Thermal expansion in hot water systems: This article defines thermal expansion in water equipment in response to temperature, and explains the concomitant increase in system pressure.

We show how to calculate hot water pressure increase in water heaters and boilers as a function of the increase in water temperature.

We also discuss problems that are caused by increased pressures caused by heating and thermal expansion in heating or plumbing systems.

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How to Measure or Predict the Increase of Pressure in Water Heater Tanks: Expansion Rate of Hot Water as it is Heated

Thermal expansion in a hot water system refers to the increase in volume of water as it is heated. If the water system is closed (say by a check valve or a blockage) the result is an increase in water system pressure as well. In other words if we heat water in a closed container, pressure in the container will increase.

Question: How much does pressure increase inside a water heater tank (geyser) as the temperature rises?

What I need to know exactly is the following;

If you pump a geyser (water heater) full of water at ground temperature, let's say 10 degrees C, with a pump that switches off at 4 bar max, what happens to the 4 bar pressure in the geyser when you heat the water in the geyser to let's say 80 degrees C? Or what will the maximum pressure in the geyser go up to if you start with 3 bar or 3.5 bar etc.?

In other words; if you know that the maximum possible incoming water pressure into your geyser is 4 bar, will the pressure ever increase to more than 4.5 bar which is the geyser's maximum specification? -- Bart K., South Africa.

Note: The chart of water density as a function of changes in water temperature (above left) is provided by Engineering Toolbox and is discussed in our answer, below.

Reply: Water is at its maximum density at 4 degC, and its volume (and thus pressure in a closed container) increases with temperature according to its coefficient of expansion and the degrees of temperature rise

How Much Will Water Pressure Increase as Water is Heated in a Domestic Water Heater or Heating Boiler?

Of course a simple and non-mathematical method of looking into the pressure that is occurring at any tank containing water and water that is heated, is discussed
at WATER PRESSURE MEASUREMENT where we simply use an instrument to measure actual water pressure that is occurring.

Hot water heater or cylinder or calorifier or geyser sketch shown here is provided courtesy of Carson Dunlop Associates, a Toronto home inspection, report writing tool & education company.

What Pressure Increase Do We Actually Observe in Water Heaters & Hot Water Heating Boilers?

As a point of reference, in a residential hydronic heating boiler we actually observe an internal water pressure rise from 12 psi cold up to 28 psi hot as the boiler temperature increases from perhaps 60 °F up to 180 °F.

(This is much hotter than we should ever see in a domestic water heater tank where to avoid scalding hazards we limit water to about 100 °F. With a mixing valve or tempering valve installed we still limit water heater temperature to around 120 °F.)

As we discuss at GAUGES on HEATING EQUIPMENT

• Typical pressure for a residential boiler serving a two story home would show 12 psi cold, and less than 30 psi hot. Over 30 psi boiler pressure will cause the pressure relief valve to open.
• Typical operating temperature settings on a boiler call for a Low temperature (boiler cut-in) between 120 °F and 160 °F.
• Typical operating temperatures on a hydronic boiler call for a high temperature (boiler cuts off) of 180-200 °F.
• At heating boiler temperatures over 200 °F we're at risk of spilling at the pressure temperature relief valve.

Calculating Water Pressure Increase in a Closed Container (water tank) due to Heating

Here we add a more theoretical discussion of how we might calculate the pressures that can be expected to occur in a water tank due to thermal expansion. In other words, if we start at a given or known water pressure (such as incoming building water pressure) and we then heat water in the water tank, how much will water tank pressure increase for a given rise in temperature?

The effect on water volume or density caused by changing water pressure is very small.

In general, and unlike the effects on gases when gas pressure changes, the effect of increasing pressure on the density of water (or any liquid) is very small - liquids are not very compressible. Increasing water pressure does not have much effect on the water volume nor water density. For example, the density of water at 3.98 °C (it's most dense temperature) is 1000 kg/m³. The density of water at 100 °C is 958.4 kg/m³ and the density of water at 030 °C is 983.854 kg/m³. - Wikipedia and other sources.

What Are the Density and Mass of Water - What is Density?

Here we look at the effects on water pressure of increasing the water temperature. Reading about the relationship between water temperature and water pressure is confusing in part because most sources talk about water density rather than water pressure. FYI,

mass / volume = density 

for any material. SI units for density are kg/m³ that is, Kilograms per cubic meter. Imperial or BG density units are in lb/ft³ or pounds per cubic foot. Technically "pounds" measures force not mass. You can also state density in slugs/ft³ if you're arguing with an engineer. 1 slug = 32.2 pounds. Or 1 pound = 0.031 slugs.

Water has a density of 1000 kg/m³ by standard definition at its temperature of maximum density 3.98 °C and at 0% salinity. Scientists and engineers use water as a baseline for comparing the relative density of various materials. Water with a density of 1000 kg/m³ at 3.98 °C has a mass of 1000kg and a volume of 1 m³.

To convert the mass of 1 cubic meter of water to pressure expressed in psi and other measures:

• 1 cubic meter of water (1m H₂O) = (1000 mm H₂O) = 0.102 kg/cm² = 1.42 psi
  or we can convert water pressure between kg/cm² and psi as follows:
• 1000 kg/cm² = 14,223 psi - this is the standard density of water.
  Water (or anything else) exerting a pressure or force of 1000 kg/cm² is equivalent to 14,223 psi
• 1 kg/cm² = 14.2 psi
• 1 psi = 0.0703 kg/cm² = 0.7 m H₂O = 27.7 in H₂O = 2.04 in Hg

Water density vs. temperature: The density of water varies according to its temperature (see the water temperature/density charts above) but is nominally close to 1000 kg/m³, or put more accurately, at 4 °C the density of water at 1 atmosphere (sea level on earth) is 999.9720 kg/m³.

Water expands rapidly at 9% by volume when it freezes. The density of ice at 0 °C is 999.8395. So we see why ice floats, right? It's less dense than water, so takes up more volume than it did when it was a liquid, so in water an iceberg occupies more space (it has expanded from its liquid state) than the same mass of water.

How Does Density Change with Temperature Change?

The total change in the density of water effected by changing its temperature is small.

Density of a material changes as we vary the material's temperature or the the pressure exerted on it in a closed container - like heating up water in a water heater, calorifier, or geyser, right?

Our friends at Engineering toolbox discuss the properties of water and other fluids, and their page http://www.engineeringtoolbox.com/water-thermal-properties-d_162.html gives a chart of water and absolute pressure at various temperatures - this is the simplest answer that we trust.

Stated very simply, and assuming our water temperature starts at 4 C (it's tricky below that number as you'll read below), then for every degree C that we increase the temperature of one unit (any unit-volume measurement) of water, its volume (expressed in the same units) will increase by 1.0208 (cubic meters, gallons, whatever).

We are using the coefficient of thermal expansion of water = 0.00021 (1/^oC)

1 deg C rise in the water tank = 1.0002 Unit Volume Rise 

or if our water container is closed, such as a water heater tank, we should be able to say

1 deg C rise in the water tank = 1.0002 Unit Water Pressure Rise 

[This may not be quite so. We are equating a unit drop in density in a closed container with an increase in pressure in the same container, but the units of measure are not necessarily identical. Technical review in process 9/2010 CONTACT us with comments. ]

Effects on Water Pressure of Heating Up Water in a Tank

So using your example above, if we heat one volumetric unit (say one cubic meter, one gallon, or whatever) of water from 4 °C up to 80 °C (that's a 76 °C rise), the new water volume (in an open container) will be 1.016 x the original volume, or the pressure (in a closed container) will be 1.016 x the original pressure [since the volume could not expand the pressure must increase instead].

What happens to the volume of water in a 40-gallon water tank (geyser) when we heat it from 4 °C to 80 °C?

The volume increases from 40.0 gallons to 40.6384 gallons - doesn't sound like much, right? Let's look at water pressure change under the same temperature change.

If our starting water pressure in the water tank was 4 bar then we think this same calculator (or equation) work as well and our new water pressure in the closed tank is 4.0638 bar. Stating the same amounts in PSI for North Americans, our water tank pressure is increasing from 4 bar = 58 psi, up to 67.2 psi, or about 10 psi of increase in pressure - if we've got this right.

(1 bar = 14.5 psi, so that's about 58 psi, or 1 psi = 0.06895 bar)

Reader Anthony Lee comments:

When converting the “new” pressure of 4.0638 bar to psi you have multiplied by 4.638 instead of 4.0638. The new pressure if 58.9 psi and not 67.2 psi

[That gives us one tenth as much pressure increase or just 1 psi per degree C not ten psi - Ed.]

Watch out for hot water scalding hazards and unsafe water tank or calorifier pressures: By the way, typical safe temperatures in water heaters or calorifiers used for washing and bathing are around 104 degF up to a max (and risk of scalding) of 120 degF, or from at about 40-49 °C so our reader's example of superheating geyser water to 80 °C is scary.

See WATER HEATER SAFETY for details.

Making a new example for domestic water heating, entering water temperature in North America is around 10 °C or 50 °F (or colder, below 40°F in northern areas such as northern Minnesota).

If we heat 40 gallons of water (a typical domestic water heater or calorifier size) from 40 °F (a cold state) up to 120 °F (hotter than most manufacturers recommend and about the limit you'd expect), then our new water tank volume would be 40.672 gallons.

Typically the pressure/temperature relief valves on domestic water heaters are set to open at 100, 125, or 150 psi (6.9, 8.61, or 10.34 bar).

Worst Case Water Heater Pressure Analysis

What happens if we start with 20 psi water in our water heater (calorifier or geyser) tank that has entered from our well at 40 °F, and we do two things: we turn on our water heater to heat the tank contents up to 120 °F, and our pump has turned on to pump up starting pressure in the water heater tank to 50 psi. We have

• Water pressure increases from 20 to 50 psi or + 30 psi
• Water temperature increases from 40 °F to 120 °F or + 80 °F

Engineering Toolbox guys and gals inform us that the formula to calculate the effect on density of changing both water pressure and water temperature at the same time is calculated as

ρ₁ = [ ρ₀ / (1 + β (t₁ - t₀)) ] / [1 - (p₁ - p₀) / E]     

Plugging in what we know:

ρ₁ = [ 999.97ρ₀ / (1 + 0.0002β (t₁ - 4.44t₀)) ] / [1 - (p₁ - 999.97p₀) / 2.15 10⁹E]     

where [ this needs a scientific calculator or software]- Ed.

• ρ1 = final density (kg/m3)
• ρ0 = 999.97 = initial density (kg/m3) water at 40 ^oF or 4.444 ^oC
• β = 0.0002 = volumetric temperature expansion coefficient (m3/m3 ^oC)
• t1 = final temperature (^oC)
• t0 = 4.44 = initial temperature (^oC) (40 degF = 4.4444 ^oC)
• E = 2.15 10⁹ = bulk modulus fluid elasticity - E - of water

[Technical review in process 9/2010 CONTACT us with comments. ]

Watch out: this is not actually the very worst case of a possible hot water pressure increase to dangerous levels in a building. For example at a property served by a municipal water main, incoming water pressures can be higher than those produced by a private well pump if someone has tampered with a pressure regulating valve.

The equation behind this calculation and a nice online water density calculator are discussed at ET's Online Water Expansion Calculator

BLEVE explosions or boiling liquid vapor expansion explosions can occur at both domestic water heaters (calorifiers or geysers) and at hot water heating boilers (hydronic heating systems).

We discuss the role of pressure/temperature relief valves in protecting against these hazards
at RELIEF VALVE, TP VALVE, BOILER

and at RELIEF VALVE, WATER HEATER

At THERMAL EXPANSION TPR VALVE LEAKS we explain how normal thermal expansion in a hot water system can cause pressure & temperature relief valve leaks that in turn can lead to valve failure and a dangerous risk of a BLEVE.

At MEASURE WATER SYSTEM PRESSURE & PRESSURE MAXIMUM we explain how to make or buy an inexpensive recording-type water pressure test gauge to detect thermal expansion T&P valve leaks.

At HOT WATER EXPANSION TANKS we explain the use of expansion tanks or relief valves designed specifically to handle thermal-expansion leaks in hot water systems.

More Detailed Explanation of the Pressure, Density, and Volume Behavior of Water as Water is Heated in a Closed Container

Our second recommended source is in academia at UCSC - Physics dept. See http://physics.ucsc.edu/~keivan/THERMO5D/sol1.pdf that gives the non-linear coefficient of volume expansion for water vs. temperature. And we presume you know that water actually expands when it freezes, but because of the crystalline structure it forms. Water can expand in two temperature directions (if we include freezing) - confusing the discussion.

It's interesting how answers to the question: "how much does water expand when heated" vary on the web all over the place. Examples of some statements we found [web search 09/16/2010]

When water is heated it expands rapidly adding about 9 % by volume. - this is probably not quite correct as the expansion rate for heated water is not linear. So when we heat water from freezing, it actually contracts in volume, up to its maximum density point. Water has its maximum density at 3.98 degrees C.

From 3.5 degrees to 4.5 degrees water doesn't expand at all. - this answer doesn't quite agree with the one above

Water between 0 and 4 degrees Celsius will contract when heated - this is consistent with the explanation about expanding when freezing but we think some of the writers are sloppy with the decimal point and precision Also see the wikipedia entry http://en.wikipedia.org/wiki/Properties_of_water - and Wiki on thermal expansion at http://en.wikipedia.org/wiki/Thermal_expansion

What are the Thermal Coefficients of Expansion for Water?

The thermal coefficient of expansion of water is 0.00021 per 1 °C at 20 °C

The thermal expansion coefficients for water varying by temperature are at http://physics.info/expansion/

How do Fluids Behave When Heated - Fluid Density, Coefficient of Expansion, Temperature Rise

A nice web page about density of fluids and a chart plotting the density of water at different temperatures is at The Engineering Toolbox, from which we quote below [with permission].

If you consider that a decrease in the density of a fluid in a closed container is analogous to a concomitant increase in the fluid pressure in that container, we're almost home-free on the question of the amount of expansion in water as it is heated.

Notice in the curves on this chart (click to enlarge) of water density (or water pressure) that as our little quotes above illustrated, the density of water increases (pressure decreases) as water temperature increases from 0 to around 4 C, then above that temperature the density of water decreases (water pressure increases) as the water temperature rises.

But since the water pressure vs. water temperature lines are not straight (they're curved) while you can read the approximate density (or pressure) change as a function of water temperature right off the chart shown here, to know the precise change in water pressure if it is heated from one temperature to another requires some calculation.

In this chart, the left side or vertical axis is water density, measured in kilograms / cubic meter or kg/m³ , and the horizontal axis is water temperature measured in ^oC.

Density Change in Water When Water Temperature is Changed

The density of a fluid can be expressed as

ρ1 = ρ0 / (1 + β (t1 - t0))  

[This is Engineering Toolbox equation # (1)]

where

• ρ1 = final density (kg/m3)
• ρ0 = initial density (kg/m3)
• β = volumetric temperature expansion coefficient (m3/m3 oC)
• t1 = final temperature (oC)
• t0 = initial temperature (oC)

The Volumetric Temperature Coefficient - β for water = 0.0002 (m3/m3 oC)

Water density and change in water pressure

When water pressure [or the pressure of a fluid] is changed, the density of a fluid can be expressed as

ρ1 = ρ0 / (1 - (p1 - p0) / E)

[This is Engineering Toolbox equation # (2)]

where

• E = bulk modulus fluid elasticity (N/m2)
• ρ1 = final density (kg/m3)
• ρ0 = initial density (kg/m3)
• p1 = final pressure (N/m2)
• p0 = initial pressure (N/m2)

The bulk modulus fluid elasticity - E - of water = 2.15 10⁹ (N/m²)

What Happens When We Simultaneously Change Both Water Pressure and Water Temperature in a Water Heater Tank?

For example, the static water pressure in a water heater (or geyser) tank at a fixed temperature might be X psi. But two different events affect the pressure and density of water in the tank:

1. The water supply source pressure varies, for example from a private well and pump system, will deliver water at varying pressures. So the psi in a water tank may sit at 20 just before the water pump comes on, and may rise to 40 psi or even 50 psi just as the water pump cuts off.
2. The water temperature varies: temperatures inside the water heater will vary as the water heating source (an electric element, gas burner, oil burner, solar source, other) is turned on and off by a thermostat.

So you can see that there are two forces, both temperature and pressure, at work at once. One way to translate these into a single number is to look at the change in water density. Our friends at Engineering Toolbox provide this general equation relating the density of a fluid to changes in both temperature and pressure, combining the information given above in equations #(1) and #(2):

 ρ₁ = [ ρ₀ / (1 + β (t₁ - t₀)) ] / [1 - (p₁ - p₀) / E]   

ET's Online Water Expansion Calculator

The Engineering Toolbox also gives us a nice online calculator of the volumetric (or cubic) expansion of a substance as a function of starting volume, density, and mass.

The volumetric temperature coefficient of water is given as water : 0.00021 (1/^oC) in other words, this is water's coefficient of volumetric expansion as it is heated.

Their calculator is at http://www.engineeringtoolbox.com/volumetric-temperature-expansion-d_315.html

The equation to calculate the change in units volume of water when the water temperature changes is given by ET as

dV = V₀ β (t₁ - t₀)         

• dV = V₁ - V₀ = change in volume (m³)
• β = volumetric temperature expansion coefficient (m³/m^{3 o}C)
• t₁ = final temperature (^oC)
• t₀ = initial temperature (^oC)

Similarly, the equation to calculate the change in units density of water when the water temperature is changed is given by ET as

ρ₁ = m / V₀ (1 + β (t₁ - t₀))

    = ρ₀ / (1 + β (t₁ - t₀))         

• ρ₁ = final density (kg/m³)
• ρ₀ = initial density (kg/m³)

Last, and least necessary for our water pressure change above, ET provides the formula for the specific volume of a unit as a function of its density and mass

Specific volume of a unit can be expressed as

v = 1 / ρ = V / m        

• v = specific volume (m³/kg)
• ρ = density (kg/m³)
• V = volume of unit (m³)
• m = mass of unit (kg)

Some Properties and Constants of Water Used in Calculations of Pressure, Temperature, Volume, and Density of Water

• The bulk modulus fluid elasticity - E - of water = 2.15 10⁹ (N/m²)
• The thermal coefficient of expansion of water is 0.00021 per 1 °C at 20 °C
• Density of water: [we mean fresh water, not seawater] expressed in kg/m³

• Water is at its highest density at 3.98 °C = 1000 kg/m³ or 1 g/cm³. The correct SI unit of density of water is
  ρ = 1000 kg/m³. [also FYI, 1 m³ = 1,000,000 cm³]
• Specific weight of water = 62.4 lb/ft³ (IU) or 9.81 kN/m³
• Specific weight of seawater = 64 lb/ft³ (IU) or 10.1 kN/m³ - must be all that extra salt making it more dense, so we float better in seawater than in fresh water, right?
• Specific gravity of water: At its maximum density of 4 °C (39 °F) the specific gravity of water is 1.

Notes: 

Conversions of density, mass, pounds, slugs, and psi (pounds per square inch)

A mass of 1000kg pressing on an area of 1 m², that is on the bottom of the one meter square cube, means that the pressure on the cube bottom is also 1000 kg over 1 m².

• 1000 kg/cm² = 14,223 psi
• 1000 kg/m² = 142,231 psi
• 1 atmosphere = 14.69 psi
• 1 mm H2O = 0.00145 psi
• 1 mm Hg = 0.49 psi
• 1 inch H2O = 0.036 psi
• 1 kg/cm² = 14.21 psi
• 1 m H₂O = 1.45 psi
• 1 mm H₂O = 0.00045 psi or 1.45 10^-3
• 1000 kg = 68.5 slug

Why any object floats or sinks: If the total volume of water displaced by any object (if that object could be pushed totally under water) has more mass than the object itself has, then that object will float with at least some part of its shape above the top level of water.

If an object has mass exactly the same as the mass of water displaced by its volume, it is neutrally buoyant (at the surface of the water) and floats with its top just touching the top surface of the water. We like to think of this as the surrounding water and its mass "pushing" on the object on all sides, pushing it "up" into the air (or atmosphere at sea level).

If an object weighs more than the water displaced by its total volume (or speaking correctly if it has more mass), it sinks.

See WATER PRESSURE MEASUREMENT

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Continue reading at BLEVE EXPLOSIONS - why water heater tanks or calorifiers might explode if the relief valve fails, or select a topic from closely-related articles below, or see our complete INDEX to RELATED ARTICLES below.

Or see HOT WATER PRESSURE EXPANSION FAQs questions & answers posted originally at this article

Or see HOT WATER EXPANSION TANKS

Or see THERMAL EXPANSION TPR VALVE LEAKS - why the relief valve leaks when heating water

Or see RELIEF VALVE LEAKS for a diagnosis of all of the causes of leaks at TPR valves.

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