Expensive cat physics

With baby Benjamin taking our attention, poor Mizuna the cat has been rather neglected recently. Unfortunately, this has proved an expensive (for us) and painful (for him) mistake. A couple of weeks ago, I noticed one morning that he was clearly in pain, and desperately trying to urinate. CLANG, CLANG, go the alarm bells. Male, neutered cat, urinary problem – there’s no mucking about with this one, but straight to the vet. It was obvious it was another bout of FLUTD – he had one about 18 months ago.

Last time, without a baby to cause distractions, we spotted it early enough and the vet had it under control fairly straightforwardly. This time, however, I picked it up much later, and the poor kitty had actually become blocked (which, for non-cat owners, means his urethra was blocked with crystals meaning he couldn’t urinate). A blocked cat is on a rapid, painful trip to kitty-heaven if he (and it is far more likely to be ‘he’ than ‘she’) doesn’t get immediate treatment.

So, a week and a half and a bill the size of an Australian Institute of Physics Congress fee later, Mizuna is back with us and appears to be doing well. But the lesson has been learned – watch the cat. 

Reading about the condition is quite fascinating. In fact, I’m left in great surprise that a male cat has a working urinary system at all. The urethra, at the base of the penis, has a tiny diameter, and that means it can block really easily. Even without a blockage, it can’t be easy for the moggie to pass urine. The flow of fluid down a very narrow pipe is governed by the Hagen-Poiseuille law – which is that the flow rate is proportional to the diameter to the power four, times the pressure difference.   That’s a steep power law – double the diameter and you get sixteen times the flow (so long as the flow stays laminar in nature) – on the other hand, a halving of diameter gives you one sixteenth of the flow rate for the same pressure. A narrow tube really isn’t much good for passing water down, and that’s the male cat on a good day. 

Interestingly, Poiseuille did his experiments with a view to understanding the flow of blood in the human body. Blood has a rather higher viscosity than water (yes, blood really is ‘thicker’, in this regard, than water) which means that Poiseuille flow remains applicable for larger diameter ‘pipes’ (i.e. arteries). Here, the steep power law is important in terms of heart problems – a narrowing of the arteries, if only by a small amount, is sufficient to reduce the flow of blood quite significantly. On the other hand, a stent doesn’t have to open up the artery by a lot in order to restore a good flow rate. I should add for completeness that there are a whole lot of other issues involved with blood flow; it’s not just Poiseuille’s law, but it does indicate that the width of the artery has a large role to play.

Going back to the cat, the last resort for a blockage is the perineal urethrostomy, which, in crude terms, is cutting off his willy. That is, getting rid of the smallest part of the pipe. Fortunately, Mizuna didn’t have to go down this route – and whether we would have agreed to pay for it is another issue too.


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