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

In summary, the conversation discusses a problem involving Bernoulli's equation and determining the pressure of water inside and outside a bottle. The solution involves treating the speed of water inside as zero, the gauge pressure outside as zero, and the water level inside as "-h." This can also be solved by considering the height of the nozzle as "+h." The work done on the liquid is P \Delta V, lifting it through the height h and giving it kinetic energy. The speed of the fluid inside is considered to be negligible.
  • #1
willworkforfood
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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.
 
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  • #2
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.
 
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  • #3
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.
 

1. What is fluid dynamics?

Fluid dynamics is the study of how fluids (liquids and gases) move and behave under different conditions, such as flow rate, pressure, and temperature.

2. What are some real-world applications of fluid dynamics?

Fluid dynamics has many practical applications, including designing efficient airplane wings, understanding weather patterns, and developing fuel-efficient cars.

3. How do you solve a fluid dynamics problem?

To solve a fluid dynamics problem, you need to first identify the type of fluid (Newtonian or non-Newtonian), the properties of the fluid (density, viscosity, etc.), and the boundary conditions (such as flow rate and pressure). Then, you can use mathematical equations and computational tools to analyze and solve the problem.

4. What is the difference between laminar and turbulent flow?

Laminar flow is a smooth, orderly movement of fluid particles in a straight line, while turbulent flow is chaotic and unpredictable. Laminar flow is typically seen in low-viscosity fluids and low flow rates, while turbulent flow occurs in high-viscosity fluids and high flow rates.

5. How does the Bernoulli's principle relate to fluid dynamics?

Bernoulli's principle states that as the speed of a fluid increases, its pressure decreases. This principle is often used in fluid dynamics to explain the behavior of fluids in motion and to calculate pressure differences in different parts of a fluid system.

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