Not bored, or nothin’…

Shower thoughts. There’s a Reddit sub for that kind of thing (for example, if 9-11 had happened two months earlier, 7-11 the convenience chain woul have had some major rebranding to do, and the like).

Me, because I’m with a geek (and have been accused of being one myself) calculate stuff. Call it an inspiration by Mark Watney, whose exploits I’m reading twice in the past four months.

Ladies and gentlemen, here is my shower:


My own shower thought: how much water would mass if it filled up to the level of the small tiles.

This is actually not that hard to do. All you need to do is know how big one of those small tiles is, and to remember the density of water (which is 1 gram per cubic centimeter). Everything else is just boring Maths.

So I tried to do it in my head. Here’s my thought process:

Because I’m doing it in my head, I’ll be rounding a lot. As we say in Physics, it’s a right answer as long as it’s of the same order of magnitude.

My shower base is about 40 tiles by 30 tiles. That’s 1200 tiles, and that’s the easiest calculation of the morning (remember, I did this within the time of my shower, which was maybe five minutes). This was an underestimate which I’ll have to make up somewhere.

Each tile is 1 inch, which is 2.54 cm. But there is grout, so if I include the joints, let’s say 2.6 cm (an under estimate). I calculated that 2.6 squared (the area of one tile) is 4 + 1.2 + 1.2 + 0.36, or 6.76  square cm. Yeh, I did that in my head, and so can you, if you think about it. (And were taught multiplication by partial products – it’s what I teach my kids, but they’ll have none of it, being indoctrinated as they are to memorizing procedures and shit.)

Anyhow, 6.76 cm^2, which I round up to 7 cm^2, to try to make up for the two under-estimates I just used. It all works out in the end. Or it’s supposed to.

Now, the tiles ride up the pan about 10 cm (I eyeballed that one). So the volume above one tile is 7 cm^2 x 10 cm, or 70 cm^3. Seventy cubic centimeters. We’re getting exciting close to the end.

One tile has a volume of 70 cm^2 above it, so 1 200 tiles is 1 200 * 70. So in my head I’m going 70 000 + 14 000 = 84 000 cm^2 for the whole shower base.

Easy peasy, and now, it only gets easier. Because now, I know (and perhaps you do too?) that one cc of water has a mass of about 1 gram. 1 cm^3 of pure water at STP has a mass of EXACTLY 1.0 gram (it’s sorta a definition thing), but this is warm shower water, and not pure. Calgary, yo.

84 000 cc of water has a mass of 84 kilos.

Now let me go and measure more exactly. And use a calculator.

Well now, I underestimated. Seems that my shower is 118 cm by 90 cm, which is 10 620 square cm. I nailed the 10 cm height though, so I have a volume of 106 000 cc, which is 106 kg. 20% off, but in the ballpark.

Well, that was fun.



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