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)
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)
- A sealed-top would change the dynamics (like trying to pour the contents of a 2 litre (or whatever the US equivalent is) pop/soda bottle, it will tend to 'glug glug glug' intermittently unless you: a) incline the bottle to allow an optimum amount lf free akr back into the emltying bottle or, b) initialise the up-ended emptying with a spin sufficient to create a 'waterspout' effect up through which the replacement air can (more) freely pass.
- Though there are other possible factors, in that example, including the potential pressure of any self-releasing carbonation pressure (e.g. giving the bottle a shake, or a foreign body, before releasing the 'pour') and/or squeezing/'milking' the soft plastic container strategically to create another form of pressurised expulsion.
- For the 'classical' problem, one should probably assume sufficient inward venting (either an open/part-open top or a second hole drilled near the top to effect this purpose) as well as a reasonably unexotic liquid (neither molasses, cornstarch-mixture, anything that is actually a very fine dry powder, anything that reacts significantly with/upon air, any liquid very close to its vapour-point nor specifically supercooled helium) or any additional elements (stirrers, baffles, spongey inners, inner membranes or the contents being a layered combination of imiscable liquids of different densities that may or may not react slightly all across the interface plane). Most things that aren't actually exotic (and even a few that are, and might warrant a warning /¡\) are close enough to water to treat as if just that, at least under the further assumption that we're working at or around Standard Temperature and Pressure. But a slightly different density, viscosity and surface tension (plus the nature of the container, e.g. extreme hydrophilic or hydrophobic inner coatings where water is involved) could (in combination) drastically change the actual outcome given enough of the right kind of simultaneous differences imparted. 172.70.86.37 14:28, 21 August 2024 (UTC)
