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| − | {{comic
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| − | | number = 2974
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| − | | date = August 19, 2024
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| − | | title = Storage Tanks
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| − | | image = storage_tanks_2x.png
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| − | | imagesize = 321x251px
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| − | | noexpand = true
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| − | | titletext = We're considering installing a pressurization system to keep the tanks at constant pressure solely to deter them.
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| − | }}
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| − | ==Explanation==
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| − | {{w|Calculus}} is a branch of mathematics which deals with continuously changing values. In order to demonstrate the application of this sort of math, introductory courses will commonly use physical examples to show how equations can be applied in real life. A [https://www.haywardflowcontrol.com/media/contentmanager/content//downloads//VessTime.pdf common example of such a problem] is to postulate a tank full of liquid, with a hole near the bottom, and ask the students to calculate how long it will take the tank to empty (generally assuming a cylindrical tank with the top at atmospheric pressure, leaking a low-viscosity fluid like water at a normal temperature flowing through a round hole.) The important variables are threefold: the radius of the tank, the height of the fluid above the hole, and the size of the hole.
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| − | In this case, the change in the liquid level is a function of the rate of flow through the hole, which is a function of the fluid pressure at the entrance to the hole (in accordance with {{w|Torricelli's law}}), and that pressure is a function of the remaining level of liquid. Accordingly, the amount of fluid left in the tank above the hole will follow a quadratic decay, a concept covered in calculus courses. A student with a mastery of foundational principles of calculus should be able to calculate the decline in tank level. More advanced versions of the problem might involve (A) one tank draining into a second, which drains to the ground, or (B) a sealed tank, in which air pressure at the top falls as the tank drains.
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| − | As mentioned, many STEM teachers like to use real-world examples, ideally physical demonstrations, to make abstract concepts more memorable for their students. A teacher might fill a jug with water, open a hole in the side, and invite students to compare the observed rate of draining to their calculations. This comic suggests that [[Miss Lenhart]] has taken this idea to extremes, having entered an industrial site and drilled a hole into a large, liquid-filled vat. One assumes that her class is either watching from afar, or that the leak is being somehow filmed.
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| − | The conversation between the employees in hardhats implies that there's a rash of calculus teachers conducting similar demonstrations, to the point that the primary job of the head of security is to prevent this pedagogically-motivated destruction. In real life, this vandalism would be serious, with safety risks from damaged vats, pressurized liquid, or hazardous contents (note the hazard warning (⚠) on the tank).
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| − | The title text jokingly alludes to the fact that by maintaining a constant pressure at the level of the leak, the rate of flow would also become constant, and the decline in level would therefore become linear, greatly simplifying the problem and eliminating the need for calculus. This easier version of the problem would presumably deter calculus teachers from using it as a demonstration — though it might attract similarly adventurous algebra teachers.
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| − | ===Analysis and Calculation===
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| − | Observation of the comic suggests the following assumptions:
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| − | * Tank height above hole: ~20 feet
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| − | * Tank radius: ~6 feet
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| − | * Type of drill bit: Normal twist drill bit (not a hole saw)
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| − | * Size of drill bit: 1 inch (largest commonly available twist drill bit)
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| − | * Goal of Miss Lenhart: To demonstrate quadratic decay to her students
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| − | With a tank that is 20 feet high, has a 6-foot radius, and a 1-inch diameter drill hole, it would take approximately 21.5 hours for the tank to empty completely — too long for a suitable class demonstration — though maybe filmed as a time-lapse video? — and nonetheless likely to be fixed by nearby workers who notice the leak.
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| − | To drain the tank in 36 minutes would take a 6-inch diameter hole.
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| − | Thus there's an apparent mismatch between the drill bit size, gushing liquid stream, and practicality of this real-world demonstration. The viscosity & density of the liquid is also an unknown factor; for ease of calculation, calculus problems tend to assume that the liquid is either ordinary water (which, by definition, has a density of 1.00* (1 kg/liter (8.35 lbs/gallon)) and a viscosity of 1.001 millipascal seconds) or a mixture mostly composed of water (depending on what exactly else it contains, such as dissolved solids or just other
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| − | * at 20°C (68°F) & sea-level air pressure
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| − | One explanation is that she was able to drill a couple dozen approx. 1-inch holes in a short time, while toxic liquid is gushing out, but the drill doesn't appear to be dripping wet.
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| − | But the most likely explanation to all this is that Randall didn't think through the drill and drill bit size in relation to the apparent hole size, leaving it only to nitpicky editors of a comic explainer website to even notice and care.
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| − | Or, the tank simply is not full at the moment the teacher drills the hole.
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| − | ==Transcript==
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| − | :[Two guards with helmets are standing on scaffolding to the left of two large tanks with labels at the top. The tanks are cylindrical with a smaller base than the tank above it. The left tank has a small sign with unreadable text and near the bottom of the right tank there is a triangular warning sign with an exclamation mark inside it and a line of unreadable text below it. The guard on the left is talking to the other guard. Miss Lenhart is seen running away from the right tank with an electric drill in one hand. There is a hole in the base of the right tank which has caused the liquid inside to leak out of the tank splashing on the ground in the direction of Miss Lenhart.]
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| − | :Left guard: As head of security, your primary task is to monitor the storage tanks and watch for calculus teachers trying to drill holes in their bases.
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| − | :Label: Tank #3
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| − | :Label: Tank #4
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| − | {{comic discussion}}
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| − | [[Category:Characters with hats]]
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| − | [[Category:Comics featuring Miss Lenhart]]
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| − | [[Category:Math]]
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| − | [[Category:Physics]]
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