labelled teaching values. Pressure piping, pressure vessels, heated water services and their safety devices are regulated: real designs follow the applicable standards and are checked by competent people, and heating parts for fitting carries burn and fire risks that must be managed.

Who this book is for

Mechanical and maintenance engineers, machinists, inspectors, plumbers and designers who need to allow for thermal growth, stress and pressure in parts, pipework, closed systems and machines.

What you will learn

  • Calculate linear, area and volume expansion of solids and liquids from published coefficients.
  • Correct measurements to the 20 °C reference temperature and recognise when temperature distorts inspection.
  • Estimate thermal stress and anchor force when expansion is restrained, and size a pipe loop by beam theory.
  • Calculate the temperature for a shrink fit and size an expansion vessel for a closed water system.
  • Predict gas pressure changes with temperature and design machines with fixed and floating locations.

Inside this book

Chapters

  1. 01How materials grow with temperatureCalculate linear, area and volume expansion from published coefficients, see why holes grow with their material, why water must be handled with density tables, and which temperature change to use.
  2. 02Measuring at the right temperatureRelate measured sizes to the 20 °C reference temperature, correct a warm part's reading, see why the instrument's own temperature matters, and set soak times and rules so good parts are not rejected.
  3. 03Thermal stress when growth is stoppedCalculate the stress and force when thermal growth is prevented, see why they do not depend on length and why a restrained pipe buckles, and what guides, anchors and equipment must carry.
  4. 04Pipe expansion: anchors, guides and loopsAbsorb pipe growth with anchors, guides and an expansion loop sized from beam theory, compare loops with bends and bellows joints, and avoid the guide, venting and thrust mistakes that defeat them.
  5. 05Shrink and expansion fitsAssemble interference fits by heating the hub or cooling the shaft: the temperature for interference plus assembly clearance, heating limits, methods, timing and fits that loosen.
  6. 06Liquids in closed systemsCalculate how much water a closed heating loop expels as it warms, size a diaphragm expansion vessel from its precharge and maximum pressure, and see what a wrong precharge or no vessel does.
  7. 07Gases: pressure and temperatureUse the gas laws with absolute pressure and temperature to predict how sealed vessels, precharges and pressure tests change with temperature, and avoid mistaking a temperature drop for a leak.
  8. 08Designing machines for movementDesign machines that stay accurate and free as they warm: fixed and floating bearings, hot alignment of pumps and motors, warm-up drift, mixed materials and slotted fixings, each with its numbers.

Apply This in Practice

Use these KEVOS® tools to try the method from this reading with your own numbers.

References and source notes

The manuscript and worked examples are original KEVOS® writing. References inform particular concepts; their authors do not endorse this book. Web references were consulted on 26 October 2026.

  • J. H. Poynting and J. J. Thomson, Charles Griffin and Company, London. A Text-Book of Physics: Heat, eighth edition (1925). Supplied source, read as a subject map of the expansion of solids, liquids and gases and of temperature measurement. Both authors died before 1955. No text, figures, examples or problems are reproduced; this book's case, calculations and figures are original and in SI units.
  • The Engineering ToolBox. Linear Thermal Expansion Coefficients of Materials (current web page). Source for the coefficients used: steel 10.8 to 12.5 (12 used here), austenitic stainless steel 304 17.3, aluminium 23, copper 16 to 16.7 and PVC 54 to 110 millionths per °C.
  • The Engineering ToolBox. Water Density, Specific Weight and Thermal Expansion Coefficients (current web page). Source for the density of water at 15 °C (999.10 kg/m³) and 85 °C (968.61 kg/m³), used for the expansion of water in Chapters 1 and 6.
  • The Engineering ToolBox. Young's Modulus of Elasticity, Values for Common Materials (current web page). Source for the modulus of stainless steel (AISI 302, 180 GPa), used for thermal stress and pipe loops in Chapters 3 and 4, and of structural steel (200 GPa).
  • David Roylance, Massachusetts Institute of Technology, 3.11 Mechanics of Materials. Beam Displacements (1999). Background on beam deflection, from which the guided-cantilever relation for pipe loops in Chapter 4 is derived in this book's own steps.
  • ISO; Standards Australia and Standards New Zealand. ISO 1, standard reference temperature for geometrical product specification; AS 4041, pressure piping; AS/NZS 3500.4, heated water services (current editions). Named by number and scope only. ISO 1 sets 20 °C as the reference temperature for dimensions; AS 4041 governs the design of pressure piping, including allowable stresses; AS/NZS 3500.4 governs heated water services, including expansion control. No values are quoted from them.

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