What is the relationship between pressure and fluid dynamics in this problem?

Click For Summary
SUMMARY

The discussion centers on the application of Bernoulli's equation in fluid dynamics to determine the relationship between pressure and fluid height in a specific problem. The gauge pressure inside a bottle is calculated by considering the height of the fluid column as "+h" and treating the speed of the fluid inside as negligible. The work done on the liquid, represented by P ΔV, is essential for lifting the fluid and imparting kinetic energy to the stream. This analysis provides a clear framework for understanding pressure dynamics in fluid systems.

PREREQUISITES
  • Understanding of Bernoulli's equation
  • Basic knowledge of fluid dynamics concepts
  • Familiarity with gauge pressure and its implications
  • Concept of work done on fluids (P ΔV)
NEXT STEPS
  • Study the derivation and applications of Bernoulli's equation in various fluid systems
  • Explore the concept of gauge pressure and its measurement techniques
  • Investigate the relationship between fluid velocity and pressure in dynamic systems
  • Learn about potential energy and kinetic energy transformations in fluid mechanics
USEFUL FOR

Students and professionals in engineering, physics, and fluid mechanics who seek to deepen their understanding of pressure dynamics and fluid behavior in various applications.

willworkforfood
Messages
54
Reaction score
0
http://portfolio.iu.edu/whoblitz/problem.png
I think Bernoulli's equation is involved in solving this problem, but past that I'm not sure what the pressure of the water inside would be or what it would be outside. Any advice appreciated, as always.
 
Last edited by a moderator:
Physics news on Phys.org
Treat the speed of the water inside the bottle as "zero." Treat the gauge pressure outside the nozzle as zero. Treat the water level inside the bottle as "-h." Go Bernoulli.

Edit: Wait, you are solving for the gauge pressure inside the bottle, so it would be more direct to have the height of the nozzle as "+h." It comes to the same thing.

The speed of the fluid inside the bottle is not exactly zero, but it is so small (and the squared value makes it smaller) that it is safe to "call" it zero.
 
Last edited:
The work done on the liquid is [itex]P \Delta V[/itex] and is required to lift the fluid through the height h and impart kinetic energy to the stream.
 

Similar threads

  • · Replies 13 ·
Replies
13
Views
2K
Replies
2
Views
1K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 8 ·
Replies
8
Views
4K
  • · Replies 56 ·
2
Replies
56
Views
4K
Replies
0
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
Replies
1
Views
2K