Talk:2974: Storage Tanks

The symmetry of the truss intrigues me. Struts that are diagonal across the faces of the cuboids is normal, but is it a real thing to also use the body diagonal? Never seen that IRL, not sure if it makes sense from the statics. --172.70.247.82 22:16, 19 August 2024 (UTC)

Seems like a pretty menial job for the "head of security". I think he would delegate this to a security guard. Barmar (talk) 00:47, 20 August 2024 (UTC)

They may be head of a department of one.172.70.85.139 08:50, 20 August 2024 (UTC)

That's part of the joke, that the #1 concern of the Head of Security is calculus teachers wielding power drills for class demonstrations. Laser813 (talk) 17:33, 20 August 2024 (UTC)

The explanation mentions there might be more complex calculus examples where the shape might not be a cylinder. I think some further explanation could be added that this does not change the pressure (hydrostatic paradox) but indeed change the rate of emptying the object. If differing cross sections are relevant at all. 108.162.221.103 05:40, 20 August 2024 (UTC)

Non-prismatic geometries are I think the ones being alluded to here, i.e a frustrum with the pointy end down will have a greater reduction in pressure for a given volume of flow towards the end than at the start, which may offset the reduction in absolute pressure. I've also seen examples where the flow rate is considered constant and the problem is to work out the fluid depth as a function of time, e.g. filling a pyramidal pool from a hose. 172.70.58.4 16:44, 20 August 2024 (UTC)

Its the most difficult job in history, even the best workers couldn't stand 1 day as head of security.I HAVE NO NAME (talk) 05:55, 20 August 2024 (UTC)

I have to admit, I thought I knew calc as I had two semesters of it, but I had to look up what he meant by this. Ouch 172.70.242.55 13:01, 20 August 2024 (UTC)student

If anyone could suggest something I can do for my class now that I can no longer drill holes in tanks, I'd appreciate the advice, thanks. Fephisto (talk) 16:18, 20 August 2024 (UTC)

Someone should do the math on the calculus problem as presented, as well as the algebra version. Laser813 (talk) 17:33, 20 August 2024 (UTC)

Randall, like all good mathematics textbook authors, left the problem as an exercise for the reader. Does this happen often enough to warrant a tag? Paddles (talk) 05:57, 21 August 2024 (UTC)

Yes... Transgalactic (talk) 10:10, 21 August 2024 (UTC)

Is there anyone else who thought the calculus teacher was abusing the tank as a model for the complex plane, demonstrating how to remove a singularity from a holomorphic function? I wasn't confronted with that particular tank-emptying problem in high school, so my first encounter with "holes" in maths was in complex analysis. The title text was a mystery. Transgalactic (talk) 10:10, 21 August 2024 (UTC)

As a mathematician, I'm surprised I didn't know about this idea. (It's definitely not my field!) I actually thought the flow would be constant, an algebraic problem. Oh, I'm sure I saw these types of problems in Calculus (and I remember problems like this in Differential Equations), but I thought those were just to make the math more complicated, not based in reality... So is it the weight of the liquid remaining above the hole that is the source of the pressure (i.e., would it be the same if the top of the tank were open), or is it the air pressure in the tank as the volume of liquid decreases and volume of air increases? Mathmannix (talk) 11:08, 21 August 2024 (UTC)