So I have been getting around a 50°C water temperature for solar shower on a good sunny day. It heats up from around 20-25°C. This is great, after all it’s the point of the thing. However, it’s been causing problems.
The shower’s storage capacity is around 8.2 litres. With this volume of water, a 35°C temperature increase is accompanied by a increase in water volume (around 85cm³, see the next section). Water is effectively incompressible, I think, so the system needs to accommodate this, and it does not really accommodate that well; not intentionally by design anyway. Stupid shower.
Furthermore, I have been turning the inflow tap off when the shower is heating as I am worried that if something did burst I would be wasting lots of good tap water until I realised there was an issue. Closing the tap, of course, creates a fixed closed volume between the inflow tap and the outflow tap at the shower. And so the 85cm³ volume increase must be dealt with within this closed system.
To date little pin hole leaks in my (solvent-welded) uPVC pipe joints, due to bad workmanship, have been serving as pressure relief outlets of sorts. But, as I have patched up holes, I unknowingly (and in retrospect foolishly) have been lessening the ability of the system to relieve the pressures. Consequently there is induced strain and stress in the piping and more-so my dodgy joints.
I am ashamed to say, since I should have known better, that it has taken a few cycles of my plugging holes and reinforcing joints, then having a leak spring up somewhere else, before my deciding to approach it another way.
Various inputs from these sources:
- Volumetric to linear conversion
- Volumetric change integration method
- Volumetric coefficient data
- Pipe hoop and longitudinal stresses from internal pressure
- uPVC properties
By my estimation, assuming the water is entirely incompressible (which is conservative ) a 35°C temperature rise induces a tension stress of around 12MPa in the uPVC pipe. In isolation, that doesn’t actually seem that much per se.
There is also pressure in the pipe from the mains supply, which is ‘trapped’ when volume is closed by the in-tap. With a bit of Googling, an estimate of around 500kPa does not seem unreasonable for mains pressure in Auckland. This induces a hoop stress of around 4.8MPa in my pipe…so the temperature-induced pressure is around x3 that of mains pressure, which puts the former in perspective and make it feel as onerous as it probably ought to. This is particularly so as the pipe I am using is not even rated for main pressures.
Combining the temperature-induced stresses and main pressure-induced stresses gives a combined stress of around 16MPa in the plastic. I do not think this is an issue for the actually monolithic unadulterated pipework – this site quotes a short-term creep rupture of 44MPa for uPVC, which seems kind of apt, but the 16MPa is evidently causing issues for my joints.
[stextbox id=”info” shadow=”false”]Update To follow. My home-made pressure relief valve,which I thought was the solution just failed ;( Hum. I installed it before doing calculations above. Dammit.[/stextbox]