This is an out-in-the-weeds topic but I was doing some HVAC calculations and it reminded me of a conversation that I had here mostly with
@betarhoalphadelta a while back so I figured I'd share this with him and anyone else who might be interested.
One of my biggest complaints with our education system is that, as I see it, the administrators and the Education leadership in general seem to want to teach EVERYBODY a college prep education and this is silly because only around 1/3 of American Adults have a college degree. On top of that, I would argue that even that 1/3 is too many. A lot of them have useless degrees and are working in fields where their degree does them no good whatsoever.
Vocational Education is, IMHO, woefully under-emphasized and under-utilized and we end up with WAY too many college drop-outs and people who barely graduated with a degree in Sociology or Art History who have the same useable job skills they would have had if they had dropped out of HS.
Anyway, along those lines I was talking about learning the Pythagorean theorem (sides of a triangle, A^2+B^2=C^2 where A and B are the sides of a right triangle that DO intersect each other at a right angle).
I had actually learned that working construction many years earlier from guys who couldn't have pronounced, spelled, nor cared about Pythagoras. I learned it as something referred to in the trades as the "rule of three, four, five". In that context it was explained to me that when you are building a house or a deck or staking it out, if you measure 3" down one leg and 4" down the other leg the distance between those two will be exactly 5" if your corner is exactly square.
Now I'm sure that the Architects who designed the houses you all live in knew about Pythagoras and his theorem but I'm equally sure that the corner of your house is ACTUALLY square because the guys who staked it out knew the rule of three, four, five.
My point was that for guys who are NOT going to college, boring them to death with useless information about some long-dead greek dude is a complete and total waste of time for everyone involved. It would make a LOT more sense and would probably interest them a LOT more to teach them that if they are building something they can check the square of the corner by using the rule of three, four, five.
Anyway, another example of this kind of thing came up as I was working out some things for an HVAC:
When you run HVAC ducts you have a trunk or several trunk lines and then you split off from there. It is important to balance those lines. Ie, you have to have as much area in the feeder as you have in the fed lines.
Now I learned Pi in some long-ago college prep math class. Off the top of my head I can go out to 3.1415926. The only reason I know it that far is that in 2015 I took my (then) girlfriend (now wife) to Chicago for the B1G Basketball Tournament and we ended up going to the Chicago Museum of Science and Industry on Pi Day March 14. At 9:26 in the morning we took a picture of ourselves eating a piece of pie because the date/time lined up with Pi.
Ok, back to the story. In reality I've NEVER done anything where I actually needed to know Pi beyond 3.14. In fact, I think that for everything I've ever actually needed it for, simply 3 would have been close enough. I'm sure if you are designing parts for the space station you need to know it pretty far out but I'm not and even those guys are using computers so the ability to recite Pi to the 15th digit is completely and totally academic.
Back to my HVAC. The final line (serving one vent) is typically a 6" line so you need to know what it takes to feed two, three, four etc 6" lines. If you are only using round lines then Pi is actually completely irrelevant. All you need to be able to do is:
- Know that a radius is half of a diamater, and
- Multiply the radius by itself.
That is it.
- So for a 6" round pipe this is 9 (6/2=3x3=9)
- For an 8" pipe this is 16 (8/2=4x4=16)
- For a 10" pipe this is 25 (10/2=5x5=25)
- For a 12" pipe this is 36 (12/2=6x6=36).
Then from there, an 8" will feed two 6" pipes. This isn't exact because the area of a 6" is actually 28.27 square inches so two of them are 56.55 square inches and the area of an 8" pipe is only 50.27 square inches but that is all completely irrelevant because:
- I'm not designing parts for the space station here, I'm just running HVAC lines for a house, and
- If you actually did the calculation exactly you would discover that the appropriately sized pipe to feed two 6" pipes is a pipe with an exact diameter of 8.4853 inches. If you want you can go to your local Home Depot and ask them for a 8.4853" HVAC pipe but be ready for them to laugh at you. We aren't building spaceships here, HVAC pipes come in 6", 8", 10", and 12". They also make them bigger but those are industrial/commercial things that I really don't deal with. In a residential home you are just dealing with the aforementioned round pipes and some square and rectangular pipes.
Similarly, it isn't exact but you can feed three 6" pipes with a 10" pipe and you can feed four of them (this one is exact) with a 12" pipe.
The square and rectangular pipes are where you actually sorta need to know Pi but again, 3 is close enough. If I'm feeding 6" round pipes off of a 14x10 rectangular (that is sized to fit between joists) line I need some way to compare areas of circles to areas of rectangles. The 14x10 pipe has an area of 140 square inches and (see above) a 6" round pipe has an area of a little over 28 square inches so the 14x10 rectangle will feed five 6" round pipes (140/28=5). If I had simply ignored the decimals and used 3, I would have calculated a value of 27 for the 6" pipe and 140/27 is a little over 5 so it literally makes no difference because either way the 14x10 rectangular pipe will feed five 6" round pipes. That is close enough and it is all I need to know to do HVAC.
Guys who were taught things like the rule of three, four, five, and how to balance HVAC runs in Tech school generally have a lot better job prospects and a lot less debt than guys who got a Sociology degree with a C average from a mediocre school. One is a sought-after HVAC tech, the other gets you your coffee at Starbucks.
