Water jet from air pressure: find velocity

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SUMMARY

The discussion centers on calculating the gauge air pressure required in a fire extinguisher tank to achieve a water jet velocity of 30.0 m/s, with the water level positioned 0.500 m below the nozzle. Key insights include the need to analyze the energy dynamics involved: the kinetic energy of the water jet, the potential energy from the height difference, and the energy contributed by the air pressure in the tank. Participants emphasize the importance of understanding the relationships between these energy forms to derive the necessary equations for the solution.

PREREQUISITES
  • Basic understanding of fluid dynamics
  • Knowledge of kinetic and potential energy concepts
  • Familiarity with Bernoulli's principle
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study Bernoulli's equation and its applications in fluid mechanics
  • Learn about energy conservation principles in fluid systems
  • Explore the relationship between pressure, velocity, and height in fluid dynamics
  • Investigate practical applications of fire extinguisher mechanics
USEFUL FOR

Students in physics or engineering fields, educators teaching fluid dynamics, and professionals involved in fire safety equipment design will benefit from this discussion.

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Homework Statement


it told: 1. Water is forced out of a fire extinguisher by air pressure
2. the water level in the tank is 0.500 m. below the nozzle
3. find gauge air pressure in the tank (above atmosphere) for water jet to have speed of 30.0 m/s

Homework Equations


i don't know what equation i need to use ...!
it ask: How much gauge air pressure in the tank (above atmosphere) for the water jet to have speed of 30.0 m/s

The Attempt at a Solution


I don't know how to do it ... it give me only
gauge air pressure in the tank (above atmosphere)
 
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You really need to have at least SOME thoughts on the physics before anyone can help. I'll give you some starting points, i) how much energy in a mass traveling at 30 m/sec? ii) how much energy to raise a mass 0.5m? iii) how much energy does a mass gain coming out of the high pressure environment inside the bottle (perhaps another property of the body is more important than the mass)? How are these three energies related? Surely you can come up with some formulas that are relevant.
 
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