Solving Water Level Puzzle: Page 6 of 1902 Exam Solutions 2004

In summary: The equation for delta h is y_1 - y_2 + \frac{D_2 - D_1}{2}. Since they are asking for the difference between the water levels at two different points, y_1 - y_2 needs to equal the delta h.
  • #1
jdstokes
523
1
Please refer to page 6 of

http://www.physics.usyd.edu.au/ugrad/jphys/jphys_webct/jp_exams/1902_exam_2004.pdf [Broken]

I'm quoting from the solution guide:

http://www.physics.usyd.edu.au/ugrad/jphys/jphys_webct/jp_exams/1902_exam_solutions_2004.pdf [Broken]

[itex]P_1 = P_A + \rho g y_1 [/itex] and [itex]P_2 = P_A + \rho g y_2 [/itex]

Hence

[itex]\Delta h = y_1 - y_2[/itex].

Is it just me or does this last step total nonsense? AIUI, [itex]y_1[/itex] and [itex]y_2[/itex] refer to the position of the water levels measured with respect to two different coordinate systems. So how is it justified to say [itex]\Delta h = y_1 - y_2[/itex]? I drew a diagram and calculated the vertical separation between the water levels to be [itex]y_1 - y_2 + \frac{D_2 - D_1}{2}[/itex]. Could someone please point out if I am missing something obvious.

Thanks.

James
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
You're only asked to calculate the height differences on the columns. That's pretty much just a fluid statics problem. The pressures are all you care about. When you ask how is it justified to say [tex]y_1 = y_2[/tex] just take a look at the fluid static FBD:

At column number 1, you have atmospheric pressure in equillibrium with the fluid static pressure at point one, or [tex]P_1 = P_a + \rho g y_1[/tex]. At point 2, you have atmospheric pressure in equillibrium with the fluid's static pressure at point 2 or [tex]P_2 = P_a + \rho g y_2[/tex].

Since it is assumed incompressible and no local changes in g, then that means that the only thing that can change as [tex]P_1[/tex] amd [tex]P_2[/tex] change is [tex]y[/tex].

I guess the best thing would be for you to post how you came up with your answer and we can go from there.
 
Last edited:
  • #3
The diagram is mislabeled. The delta h in the diagram is [itex]y_1 - y_2 + \frac{D_2 - D_1}{2}[/itex]. The question makes sense as long as you "assume" that they actually want [itex]y_1 - y_2[/itex]. Quite a silly question.
 
  • #4
jdstokes said:
The diagram is mislabeled. The delta h in the diagram is [itex]y_1 - y_2 + \frac{D_2 - D_1}{2}[/itex]. The question makes sense as long as you "assume" that they actually want [itex]y_1 - y_2[/itex]. Quite a silly question.

You've lost me on that one. The [tex]\Delta h[/tex] is the pressure drop across the venturi. [tex]\Delta h[/tex] has to equal [tex]y_1 - y_2[/tex]. How can they be different values? All that is done is to take the relationship derived for [tex]P_1 - P_2 = \frac{1}{2}\rho \Delta V^2[/tex] and replace the velocity terms with [tex]V = \frac{R}{A}[/tex]

Show how you arrived at your conclusion. That would help.
 

1. How does the water level puzzle work?

The water level puzzle works by using the principle of displacement. When an object is placed in a container filled with water, it will displace an amount of water equal to its own volume. This displacement leads to an increase in the water level.

2. What is the purpose of solving the water level puzzle?

The purpose of solving the water level puzzle is to test the understanding of basic principles of physics, particularly the concept of volume and displacement. It also helps to develop critical thinking and problem-solving skills.

3. What are the steps involved in solving the water level puzzle?

The steps involved in solving the water level puzzle include:

  • Identifying the volume of the objects in the puzzle
  • Filling the container with water up to a certain level
  • Placing the objects in the container and measuring the new water level
  • Calculating the volume of water displaced by each object
  • Adding up the volumes to determine the final water level

4. What are some tips for solving the water level puzzle?

Some tips for solving the water level puzzle include:

  • Start by identifying the largest object and working your way down to the smallest
  • Use a measuring cup or ruler to get accurate measurements
  • Double check your calculations to avoid errors
  • Don't forget to take into account the volume of the container itself

5. Are there any real-world applications for the water level puzzle?

While the water level puzzle is primarily used as an educational tool, it does have some real-world applications. For example, it can be used to determine how much liquid can fit into a container without overflowing, or to calculate the volume of irregularly shaped objects.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
4K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Math Proof Training and Practice
2
Replies
46
Views
4K
Replies
5
Views
10K
Back
Top