Fluid Dynamics of saltwater in sealed tank

So, in summary, we have a sealed tank containing seawater and air, with a height difference of 12.8 m between the water and the air. The water flows out through a small hole at atmospheric pressure, and the gauge pressure of the air above the water is 2.90 atm. To find the speed of the water, Bernoulli's equation can be used, where the pressure difference between the air and the water can be calculated using the given gauge pressure and atmospheric pressure. Since the outlet is a small hole, the initial velocity can be assumed to be negligible.
  • #1
QuarkCharmer
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Homework Statement


A sealed tank containing seawater to a height of 12.8 m also contains air above the water at a gauge pressure of 2.90 atm. Water flows out from the bottom through a small hole.

How fast is this water moving?


Homework Equations


I believe that Bernoulli's equation is to be applied here somehow.

The Attempt at a Solution


I hate that I don't have more work to show, but I really don't know how to approach this one at all.

[tex]p_1 + \frac{1}{2}ρV_{1}^{2} + ρgh_{1}= p_2 + \frac{1}{2}ρV_{2}^{2} + ρgh_{2}[/tex]

I'm not really sure how to apply this for this type of problem. The gauge pressure air at the top is confusing me. The other questions I have worked on so far were all liquids moving through pipes and such, where the application of the equation is apparent. Can someone just point me in the right direction here?
 
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  • #2
Guage pressure is, of course, pressure above atmospheric pressure. And the "small hole" is at atmospheric pressure. Whence,

P1 - P2 = 2.9 atm.

And since the problem says the outlet is a small hole, it is reasonable to assume:

V1 ≈ 0.
 

Related to Fluid Dynamics of saltwater in sealed tank

1. What is fluid dynamics?

Fluid dynamics is the branch of physics that studies the movement of fluids, including liquids and gases. It involves understanding the forces and motions of fluids, as well as how they interact with their surroundings.

2. How does saltwater behave differently than freshwater in a sealed tank?

Saltwater is denser than freshwater, which means it has a higher mass per unit volume. This leads to differences in fluid dynamics, such as increased pressure and slower flow rates. Saltwater also has different chemical properties that can affect its behavior.

3. What factors affect the fluid dynamics of saltwater in a sealed tank?

The fluid dynamics of saltwater in a sealed tank can be influenced by various factors, including the temperature, pressure, salinity, and shape of the tank. Other factors such as the presence of objects or barriers in the tank can also impact the fluid's behavior.

4. How can fluid dynamics of saltwater in a sealed tank be studied?

Fluid dynamics of saltwater in a sealed tank can be studied through experiments, mathematical modeling, and simulations. These methods allow scientists to observe and analyze the behavior of the fluid under different conditions and make predictions about its movement and interactions.

5. What are the practical applications of understanding the fluid dynamics of saltwater in a sealed tank?

Understanding the fluid dynamics of saltwater in a sealed tank has various practical applications. For example, it can help in designing efficient filtration systems, predicting the behavior of ocean currents, and developing better strategies for managing and controlling oil spills in the ocean.

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