# Pipes and water pressure

The warm sunny weather has led to a discovery under the front lawn. The clue was the fact that the ground was squelchy after three weeks with no rain.  Either a new hot spring was in the process of popping up out of the lawn, or our water pipe had sprung a leak.

It’s not the first time (or even the second time) that it’s had a leak. The plumber says that the problem is that the pipe (a plastic one) isn’t tough enough for the high Cambridge water pressure. True, he might be fishing for a contract to replace the whole pipe, but with three leaks in the last few years (and how many more before we moved into the house, I don’t know) he probably has a point.

This has reminded me about a bit of theory I did back as an undergraduate on how the pressure of the water in a pipe relates to the stress in the wall of the pipe. It’s a relatively simple calculation to do – if you consider the top half of a section of pipe, you can balance the force upward on the pipe due to the water pressure with the force downward due to the stress in the pipe wall.

We find that the stress (tension force per unit area) is proportional to the pressure (unsurprisingly) multiplied by the pipe radius but divided by its thickness. That is, a thin pipe (by which I mean a pipe with a thin wall, not one with small diameter) is under a greater stress than a thick one. What the pipe is made of doesn’t influence the stress it is under, but it will influence the breaking stress.

So, to get a more suitable pipe, it either needs to have a thicker wall (and therefore less flexible), or made from a material with higher breaking stress. (Or of smaller radius, which constricts water flow, so that’s not necessarily an option.)  Which, I’m not fussed, just so long as it doesn’t break again!  Fed up with digging holes in the lawn.