Compressing a bottle with water - initial velocity of water

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SUMMARY

The discussion focuses on calculating the initial velocity of water ejected from a closed plastic bottle when squeezed, applying stress S. Key factors include the area A of the hole in the cap, the interior pressure of the bottle, and the material properties of the bottle itself. The use of Pascal's law is acknowledged, but it is emphasized that understanding the interior pressure and hole diameter is crucial. An experimental method is suggested to approximate the velocity by measuring the horizontal distance traveled by the water after ejection.

PREREQUISITES
  • Understanding of fluid dynamics principles, particularly Pascal's law.
  • Knowledge of pressure measurement and calculation in closed systems.
  • Familiarity with the properties of materials used in bottle construction.
  • Basic physics concepts related to projectile motion.
NEXT STEPS
  • Research methods for calculating fluid pressure in closed containers.
  • Explore the relationship between hole diameter and fluid velocity using orifice flow equations.
  • Learn about the effects of material properties on fluid dynamics in practical applications.
  • Conduct experiments to measure fluid ejection velocity and analyze results.
USEFUL FOR

Physics students, engineers, and anyone interested in fluid dynamics and experimental mechanics will benefit from this discussion.

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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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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.
 

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