Pressure in a water heater - does it depend on size?

[TSN79]

Picture two water heaters - one 10 liters and the other 100 liters, initially filled with cold water. If both of them are heated to the same temperature, will a pressure meter display the same pressure for both tanks, or is the resulting pressure somehow dependent on the size of the tank?

 

[anorlunda]

The pressures should be the same, not sensitive to tank size.

However, if you put equal energy into the tanks instead of saying "same temperature", the answer would be different.

 

[russ_watters]

Picture two water heaters - one 10 liters and the other 100 liters, initially filled with cold water. If both of them are heated to the same temperature, will a pressure meter display the same pressure for both tanks, or is the resulting pressure somehow dependent on the size of the tank?

Are you talking about actual residential water heaters or hypothetical sealed tanks? The pressure inside a water heater is the supply pressure into the building (plus or minus any hydraulic head). It doesn't change with size or heating.

 

[jrmichler]

Since the OP specified water heaters, @russ_watters answer was correct, but too easy. Another easy way to solve this is to assume mathematical physics tanks with zero coefficient of thermal expansion and infinite rigidity. In that case, @anorlunda gave you the answer.

On the other hand, if you want to entertain yourself with some calculations, assume that the two tanks are made of real materials, filled with water (no air bubbles), sealed, and then heated. The calculation for each tank has three parts:

1) Thermal expansion of the water, which increases the pressure (water expands as it gets hotter).
2) Bulk modulus of the water (increased pressure decreases volume).
3) Thermal expansion of the tank, which makes it larger, so the pressure increases less (thermal coefficient of expansion of the tank).
4) Increased stress in the tank from the pressure, which makes it larger, so the pressure increases less (elastic modulus of the tank).

I have not put enough thought into this to know if there is a practical analytic solution. If I was solving it, I would use an iterative approach in a spreadsheet and let the solver do the work.

Data point: When the water line to my house cracked a couple months ago, we turned the pump off at night and shut off the valve to the water heater to keep it from draining down. On two occasions, the water heater thermostat kicked on while the valve was shut off. The pressure increased about 75 PSI.

 

[NTL2009]

Actually, both answers from @anorlunda and @russ_watters can be correct. Many municipal water systems include a check valve at the inlet to the house. So when the water is heated, the expansion raises the pressure in the home. These should have an expansion tank to avoid stresses.

A system without a check valve will be buffered by the supply, and remain at the system pressure.

 

[russ_watters]

Actually, both answers from @anorlunda and @russ_watters can be correct. Many municipal water systems include a check valve at the inlet to the house. So when the water is heated, the expansion raises the pressure in the home. These should have an expansion tank to avoid stresses.

True, though an expmansion tank should expand the volume without a significant pressure increase...though I'll admit I don't know what the typical amount should be.

 

[NTL2009]

You can find density changes with temperature here:

https://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html?vA=60&units=F#
Using US units, a change from 60F to 135F would be an expansion of ~ 1.4%. That would be a bit more than 1/2 gallon on a 40 gallon water heater. With a check valve in the supply (to avoid back-feeding house water into the municipal system when there is a pressure drop - a safety feature), this expansion also includes all the pipes in the system. And assumes no one draws off any water during the heating cycle, which would blow off the excess pressure.

I know that expansion tanks are recommended with check valve systems. Sometimes, this pressure increase will trip the safety pressure valve that is on every water heater. If you see occasional drips from that, that could be the reason.

Any air hammers that are installed at faucets would also absorb some this pressure. I'm on a well, so I have a large expansion tank which would absorb this. A well tank let's the pump run and pump up the pressure, then this built up pressure feeds the home, the pump cycles again when pressure drops. The pump is supposed to run for at least one minute, shorter times will decrease the pump life. If the expansion tank loses the air buffer, the pump will cycle every time you draw water, and pressure will jump up and down rapidly.

 

[Nik_2213]

Our 'closed' heating system includes a filling loop with valve and gauge. The 'boiler' safeties will not permit operation unless the system is pressurised to its 'green' comfort zone. Expansion etc handled by a safely enclosed bellows arrangement resembling a truck's pneumatic suspension...

IIRC, traditional pumped or older, passive 'back-boiler' systems used a 'header' tank in loft or attic to both provide a 'pressure head' for the boiler and serve as an expansion space. Logically, the 'cold' system pressure was a bit less than the 'hot' pressure, as expansion made the narrow 'header tank' level rise several inches...

Note you must keep radiators 'bled', lest trapped air's expansion drove much heated water into the cold 'header' tank, wasting its expensive energy...

 

[NTL2009]

Before I closed the tabs I was searching, I came across this interesting aside, due to the fact that water is densest @ 4C:

https://van.physics.illinois.edu/qa/listing.php?id=1736

An interesting consequence of this peculiar feature of water is that the temperature of water at the bottom of a lake in the winter is almost always 4 degrees C, since the densest water will settle to the bottom -- if it gets any colder or warmer, it will rise.

 

[Nik_2213]

Per this 4'C aside: Long, long before Google, a bunch of us Phys-Chem students spent a LOT of time trying to find a non-aqueous system that matched water's behaviour thus.
Our consensus, water may look simple, but is TOTALLY WEIRD.
Yup, we're the 'aliens'...

 

[anorlunda]

@TSN79 , can you clarify the original question? We still can't be sure if you are asking about a traditional plumbing system.

 

[hansDaniel2]

Of course density of water depends on the temperature, just read some article about it like that one https://amazingconverter.com/density-converter/density-of-water-lb-ft3