3087: Pascal's Law - Revision history

Boilersuit: /* Trivia */ corrected spelling of 'ruina'

2025-09-16T09:21:51Z

‎Trivia: corrected spelling of 'ruina'

Boilersuit: /* Explanation */ corrected spelling of 'minuscule'

2025-09-16T09:19:09Z

‎Explanation: corrected spelling of 'minuscule'

Tromag: /* Explanation */

2025-09-05T15:20:37Z

‎Explanation

FaviFake: complete now

2025-07-20T10:32:25Z

complete now

98.96.73.21 at 03:59, 3 July 2025

2025-07-03T03:59:28Z

Whyisjohngalt: The person who did the description assumed that the diagram includes an open tube into which is poured water, but to me it looks more like a piston is being depressed. So I clarified the description to make that clear.

2025-06-18T22:00:00Z

The person who did the description assumed that the diagram includes an open tube into which is poured water, but to me it looks more like a piston is being depressed. So I clarified the description to make that clear.

165.225.32.168 at 19:57, 17 June 2025

2025-06-17T19:57:09Z

FaviFake: Copy-pasted from the talk page, someone who knows this stuff well should take a look: :''> The bottom of this piston is fed by a narrow tube which rises to an opening, into which someone is pouring water, which fills the cylinder, raising the piston.''

2025-06-10T21:30:09Z

Copy-pasted from the talk page, someone who knows this stuff well should take a look: :''> The bottom of this piston is fed by a narrow tube which rises to an opening, into which someone is pouring water, which fills the cylinder, raising the piston.''

172.68.174.73: /* Explanation */

2025-05-29T17:17:43Z

‎Explanation

198.41.227.35 at 17:50, 15 May 2025

2025-05-15T17:50:11Z

@@ Line 41: / Line 41: @@
 In the image, assuming a 2,200 lb weight (1000 kg) and an adult who weighs around 200 lb, both on a circular piston with a 6-foot diameter, the water pressure would need to be about 0.6 psi to lift them. How easy that would be to hold in place depends entirely on the area of the piston that was being pushed down (the proportions in the drawing are likely off, as the piston size shown there would take more force to push down than most people could easily hold). An alternate demonstration would be to have no piston in the tube, and simply have the tube extend higher than the platform, so that the water column in the tube could exert enough pressure to keep the platform up. A tube around 16 inches higher than the bottom of the piston would be adequate to hold the entire massive weight in place.
-The concept of "runia montium" is similar to a demonstration which was attributed to Pascal himself, in which he supposedly inserted a tall, thin tube into an otherwise sealed barrel full of water. By adding water to the top of the tube, increasing pressure would be exerted inside the barrel, until it burst. This story may be apocryphal (all surviving accounts were written centuries after Pascal's death), but [https://www.youtube.com/watch?v=EJHrr21UvY8 the demonstration works], if you can get enough height.
+The concept of "ruina montium" is similar to a demonstration which was attributed to Pascal himself, in which he supposedly inserted a tall, thin tube into an otherwise sealed barrel full of water. By adding water to the top of the tube, increasing pressure would be exerted inside the barrel, until it burst. This story may be apocryphal (all surviving accounts were written centuries after Pascal's death), but [https://www.youtube.com/watch?v=EJHrr21UvY8 the demonstration works], if you can get enough height.
 {{comic discussion}}<noinclude>

@@ Line 16: / Line 16: @@
 The strip shows a classroom in which a character (presumably Randall) is sitting, being shown an image of a simple {{w|hydraulic press}}, which demonstrates the first "absurd" concept. In the image, a large cylinder, fitted with a large piston, is weighed down by a person and a weight labeled "1000 kg". The bottom of this piston is fed by a narrow tube which rises to an opening, which contains a smaller piston which is being pushed down by hand. The notion that simply pushing a small piston down, by hand, would be able to lift over a tonne of weight seems absurd, but the very large surface of the platform means that even a relatively small pressure is able to exert large amounts of force.
-The trade-off is that the cylinder has a huge volume, so any movement in the small piston would raise the platform only by a miniscule distance. The effect is an example of mechanical advantage: a small force applied over a relatively large distance is converted into a much larger force exerted over a much smaller distance. This principle is the basis of hydraulic machinery: a pressurized fluid is used to drive a piston, and the pressure is multiplied by the area of the piston to determine how much force is exerted. A relatively small pump can exert almost arbitrarily large forces with a large enough piston (with the tradeoff that it takes more time to exert that force).
+The trade-off is that the cylinder has a huge volume, so any movement in the small piston would raise the platform only by a minuscule distance. The effect is an example of mechanical advantage: a small force applied over a relatively large distance is converted into a much larger force exerted over a much smaller distance. This principle is the basis of hydraulic machinery: a pressurized fluid is used to drive a piston, and the pressure is multiplied by the area of the piston to determine how much force is exerted. A relatively small pump can exert almost arbitrarily large forces with a large enough piston (with the tradeoff that it takes more time to exert that force).
 A second objection Randall raises is that this principle would allow the destruction of entire mountains, with the very low-tech solution of digging tunnels and filling them with water, a technique that would have been available to ancient peoples. By digging even narrow vertical cavities with enough height, the pressure exerted by water at the bottom could become very high. If these channels feed into larger cavities, that pressure would exert across the entire area, creating forces that are potentially enough to shatter the rock face of the mountain. He points out that he later learned of the practice of ''{{w|Ruina montium}}'' ("wrecking of mountains" in Latin), which used exactly this principle. This was an ancient Roman mining technique in which small tunnels were dug into the side of a mountain. When the tunnels were filled with water, the rock adjacent to the tunnels would fracture, making it significantly easier to remove.

@@ Line 16: / Line 16: @@
 The strip shows a classroom in which a character (presumably Randall) is sitting, being shown an image of a simple {{w|hydraulic press}}, which demonstrates the first "absurd" concept. In the image, a large cylinder, fitted with a large piston, is weighed down by a person and a weight labeled "1000 kg". The bottom of this piston is fed by a narrow tube which rises to an opening, which contains a smaller piston which is being pushed down by hand. The notion that simply pushing a small piston down, by hand, would be able to lift over a tonne of weight seems absurd, but the very large surface of the platform means that even a relatively small pressure is able to exert large amounts of force.
-The trade-off is that the cylinder has a huge volume, so the water being introduced by the small piston would raise the weight only by a miniscule amount. The effect is an example of mechanical advantage: a small force applied over a relatively large distance is converted into a much larger force exerted over a much smaller distance. This principle is the basis of hydraulic machinery: a pressurized fluid is used to drive a piston, and the area of the piston determines how much force is exerted. A relatively small pump can exert almost arbitrarily large forces with a large enough piston (with the tradeoff that it takes more time to exert that force).
+The trade-off is that the cylinder has a huge volume, so any movement in the small piston would raise the platform only by a miniscule distance. The effect is an example of mechanical advantage: a small force applied over a relatively large distance is converted into a much larger force exerted over a much smaller distance. This principle is the basis of hydraulic machinery: a pressurized fluid is used to drive a piston, and the pressure is multiplied by the area of the piston to determine how much force is exerted. A relatively small pump can exert almost arbitrarily large forces with a large enough piston (with the tradeoff that it takes more time to exert that force).
 A second objection Randall raises is that this principle would allow the destruction of entire mountains, with the very low-tech solution of digging tunnels and filling them with water, a technique that would have been available to ancient peoples. By digging even narrow vertical cavities with enough height, the pressure exerted by water at the bottom could become very high. If these channels feed into larger cavities, that pressure would exert across the entire area, creating forces that are potentially enough to shatter the rock face of the mountain. He points out that he later learned of the practice of ''{{w|Ruina montium}}'' ("wrecking of mountains" in Latin), which used exactly this principle. This was an ancient Roman mining technique in which small tunnels were dug into the side of a mountain. When the tunnels were filled with water, the rock adjacent to the tunnels would fracture, making it significantly easier to remove.

← Older revision		Revision as of 10:32, 20 July 2025
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	==Explanation==		==Explanation==
−	~~{{incomplete\|Copy-pasted from the talk page, someone who knows this stuff well should take a look:~~
−
−	~~:''> The bottom of this piston is fed by a narrow tube which rises to an opening, into which someone is pouring water, which fills the cylinder, raising the piston.''~~
−
−	She is not pouring water; she seems to be depressing a small piston. This effects the next section, which claims that the lift would not work as drawn. However, I don't know just how it affects it; would it actually work? --[[User:Calion\|Calion]] ([[User talk:Calion\|talk]]) 04:40, 8 June 2025 (UTC)}}
−
	{{w\|Pascal's law}} states that when a change in pressure occurs in a static incompressible fluid, it is transmitted throughout the fluid and the same change occurs everywhere. That same pressure is applied outward to the walls of the container. It was discovered by mathematician {{w\|Blaise Pascal}} in 1653. This principle has significant implications. Because force is a product of pressure times area, static pressure can be used to exert arbitrarily large (or small) forces by using larger or smaller pistons. This is the principle underlying {{w\|hydraulics}}. Also, when under gravity, liquids exert greater pressure at greater depths, but Pascal's law means that the pressure will be the same at any given depth. Consequently, even a narrow column of water, if it's tall enough, will result in high pressure at the bottom of the column. If the bottom of the column spreads out over a huge area, that pressure will remain high, exerting tremendous force.		{{w\|Pascal's law}} states that when a change in pressure occurs in a static incompressible fluid, it is transmitted throughout the fluid and the same change occurs everywhere. That same pressure is applied outward to the walls of the container. It was discovered by mathematician {{w\|Blaise Pascal}} in 1653. This principle has significant implications. Because force is a product of pressure times area, static pressure can be used to exert arbitrarily large (or small) forces by using larger or smaller pistons. This is the principle underlying {{w\|hydraulics}}. Also, when under gravity, liquids exert greater pressure at greater depths, but Pascal's law means that the pressure will be the same at any given depth. Consequently, even a narrow column of water, if it's tall enough, will result in high pressure at the bottom of the column. If the bottom of the column spreads out over a huge area, that pressure will remain high, exerting tremendous force.

@@ Line 20: / Line 20: @@
 [[Randall]] muses that, when he first heard of this law, he found it implausible, because it would be able to do things that, on the surface, appear "absurd". He then realized that, not only are these things possible, they either are or have been regularly used for practical purposes.
-The strip shows a classroom in which a character (presumably Randall) is sitting, being shown an image of a simple {{w|hydraulic press}}, which demonstrates the first "absurd" concept. In the image, a large cylinder, fitted with a large piston, is weighed down by a person and a weight labeled "1000 kg". The bottom of this piston is fed by a narrow tube which rises to an opening, which contains a smaller piston which is being pushed down by hand. The notion that simply pushing a small piston down, by hand, would be able to lift over a tonne of weight seems absurd, but the pressure exerted by the height of the water, spread over the large surface area of the large piston, is able to exert large amounts of force.
+The strip shows a classroom in which a character (presumably Randall) is sitting, being shown an image of a simple {{w|hydraulic press}}, which demonstrates the first "absurd" concept. In the image, a large cylinder, fitted with a large piston, is weighed down by a person and a weight labeled "1000 kg". The bottom of this piston is fed by a narrow tube which rises to an opening, which contains a smaller piston which is being pushed down by hand. The notion that simply pushing a small piston down, by hand, would be able to lift over a tonne of weight seems absurd, but the very large surface of the platform means that even a relatively small pressure is able to exert large amounts of force.
-The trade-off is that the cylinder is very large, so even large depressions of the small piston would lead to very small changes in height to the large piston. If you were pouring water in instead of pushing a piston down, for instance, you would have to lift hundreds or thousands of beakers of water to the top of the tube in order to lift the weight by a small distance.
+The trade-off is that the cylinder has a huge volume, so the water being introduced by the small piston would raise the weight only by a miniscule amount. The effect is an example of mechanical advantage: a small force applied over a relatively large distance is converted into a much larger force exerted over a much smaller distance. This principle is the basis of hydraulic machinery: a pressurized fluid is used to drive a piston, and the area of the piston determines how much force is exerted. A relatively small pump can exert almost arbitrarily large forces with a large enough piston (with the tradeoff that it takes more time to exert that force).
 A second objection Randall raises is that this principle would allow the destruction of entire mountains, with the very low-tech solution of digging tunnels and filling them with water, a technique that would have been available to ancient peoples. By digging even narrow vertical cavities with enough height, the pressure exerted by water at the bottom could become very high. If these channels feed into larger cavities, that pressure would exert across the entire area, creating forces that are potentially enough to shatter the rock face of the mountain. He points out that he later learned of the practice of ''{{w|Ruina montium}}'' ("wrecking of mountains" in Latin), which used exactly this principle. This was an ancient Roman mining technique in which small tunnels were dug into the side of a mountain. When the tunnels were filled with water, the rock adjacent to the tunnels would fracture, making it significantly easier to remove.
@@ Line 45: / Line 45: @@
 ==Trivia==
-In the image, assuming a 2,200 lb weight (1000 kg) and an adult who weighs around 200 lb, both on a circular piston with a 6-foot diameter, the water pressure would need to be about 0.6 psi to lift them. That means the water column into which water is being poured would have to be about 16 inches higher than the bottom of the piston.
+In the image, assuming a 2,200 lb weight (1000 kg) and an adult who weighs around 200 lb, both on a circular piston with a 6-foot diameter, the water pressure would need to be about 0.6 psi to lift them. How easy that would be to hold in place depends entirely on the area of the piston that was being pushed down (the proportions in the drawing are likely off, as the piston size shown there would take more force to push down than most people could easily hold). An alternate demonstration would be to have no piston in the tube, and simply have the tube extend higher than the platform, so that the water column in the tube could exert enough pressure to keep the platform up. A tube around 16 inches higher than the bottom of the piston would be adequate to hold the entire massive weight in place.
 The concept of "runia montium" is similar to a demonstration which was attributed to Pascal himself, in which he supposedly inserted a tall, thin tube into an otherwise sealed barrel full of water. By adding water to the top of the tube, increasing pressure would be exerted inside the barrel, until it burst. This story may be apocryphal (all surviving accounts were written centuries after Pascal's death), but [https://www.youtube.com/watch?v=EJHrr21UvY8 the demonstration works], if you can get enough height.

@@ Line 20: / Line 20: @@
 [[Randall]] muses that, when he first heard of this law, he found it implausible, because it would be able to do things that, on the surface, appear "absurd". He then realized that, not only are these things possible, they either are or have been regularly used for practical purposes.
-The strip shows a classroom in which a character (presumably Randall) is sitting, being shown an image of a simple {{w|hydraulic press}}, which demonstrates the first "absurd" concept. In the image, a large cylinder, fitted with a large piston, is weighed down by a person and a weight labeled "1000 kg". The bottom of this piston is fed by a narrow tube which rises to an opening, into which someone is pouring water, which fills the cylinder, raising the piston. The notion that simply pouring water into a tube, by hand, would be able to lift over a tonne of weight seems absurd, but the pressure exerted by the height of the water, spread over the large area of the piston, is able to exert large amounts of force. The trade-off, of course, is that the cylinder is very large, so a huge amount of water would need to be poured in to lift the piston by an appreciable height. Actual hydraulic presses generally pump the liquid under pressure, rather than relying on gravitational force, but otherwise the same principle applies.
+The strip shows a classroom in which a character (presumably Randall) is sitting, being shown an image of a simple {{w|hydraulic press}}, which demonstrates the first "absurd" concept. In the image, a large cylinder, fitted with a large piston, is weighed down by a person and a weight labeled "1000 kg". The bottom of this piston is fed by a narrow tube which rises to an opening, into which someone is pouring water, which fills the cylinder, raising the piston. The notion that simply pouring water into a tube, by hand, would be able to lift over a tonne of weight seems absurd, but the pressure exerted by the height of the water, spread over the large area of the piston, is able to exert large amounts of force.
-Note that the diagram shown in the comic would not work, however, because the height of the opening of the narrow tube is about the same as the height of the large piston carrying the large weight.  Because the heights are the same, the pressure due to gravity would also be the same, and the 1000kg weight would easily push the water out of the small tube against only the "weight" (pressure) of the air above it.  For this system to work by only pouring water into the tube the narrow tube would need to be much much higher than the piston.  Viewed this way, hydraulics are not all that absurd.  To raise the large piston 1mm would require putting several meters worth of water into the small tube to get the same volume (or in a hydraulic machine, moving the small piston several meters).  This is no different than how a pulley works, where a large weight can be moved 1 meter by pulling several meters of rope out at a much smaller force.  Conversely, if the person pouring the water into the tube started out at the same level as the large weight, the energy expended to raise the water up to the opening to pour it in (by pumping or carrying it up) would be considerable, and equivalent to the energy needed to raise the weight directly, so hydraulics are not some magic way to get around physics.
+The trade-off is that the cylinder is very large, so a huge amount of water would need to be poured in to lift the piston by an appreciable height. This means that a person would have to lift hundreds or thousands of beakers of water to the top of the tube in order to lift the weight by a small distance. Similar trade-offs are at the heart of every system that uses mechanical advantage. It should be noted that there's a flaw in the diagram as drawn, because the height of the water in the narrow tube appears to be about the same as the height of the water under the piston. Because the tube is open to the atmosphere, the only source of additional pressure comes from the water's height, which means the water in the tube needs to be higher than the water under the piston. Actual hydraulic presses generally avoid the need for height by using pumps to create liquid pressure, rather than relying on gravitational force, but otherwise the same principle applies.
 A second objection Randall raises is that this principle would allow the destruction of entire mountains, with the very low-tech solution of digging tunnels and filling them with water, a technique that would have been available to ancient peoples. By digging even narrow vertical cavities with enough height, the pressure exerted by water at the bottom could become very high. If these channels feed into larger cavities, that pressure would exert across the entire area, creating forces that are potentially enough to shatter the rock face of the mountain. He points out that he later learned of the practice of ''{{w|Ruina montium}}'' ("wrecking of mountains" in Latin), which used exactly this principle. This was an ancient Roman mining technique in which small tunnels were dug into the side of a mountain. When the tunnels were filled with water, the rock adjacent to the tunnels would fracture, making it significantly easier to remove.

@@ Line 10: / Line 10: @@
 ==Explanation==
-{{incomplete|This page was created by PASCAL’S HYDRAULIC PRESS. Don't remove this notice too soon.}}
+{{incomplete|Copy-pasted from the talk page, someone who knows this stuff well should take a look:
 {{w|Pascal's law}} states that when a change in pressure occurs in a static incompressible fluid, it is transmitted throughout the fluid and the same change occurs everywhere. That same pressure is applied outward to the walls of the container. It was discovered by mathematician {{w|Blaise Pascal}} in 1653. This principle has significant implications. Because force is a product of pressure times area, static pressure can be used to exert arbitrarily large (or small) forces by using larger or smaller pistons. This is the principle underlying {{w|hydraulics}}. Also, when under gravity, liquids exert greater pressure at greater depths, but Pascal's law means that the pressure will be the same at any given depth. Consequently, even a narrow column of water, if it's tall enough, will result in high pressure at the bottom of the column. If the bottom of the column spreads out over a huge area, that pressure will remain high, exerting tremendous force.