How much extra pressure do you get when you heat water in a closed system?

Question

Hi.

Could someone help me with a temperature pressure volume of fluids problem? Especially pressure.

Assume:

200 feet of 3/4" copper pipe in a closed loop, with a pump.

The pipe is filled with 4.6 gallons of water.

The pipe is filled at 68 degree Fahrenheit, then the loop is closed.

The water is heated to 140 degrees F.

In Celsius, 140 F - 68 F = 22 C.

Water's coefficient of volumetric thermal expansion is .000207 / ºC.

I calculate that extra volume in the heated water is 4.6 x .000207 x 22 = .021 gallons.

Please could someone with engineering skill validate this calculation?

More importantly, and the reason that I'm writing: what happens to the pressure?

Thanks.

Answer 1

If you remember PV=RT, that also applies to fluids, so to speak.  Essentialy, PV/T is a constant, or PV/T of system 1 = PV/T of system 2.  So with a closed loop (no air), V is fixed, and then P/T = P/T

So as temp. increases, proportionally, the pressure increases as well.

Answer 2

First, 140°F-68°F= 72F° = 40C°

Now, 0.000 207/C° * 40C° = 0.828% raw expansion.

Water is only slightly compressible. In basic science they incorrectly over-simplify this to say it is incompressible. The compressibilty of water is calculated with bulk modulus, which is 2.2x10^9 Pa. So, change in pressure is:

2.2x10^9 Pa * 0.8% = 18.2MPa.

OK, so here's what theoretically happens:

As the trapped water heats up, it tries to expand. If the tubing is very rigid compared to the water, it just holds the water in, increasing the water pressure. The increased pressure compresses the water. End result is that the water remains at the same volume, but the pressure increases.

In real life, the expansion of the copper would be considered as well. The copper tubing expands slightly in both length and diameter with temperature, but not as much as the water. More important, copper is not particularrly stiff, so the pressure of the water increases the size of the tube, both in length and in diameter. So, the tube actually expands some, and pressure increase is less than predicted above. The corrent pressure is readily calculated within a few percent if the tubing material properties and dimensions are known.

Answer 3

Water is incompressible, so the pressure will increase. So good practice for hot water systems, or any time liquid changes temperature is to include an expansion tank.

The expansion tank will take up the water that expands.

Your calc looks correct.