Compressing a bottle with water - initial velocity of water

In summary, the conversation discusses finding the initial velocity of water ejected from a plastic bottle with a hole in the cap. The exterior pressure is assumed to be 1 atmosphere and the interior pressure and diameter of the hole need to be known. A link to a calculator is provided, but it is suggested to determine the pressure through experimentation by measuring the distance the water travels when ejected horizontally from a height of 1 meter.
  • #1
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Imagine that we have a closed plastic bottle filled with water and then we punch a hole with area A in its cap. How can I find the initial velocity the water will he "fired" with if we squeeze the bottle applying stress S?
Assume that we know all about the bottle (moduli, change in volume etc.
I guess that the Pascal's law is not enough here and it's got a lot to do with the material the bottle is made of.
 
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  • #2
The exterior pressure will be 1 atmosphere. So you need to know the interior pressure and the diameter of the hole you cut.
Here is a link to a calculator:
http://www.tlv.com/global/TI/calculator/water-flow-rate-through-orifice.html

You do need to determine the pressure of the fluid in the bottle.

Perhaps the easiest way of determining this is to perform the experiment. When you squeeze the bottle, hold it horizontally 1 meter above the floor. The fluid will eject horizontally and the fall to the floor. The height above the floor will give you about a 0.31 second delay. The distance that the water moves horizontally before hitting the floor will tell you how far it traveled in that amount of time. It would be a rough approximation.
 

1. How does the initial velocity of water affect the compression of a bottle?

The initial velocity of water affects the compression of a bottle by determining the force with which the water molecules collide with the walls of the bottle. A higher initial velocity means a greater force of impact, resulting in a greater compression of the bottle.

2. What factors can affect the initial velocity of water in a compressed bottle?

The initial velocity of water in a compressed bottle can be affected by factors such as the temperature of the water, the pressure inside the bottle, and the size and shape of the bottle itself. Other variables, such as the type of water and the presence of impurities, can also have an impact on the initial velocity.

3. Is the initial velocity of water the only factor that affects the compression of a bottle?

No, the initial velocity of water is not the only factor that affects the compression of a bottle. Other factors, such as the elasticity of the bottle material and the external forces acting on the bottle, can also have an impact on the compression. Additionally, the initial velocity of water can change as the bottle continues to compress, further complicating the relationship between initial velocity and compression.

4. How can the initial velocity of water be measured in a compressed bottle?

The initial velocity of water in a compressed bottle can be measured using a variety of methods, such as high-speed cameras or pressure sensors. These methods can track the movement of the water molecules or the changes in pressure inside the bottle, providing valuable data on the initial velocity of the water.

5. What practical applications can be derived from studying the initial velocity of water in compressed bottles?

Studying the initial velocity of water in compressed bottles can have practical applications in various fields, such as engineering and materials science. Understanding how different factors affect the initial velocity and compression of bottles can help in designing more efficient and durable containers. This knowledge can also be applied in industries that involve compressed gases or liquids, such as scuba diving and aerosol packaging.

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