Relation of shape of bottle to water pressure

In summary: However, this is not entirely true. In reality, the shape of the bottle does play a role in determining the water pressure. This is because the pressure at any given point in the water is not only dependent on the height of the water column above it, but also on the direction of the pressure force. In a straight column of water, the pressure force is only acting downwards. But in a slanted bottle, the pressure force also has a horizontal component, which affects the pressure at that point. So, in summary, the shape of the bottle does matter when measuring water pressure because it affects the direction of the pressure force and the relationship between
  • #1
arien
2
0
So, I know that according to everything online water pressure is independent from everything except gravity, height, and density of fluid. The situation I'm talking about is slight different.

Imagine a standard water bottle that angles inwards near the top. Now imagine a point on the side of the water bottle, near the on the slanted part. I know that what matters is the height of a "column" of water above your point, but you can't make a column of water here -- once the bottle starts slanting inwards, going straight up would mean you hit the slanted side of the bottle.

I mean, think about the way the equation cancels out.
P = F/A
P = MG/A
P = Density x Volume x Gravity / Area

In the column-of-water scenario, the volume of the column (m^3) cancels out with the area (m^2), leaving behind just M, aka height. But in my scenario, the volume and the area wouldn't cancel out to produce height because the volume isn't just a function of length, width, and height: it's irregular.

I can add some diagrams later if this is a confusing scenario to envision.

All I really need to know is, am I correct in assuming that here, the shape of the bottle is not irrelevant?
 
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  • #2
Not entirely sure what you mean, but if you have a known volume of water in a container and weigh it, you will always get the same answer of 'X' kg, no matter what the shape of the container is.
 
  • #3
arien said:
Imagine a standard water bottle that angles inwards near the top. Now imagine a point on the side of the water bottle, near the on the slanted part. I know that what matters is the height of a "column" of water above your point, but you can't make a column of water here -- once the bottle starts slanting inwards, going straight up would mean you hit the slanted side of the bottle.

You could make a column of water above that point, just imagine drilling a hole and glueing and sealing a vertical plastic straw to your water bottle and fill it with water to the proper height.
 
  • #4
So, is that what happens, then? The bottle could be absolutely any shape and all that matters is the height to the top? I have a lab on this, and although I didn't take any data on the slanted part of the bottle I still need to say definitively if it matters whether data is taken on the slanted part or not. If you were graphing pressure against water height on an irregularly-slanted bottle, would the relationship still be linear across all parts of the bottle?
 
  • #5
The slanted side of the bottle has water pressure pressing against it, and it presses back on the water. The pressure force applied by the slanted side to the water is oriented perpendicular to the slanted side, so it has a component in the downward direction. This applies a downward force on the fluid below.

You also need to be aware of Pascal's law. It is based on observation, and says that, at a given spatial location in the water, the pressure acts equally in all directions. So, at a given depth the pressure is acting horizontally also. If you have a continuous vertical column of water away from the sides, you can get the pressure at the bottom of that column. That pressure is also acting horizontally, and the pressure does not change in the horizontal direction (from a horizontal force balance). So, the pressure at the bottom of the column is also transmitted horizontally to the slanted walls of the bottle. So the only thing that matters is the depth below the upper surface.
 
  • #6
There's a variation of the hydrostatic paradox, where the pressure in a barrel is increased by adding a small but long tube to the top and filling the tube with water, until the barrel bursts. It might not be intuitive how a narrow tube of water can contribute so much to the pressure in a much larger barrel. (Of course, if the tube is too narrow, then there will be capillary action which complicates things.)
 
  • #7
Khashishi said:
There's a variation of the hydrostatic paradox, where the pressure in a barrel is increased by adding a small but long tube to the top and filling the tube with water, until the barrel bursts. It might not be intuitive how a narrow tube of water can contribute so much to the pressure in a much larger barrel. (Of course, if the tube is too narrow, then there will be capillary action which complicates things.)

I didn't understand single bit of it. Pls help what you are trying to say; a schematic diagram would do wonder for me.
 
  • #8
straw paradox.jpg
 
  • #9
There is no paradox .

Hint : Think about energy as well as pressure .
 
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  • #10
That's why I love physics; very non-intuitive yet fascinating. Thanks for the picture
 
  • #11
arien said:
So, is that what happens, then? The bottle could be absolutely any shape and all that matters is the height to the top? I have a lab on this, and although I didn't take any data on the slanted part of the bottle I still need to say definitively if it matters whether data is taken on the slanted part or not. If you were graphing pressure against water height on an irregularly-slanted bottle, would the relationship still be linear across all parts of the bottle?

See..
Pressure.png
Pressure2.png
 

Related to Relation of shape of bottle to water pressure

1. How does the shape of a bottle affect water pressure?

The shape of a bottle can affect water pressure in several ways. First, the volume of the bottle can impact the amount of water that can be held, which can affect the pressure. Additionally, the shape of the bottle can influence the flow of water, which can also impact the pressure. For example, a narrow-necked bottle will have a higher pressure as the water is forced through a smaller opening, while a wide-mouthed bottle will have a lower pressure due to the larger opening.

2. Does the material of the bottle affect the water pressure?

Yes, the material of the bottle can also affect water pressure. A more rigid material, such as glass, will maintain a higher pressure compared to a more flexible material, such as plastic. This is because the rigid material does not expand or deform as easily when pressure is applied.

3. Is there an ideal shape for a bottle to maintain a high water pressure?

There is no one ideal shape for a bottle to maintain a high water pressure. Different shapes can provide different levels of pressure depending on the factors mentioned above, such as volume and flow. However, a bottle with a narrow neck and a rigid material may provide the highest water pressure.

4. How does the water pressure change when a bottle is filled with different amounts of water?

The water pressure will increase as more water is added to the bottle. This is because there is more force pushing down on the water in the bottle, resulting in a higher pressure. However, the shape of the bottle and the material it is made of will also play a role in determining the final water pressure.

5. Can the shape of a bottle affect the overall strength of the bottle when filled with water?

Yes, the shape of a bottle can affect its overall strength when filled with water. The shape can impact the distribution of weight and pressure within the bottle, which can affect its structural integrity. A bottle with a wider base and a gradual slope towards the neck may be stronger compared to a bottle with a narrow base and a sudden curve towards the neck.

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