Bernoulli's Principle (Possibly involving Venturi's Effect)

In summary, the conversation discusses the problem of determining the height of liquid in a vertical pipe connected to two large open tanks with a constriction in the horizontal pipe connecting the tanks. The discussion mentions using Bernoulli's equation and the Venturi effect, but the correct application of Bernoulli's principle is explained. The conversation suggests simplifying the pipeline and considering the pressure at the bottom of the pipe without the constriction.
  • #1
JPOconnell
2
0

Homework Statement


Two very large open tanks A and F (the figure (Figure 1) ) contain the same liquid. A horizontal pipe BCD, having a constriction at C and open to the air at D, leads out of the bottom of tank A, and a vertical pipe E opens into the constriction at C and dips into the liquid in tank F. Assume streamline flow and no viscosity.

If the cross-sectional area at C is one-half the area at D and if D is a distance below the level of the liquid in A, to what height will liquid rise in pipe E? (in ration of (h2/h1), or just an equation for h1 in h2 is fine)

Link to picture:

Homework Equations


d here is density of the fluid, in this case it is constant.

Bernoulli's equation: p1 + dgy1 + (1/2)(dv1)2 = p2 + dgy2 + (1/2)d(v2)2

Density = Av (A is the area of flow surface, while v is the velocity)

The Attempt at a Solution



I tried to set up a Bernoulli's equation for this, but there are 3 sections of the pipe, and I'm not sure how to add them together. I was looking for a solution and I saw Venturi's Effect, which just basically said that the pressure in the choked pipe is lower, and I don't know if it is even relevant.

But I know for sure that the height h2 got to do with the fluid kinetic energy in pipe C, but I don't know how to find the velocity in pipe C... Well, I tried to mix it around and ended up cancelling out and nothing remained. Really weird problem, given it just today that I learned about this guy's equation.

Thanks in advance
 
Physics news on Phys.org
  • #2
Wil try to be of some assistance.
First off
"Density = Av (A is the area of flow surface, while v is the velocity)" this is incorrect, what is the units of Area and velocity? m^2 and m/s so multiplying this, what is the end unit? Is this the units of density, check what you get.

Bernoulli's principle:
P/Rho is the pressure energy, V^2/2 is the kinetic energy and gh is the potential energy. So to say that h_2 is a result of the kinetic energy in C is somewhat correct but in itself it is potential energy.

If there was no constriction at C, what would you say would be the pressure in the pipe at D? First simplify the pipeline... Answer these questions and let's work from there.
 

1. What is Bernoulli's Principle?

Bernoulli's Principle states that as the speed of a fluid (such as air or water) increases, its pressure decreases. This principle is based on the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted into different forms.

2. How does Bernoulli's Principle relate to the Venturi effect?

The Venturi effect is a specific application of Bernoulli's Principle, where a fluid's velocity increases as it flows through a narrow section of a pipe or tube. This increase in velocity results in a decrease in pressure, creating a pressure difference between the high-velocity region and the surrounding areas.

3. What are some real-world applications of Bernoulli's Principle and the Venturi effect?

Some common examples include airplane wings, where the shape of the wing creates a pressure difference between the top and bottom surfaces, creating lift. Other examples include carburetors in cars, where the Venturi effect is used to mix air and fuel, and in medical devices such as nebulizers, where the Venturi effect is used to create a fine mist for inhalation.

4. Can Bernoulli's Principle and the Venturi effect be applied to gases as well as liquids?

Yes, Bernoulli's Principle and the Venturi effect can apply to both gases and liquids. However, the density of gases is much lower than that of liquids, so the effects may be less noticeable.

5. Are there any limitations or exceptions to Bernoulli's Principle and the Venturi effect?

While Bernoulli's Principle and the Venturi effect are generally applicable, there are some limitations and exceptions. For example, they do not take into account factors such as viscosity and turbulence, which can affect the results. Additionally, the shape and size of the object or flow channel can also impact the results. In some cases, other factors may need to be considered for a more accurate analysis.

Similar threads

  • Introductory Physics Homework Help
2
Replies
61
Views
3K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
30
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
1K
Replies
204
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
4K
  • Introductory Physics Homework Help
Replies
14
Views
1K
Back
Top