Confusion over Pascal's Experiment

[Jimmy87]

I have been trying to understand pascal's barrel experiment in a more qualitative sense but I can't get my head around it at all. Pascal supposedly had a strong wooden barrel which he attached onto it a very thin pipe which was 20m tall. He then poured water into the top of the pipe until both the barrel and pipe were filled. The outcome of the experiment was that the barrel burst due to the pressure generated by the pipe. If the pipe was 20m high then this would generate 20m of hydrostatic pressure apparently?! How does this work? I know quantitatively that it needs to work as there is no volume term in the pressure equation (P = ρgh). How can such a tiny mass of liquid exert so much pressure? Apparently the pipe was only 0.4cm wide! It almost seems like your getting a huge amount of pressure from almost nothing. If anybody can help explain how this experiment works that would be great!

 

[HallsofIvy]

"pressure" is the force applied to a surface divided by the area of the surface. Now, water, or any "fluid", applies the same force in any direction (that is, essentially, the definition of "fluid".). We can calculate the force the water in the pipe applies to an imaginary surface, of area A, the cross section area of the pipe, at the bottom of the pipe by calculating the weight of the water in the pipe: density times volume. Because the volume is "cross section area times length" that volume is Ah where h is the height of the pipe, the weight of water pressing on that surface is $g\rho Ah$ where "g" is the acceleration due to gravity (about 9.81 m/s^2) and $\rho$ is the density of water. We get the pressure by dividing that by the area, A: $g\rho h$.

Now, the point is that the pressure at each point in the barrel is $g\rho h$ (actually slightly more as we go down into the barrel because we are not taking the weight of the additional water in the barrel into account- but certainly "at least" that value. If the side area of the barrel is B, then the total force on the sides of the barrel is (at least) $g\rho hB$ which can be very large. You do the calculations.

 

[Philip Wood]

A hand-waving approach. Suppose the barrel is straight-sided: a cylinder. I imagine you'd find it less hard to accept that the barrel would burst if, instead of the narrow tube, the pressure were provided simply by extending the barrel upwards, i.e by making the head of water wide as well as just tall? Well, with the narrow 'header' tube full of water, the pressure just under the lid of the barrel will be the same all the way across the lid, and the same as the pressure at the bottom of the 'header tube'. So the water pushes on the lid of the barrel, and the lid of the barrel pushes back on the water with the same force that a column of water as wide as the barrel would push!

 

[Jimmy87]

Thanks for your time guys, those answers really helped me to understand!

 

[PJC01]

Pascal's barrel experiment is a classic demonstration of the principle of hydrostatic pressure, which states that the pressure in a fluid increases with depth. In this experiment, the height of the pipe (20m) is what determines the amount of pressure exerted on the barrel. The narrow width of the pipe (0.4cm) does not affect the pressure, as you correctly noted that there is no volume term in the pressure equation.

To better understand this, imagine a column of water that is 20m tall and 0.4cm wide. The weight of this column of water is what creates the pressure at the bottom of the pipe. As the water flows down the pipe and fills the barrel, the pressure at the bottom of the pipe (and therefore the bottom of the barrel) increases. Eventually, the pressure becomes too great for the barrel to withstand, causing it to burst.

It may seem counterintuitive that such a small amount of liquid can exert so much pressure, but this is due to the density of water and the height of the column. Water is quite dense, meaning that even a small amount of it can have a significant weight. In addition, the height of the column amplifies this weight and creates a large amount of pressure at the bottom.

I hope this explanation helps you understand Pascal's barrel experiment better. It is a simple yet powerful demonstration of hydrostatic pressure and the effects of gravity on fluids.

 

[PJC01]

Pascal's barrel experiment is a classic demonstration of the principles of hydrostatic pressure. Essentially, the experiment shows how a small amount of liquid can exert a large amount of pressure due to its height and density.

In this experiment, the 20m tall pipe acts as a vertical column for the water to flow through. As the water is poured into the pipe, it begins to fill the barrel as well. The water in the pipe is subject to the force of gravity, causing it to exert pressure on the bottom of the barrel. This pressure increases as the column of water gets taller.

The key factor here is the density of the liquid. Water has a relatively high density, which means that even a small amount of it can exert a significant amount of pressure. In this case, the 20m tall column of water exerts a pressure of 20m of hydrostatic pressure, which is equivalent to about 2 atmospheres of pressure.

As for the small diameter of the pipe, this actually works to increase the pressure even more. The smaller the diameter of the pipe, the greater the pressure exerted by the column of water. This is because the same amount of water is being forced through a smaller area, resulting in a higher pressure.

In summary, Pascal's barrel experiment demonstrates how a small amount of liquid, with the right height and density, can exert a significant amount of pressure. This principle is important in understanding many aspects of fluid mechanics and engineering. I hope this explanation helps to clarify the concept for you.