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Thermal expansion in hot water systems: This article defines thermal expansion in water equipment in response to temperature, and explains the concomitant increase in sysem 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. Green links show where you are. © Copyright 2014 InspectApedia.com, All Rights Reserved. How to Measure or Predict the Increase of Pressure in Water Heater Tanks: Expansion Rate of Hot Water as it is HeatedThermal 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 riseHow Much Will Water Pressure Increase as Water is Heated in a Domestic Water Heater or Heating Boiler?Of course a simple and nonmathematical method of looking into the pressure that is occurring at any tank containing water and water that is heated, is discussed at WATER PRESSURE & FLOW MEASUREMENT where we simply use an instrument to measure actual water pressure that is occurring. 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:
Calculating Water Pressure Increase in a Closed Container (water tank) due to HeatingHere 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?
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/m^{3}. The density of water at 100 °C is 958.4 kg/m^{3} and the density of water at 030 °C is 983.854 kg/m^{3}.  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,
for any material. SI units for density are kg/m^{3} that is, Kilograms per cubic meter. Imperial or BG density units are in lb/ft^{3} or pounds per cubic foot. Technically "pounds" measures force not mass. You can also state density in slugs/ft^{3} 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/m^{3} 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/m^{3} at 3.98 °C has a mass of 1000kg and a volume of 1 m^{3}. To convert the mass of 1 cubic meter of water to pressure expressed in psi and other measures:
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/m^{3}, or put more accurately, at 4 °C the density of water at 1 atmosphere (sea level on earth) is 999.9720 kg/m^{3}. 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?
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/waterthermalpropertiesd_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 unitvolume 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/^{o}C)
or if our water container is closed, such as a water heater tank, we should be able to say
[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 TankSo 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 40gallon 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:
[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 4049 °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 AnalysisWhat 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
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
Plugging in what we know:
[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 VALVES  TP Valves on Boilers and at RELIEF VALVES  Water Heaters. As we further explain at RELIEF VALVES  Water Heaters, in some locations where hard water is found, an expansion control valve is also used to drain excess hot water tank pressure. More Detailed Explanation of the Pressure, Density, and Volume Behavior of Water as Water is Heated in a Closed ContainerOur second recommended source is in academia at UCSC  Physics dept. See http://physics.ucsc.edu/~keivan/THERMO5D/sol1.pdf that gives the nonlinear 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 RiseA 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 homefree 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/m^{3} , and the horizontal axis is water temperature measured in ^{o}C. Density Change in Water When Water Temperature is ChangedThe density of a fluid can be expressed as ρ1 = ρ0 / (1 + β (t1  t0)) [This is Engineering Toolbox equation # (1)] where
The Volumetric Temperature Coefficient  β for water = 0.0002 (m3/m3 oC) Water density and change in water pressureWhen 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
The bulk modulus fluid elasticity  E  of water = 2.15 10^{9 }(N/m^{2}) 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:
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):
ET's Online Water Expansion CalculatorThe Engineering Toolboxalso 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/^{o}C) in other words, this is water's coefficient of volumetric expansion as it is heated. Their calculator is at http://www.engineeringtoolbox.com/volumetrictemperatureexpansiond_315.html The equation to calculate the change in units volume of water when the water temperature changes is given by ET as
Similarly, the equation to calculate the change in units density of water when the water temperature is changed is given by ET as
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
Some Properties and Constants of Water Used in Calculations of Pressure, Temperature, Volume, and Density of Water
Notes: Conversions of density, mass, pounds, slugs, and psi (pounds per square inch) A mass of 1000kg pressing on an area of 1 m^{2}, 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 m^{2}.
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 & FLOW MEASUREMENT and also WATER TANK PRESSURE GAUGE and WATER PRESSURE GAUGE ACCURACY for a discussion of builtin water pressure gauges. See WATER HEATER SAFETY for a discussion of types of safety devices, including expansion tanks and pressure/temperature relief valves used on water heaters. More ReadingGreen link shows where you are in this article series.
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Frequently Asked Questions (FAQs) about Thermal Expansion in Hot Water SystemsQuestion: can thermal expansion cause my hot water tank relief valve to dripI was told that thermal expansion is the reason the temperature & pressure relief valve on my water heater is dripping. Is that OK? Reply:No. The cause of the dripping, which could be due to a hot water thermal expansion sysem in a closed system, could also be due to any of a number of other problems. In all cases a drippy TP valve is potentially dangerous both because we don't yet know the reason for the drip (the system may already be unsafe) and because the safety valve may clog and then fail to protect the system. See RELIEF VALVES  Water Heaters. ... Ask a Question or Search InspectApediaUse the "Click to Show or Hide FAQs" link just above to see recentlyposted questions, comments, replies, try the search box just below, or if you prefer, post a question or comment in the Comments box below and we will respond promptly. Search the InspectApedia website HTML Comment Box is loading comments...
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