Pressure in two Different Sized Plastic Bottles

In summary, both bottles are likely to rupture at similar pressures due to having the same material and wall thickness. However, the larger bottle will have a lower burst pressure due to the hoop stress equation. Factors such as size and material strength play a role in determining the bottle's ability to withstand pressure. For example, a larger bottle with the same material and wall thickness would have a lower burst pressure compared to a smaller one. This is evident in the example of a one mile diameter glass dome, where a thicker window is required to withstand the internal pressure.
  • #1
Michael Strong
1
0
I have two different sized plastic bottles of the same material and with the same wall thickness and I raise the pressure inside the bottles at the same rate then which bottle will rupture first? The bigger bottle or the smaller one?

I would think that both bottles would rupture at about the same pressure because the bottle walls are the same and they are made out of the same material.
Is there any theory that states otherwise? Or what could be some factors that would cause one bottle to rupture before the other one?
 
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  • #2
See "hoop stress."
 
  • #3
The hoop stress equation relates the tension in a curved member to the radius of curvature and internal pressure.
Pressure = Tension/radius
Suppose you have a plastic wall that can withstand an ultimate tension in a one inch wide strip of say 100 pounds. If the large bottle had a diameter of 6 inches then the burst pressure would be equal to 100 pounds per inch/ 3 inches or 33 psi.
A bottle of diameter 3 inches would have a burst pressure of 100 pli/1.5 in or 67 psi.

So, for a given wall thickness, the larger the bottle, the less pressure it can hold.

Imagine the problem of putting a one mile diameter clear glass dome in space with an internal pressure equal to Earth's sea level.
In that case the tension in a one inch wide strip of the glass dome would be equal to 14.7 psi times 31680 inches or 466,000 pounds. Really strong window glass has an ultimate yield strength of about 20,000 psi. A one inch wide strip would have to be at least 23 inches thick. With the customary 2.5 safety factor, the space colony would require a window that was about 5 feet thick.
 

FAQ: Pressure in two Different Sized Plastic Bottles

FAQs about Pressure in Two Different Sized Plastic Bottles

1. How does the pressure differ between two different sized plastic bottles?

The pressure inside a bottle is directly related to its volume. This means that the larger the bottle, the higher the pressure will be, and vice versa. This is because the same amount of gas molecules inside a smaller bottle will have less space to move around, resulting in higher pressure compared to the same amount of gas molecules in a larger bottle.

2. What factors affect the pressure inside a plastic bottle?

Aside from the size of the bottle, the temperature, type of gas, and amount of gas inside the bottle can also affect the pressure. As temperature increases, the gas molecules inside the bottle will have more energy, resulting in higher pressure. Different types of gas also have different properties that can affect pressure. Lastly, adding or removing gas from the bottle will also change the pressure.

3. Can the pressure inside a bottle be changed without altering its size?

Yes, the pressure inside a bottle can be changed without changing its size by adjusting the temperature or the amount of gas inside the bottle. As mentioned earlier, temperature and gas amount directly affect pressure. By increasing or decreasing these factors, the pressure inside the bottle can be altered.

4. What happens to the pressure inside a plastic bottle when it is squeezed?

When a plastic bottle is squeezed, the volume of the bottle decreases, but the amount of gas inside remains the same. This means that the pressure inside the bottle will increase because the gas molecules have less space to move around. This is why the bottle feels harder when squeezed.

5. Why do plastic bottles sometimes explode when left in a hot car?

Plastic bottles can explode when left in a hot car because heat causes the gas molecules inside the bottle to have more energy, resulting in an increase in pressure. If the pressure becomes too high, the bottle may not be able to contain it and can burst, causing an explosion.

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