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

[jdstokes]

Please refer to page 6 of

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

I'm quoting from the solution guide:

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

P_1 = P_A + \rho g y_1 and P_2 = P_A + \rho g y_2

Hence

\Delta h = y_1 - y_2.

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

Thanks.

James

 

[FredGarvin]

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 y_1 = y_2 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 P_1 = P_a + \rho g y_1. At point 2, you have atmospheric pressure in equillibrium with the fluid's static pressure at point 2 or P_2 = P_a + \rho g y_2.

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

I guess the best thing would be for you to post how you came up with your answer and we can go from there.

 

[jdstokes]

The diagram is mislabeled. The delta h in the diagram is y_1 - y_2 + \frac{D_2 - D_1}{2}. The question makes sense as long as you "assume" that they actually want y_1 - y_2. Quite a silly question.

 

[FredGarvin]

The diagram is mislabeled. The delta h in the diagram is y_1 - y_2 + \frac{D_2 - D_1}{2}. The question makes sense as long as you "assume" that they actually want y_1 - y_2. Quite a silly question.

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

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