Pressure Paradox: Same P1 & P2, Different Weights

In summary, the two open tanks with the same bottom area, A, but different shapes will have the same pressure on the bottom when the depth, h, of the liquid is the same. However, the weight of the liquid in each tank may be different due to differences in density. This does not create a paradox because pressure is only dependent on the depth of the liquid, not the horizontal dimensions of the container. The pressure at a point is only caused by the amount of material directly above it, with area "A". The difference in weight is due to the difference in volume and density of the liquids, not the pressure exerted on the bottom of the containers.
  • #1
physicsss
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The two open tanks have the same bottom area, A, but different shapes.
When the depth, h, of a liquid in the two tanks is the same in accordance with P1 = pgh + P2 the pressure on the bottom of the two tanks will be the same. However, the weight of the liquid in each of the tanks is different. How do you account for this apparent paradox?

picture:
http://img296.imageshack.us/my.php?image=untitled7jl2.jpg

Is it because weight of the liquid is the specific weight times the volume of the liquid, which the tank on the right has more of?
 
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  • #2
Consider that pressure (hence force) is exerted by the liquid on the walls of the containers.
 
  • #3
When the depth, h, of a liquid in the two tanks is the same in accordance with P1 = pgh + P2 the pressure on the bottom of the two tanks will be the same.

Not if the densities of the two liquids are different. The rho term will not be the same in both cases.
 
  • #4
I really don't think that there is any paradox right here if you think about what pressure is. The amount of matter on top of the bottom of the containers is the the same in both situations (it would help if I could draw a picture).

As per Resnick, Halliday, and Walker "Fundmental of Physics" 7th edition "The pressure at a point in a fluid in static equilibrium depends on the depth of that point but not on any horizontal dimension of the fluid or its container."

Basically, the matter that is causing the pressure at the bottom of the container is only the matter that is directly above that area. So it doesn't matter if the container kind of "V"s out like the picture shows. The way I like to think about it (I may be completely wrong in this) is the pressure at a point with area "A" is only caused by the amount of material above it with area "A".

As far as having different weights, well one has more volume hence more mass is in it (because they are filled to the same height being key here). More mass equals more weight. More mass does not mean more pressure. A higher density will cause a higher pressure though.
 

Related to Pressure Paradox: Same P1 & P2, Different Weights

1. What is the pressure paradox?

The pressure paradox refers to a phenomenon where two objects with the same weight but different surface areas exert different amounts of pressure on a surface. This is contrary to what we would expect, as we would assume that the object with the larger surface area would exert more pressure.

2. How does the pressure paradox occur?

The pressure paradox occurs due to the relationship between pressure, force, and surface area. Pressure is defined as force per unit area, which means that the smaller the surface area, the greater the pressure. This means that even though the objects may have the same weight, the one with the smaller surface area exerts more pressure on a surface.

3. Can you provide an example of the pressure paradox?

One example of the pressure paradox is when you try to balance a nail on its head on a flat surface. The nail will stand upright, even though its weight is concentrated on a very small surface area, resulting in high pressure exerted on the surface.

4. How does the pressure paradox relate to real-life situations?

The pressure paradox is relevant in many real-life situations, such as when wearing high heels or when using sharp objects like needles or knives. These objects have small surface areas, so even though they may not weigh much, they can still exert a lot of pressure on the surface they come into contact with.

5. How can we use the pressure paradox in practical applications?

The pressure paradox is utilized in many practical applications, such as in the design of bridges, buildings, and other structures. Engineers use the concept to distribute weight evenly and prevent excessive pressure on certain areas that could lead to structural failure. It is also used in manufacturing processes, such as in the production of specialized tools and equipment.

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