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# Temperature Pressure (TP) Relief Valve Conditions / Thermal Expansion of Water

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Member Posts: 4
Hello there everyone,

I have some concerns regarding formulations of temperature and pressure in hot water tanks / water heaters.

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

Assuming we are dealing with a closed system.

What is the pressure change of water inside the tank when the temperature increase from 16°c to 99°c

Since the TP valve will trip at 99°c / 150 psi - will those conditions ever exist? Can you get 150 psi and 99°c?

This is confusing to me because it seems as though the valve will trip only at 99°c since it will reach that temperature way before the pressure getting to 150 psi..

How can we obtain some sort of pressure-temperature plot? or calculate the thermal expansion pressure due to a specific change in temperature?

If the system goes from 80 psi to 150 psi for example, what is the resultant change in temperature?

Once TP valve trips, how much water will be discharged?

• Member Posts: 23,446
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The general equation for thermal expansion of a fluid is:

dV = V*beta*dt. Where beta is the coefficient of expansion.

As you can see, pressure doesn't show up. So the question doesn't have a simple answer; what one needs to know is what is the change in system pressure with a change in volume -- and that depends on the kinds of pipes and tanks etc. which have been used.

Some kinds of pipe expand a lot with very little pressure (relatively speaking) -- such as any of the plastics. Some, such as heavy wall copper of ductile iron, take a lot of pressure to expand.

Further, if there is any air in the system, that compresses pretty easily, and allows the water to expand. Which is why we use expansion tanks.

However, for a more direct answer, yes, depending on the system, you could get to 150 psi simply by thermal expansion. Probably you wouldn't -- some fitting somewhere would almost surely leak -- but you could. As to how much water will be lost when and if you do, so long as the temperature in the system is below the atmospheric boiling point of water at your elevation, very little.

If it is greater than the atmospheric boiling point... trust me, you don't want to be there.
Br. Jamie, osb
Building superintendent/caretaker, 7200 sq. ft. historic house museum with dependencies in New England
• Member Posts: 4
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Hi Jamie,

Thank you so much for your response!

So if the thermal expansion formula does not include pressure in the equation , how can we relate the change in volume to a change in pressure?
Also, in the case of a completely closed system - and assuming there's no expansion tank - how can the tank handle this expansion when it has nowhere to go? What is going on in the system at that point?

Assuming the tank contains a TP value with an 18" copper tubing, where the end of that discharge tube connects to a PEX (Cross-linked PE) pipe - would it be possible to know what the thermal lag is across that pipe?

What approach can I follow to validate these conditions? Knowing that thermal expansion is possible at 150 psi, what is the resulting temperature at that pressure? Any sort of formulations that you can recommend?

I'm trying to somehow challenge these ASTM standards for PT relief valves. Are these conditions excessive? If so, why, if not then why not? I'm having trouble trying to rationalize this with some form of engineering principles.

As to the presence of air in the system, is it a fair assumption to assume there isn't? Or would that not be physically possible? If that's the case, what is the outcome?

Sorry for asking way too many questions..

PS lol @ not wanting to be at greater than atmospheric boiling point
• Member Posts: 4
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Just to reiterate and simplify things a bit more, I think my main struggle is putting the following into a formula:

How much does pressure increase inside a closed water heater tank (without expansion tank and without compressed air - aka worst case scenario) as the temperature rises? And would it be possible to turn that into some form of a P/T plot?
• Member Posts: 4
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Does the following sound reasonable:

Using the Keenan-Keyes-Hill-Moore (KKHM) steam table formulation for water, I approximate the spec vol at 20C, 1 atm at about
1.00172(10^-3)m^3/kg

with that const spec vol, my forumulation yields

20C 0.14MPa which I approximate as one atm.
70C 49.5MPa
90C 79.3MPa
120 130.5 MPa

The KKHM formulation for properties are based on input of v and t. Therefore, I had to iterate to come up with the approximate specific volume

Please let me know if this makes sense.

Thank you!
• Member Posts: 23,446
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You relate the potential change in volume given by the simple volume formula to the change in pressure which may or may not happen through the elasticity of the system as a whole. This elasticity contains several factors, which makes it difficult to give a simple answer. One is the elasticity of the water itself; that is very small -- 0.000053 for a change in pressure of 1 atmosphere. Pretty close to negligible (for most purposes). Then you have to figure in the change in volume of the container for the change in pressure due to the elasticity of its material or materials. As I said before, for some materials -- plastics, rubber, that sort of thing -- the elasticity of the material is very high, and the change in pressure with a change in volume of the container will be very small. Other materials -- most metals -- have very small elasticity, and thus for them to change their volume the change in pressure has to be very large (ceramics have even lower elasticity).

Thus if you have a closed container system of a relatively inelastic material or materials the pressure rise can be dramatically high, but without knowing the full configuration and construction of the system one can't figure it out in any simple way (in fact, for anything more complicated than a simple spherical or cylindrical container with rigid ends it gets to be a very very complex problem, as one may also have to figure in the change in volume from deflection of the material -- if you have flat ends to a cylinder, for instance, they will bow out).

The introduction of air or some other gas into the system changes things radically, as gasses are very compressible and thus will accommodate the small change in volume due to temperature with very little change in pressure. Hence, expansion tanks.

All this, incidentally, is why hydraulic systems work at all!

The settings for temperature and pressure relief valves are for safety, of course. Temperature is obvious -- the water in the system must be kept below the atmospheric boiling point, unless the system is designed for higher operating pressures (such as some engine cooling systems), in which cases, though there will be a pressure relief mechanism only slightly above the design operating pressure -- and spectacular results if the pressure is removed abruptly, as by a failure (or some idiot taking the radiator cap off...). The pressure relief setting -- which in my humble opinion is too high -- is also related to the design maximum pressure of the system -- pipes, valves, that sort of thing -- and is, hopefully, below the pressure at which they will fail.

As a practical matter, in most plumbing work you will find that one or more valves will leak before you reach the pressure relief setting; one rather hopes that it is that, and not a poor solder joint or PEX joint somewhere deep in a wall! And also, as a practical matter, if one has a plumbing system generating hot water -- such as might be a house -- which has check valves or pressure reducing valves, it is good practice (as well as code in some places) to have an expansion tank on the hot water lines.
Br. Jamie, osb
Building superintendent/caretaker, 7200 sq. ft. historic house museum with dependencies in New England