Fluid Mechanics- Two liquids in a U-Bend

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Homework Help Overview

The problem involves analyzing the behavior of two different liquids in a U-bend, focusing on the pressure relationships and heights of the liquid columns. The subject area is fluid mechanics, specifically dealing with hydrostatic pressure and equilibrium in fluid columns.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the fundamental equations related to fluid pressure and equilibrium, questioning which specific equations apply to their scenario. There is uncertainty about how to determine the heights of the liquid columns and how to utilize the mass of the added fluid in the calculations.

Discussion Status

Some participants have offered insights into the pressure relationships at the interface of the two liquids, while others are exploring how to calculate the heights based on the mass of the fluid. Multiple interpretations of the problem are being considered, and there is a collaborative effort to clarify the relationships between the variables involved.

Contextual Notes

Participants are working with limited information, particularly regarding the specific values for heights and how to relate them to the mass of the fluid added. There is an emphasis on understanding the implications of the given data within the context of the problem.

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Homework Statement


The problem- http://img87.imageshack.us/my.php?image=physics4cw0.jpg


Homework Equations


Part of the problem is, I don't know which equations to use. (See below)


The Attempt at a Solution


Ok, I'm not quite sure how to approach this problem. It would help if I knew which equation to use here.

I'm pretty sure it's something basic, but I just can't figure out. Any help would be appreciated...
 
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The pressure at the bottom of a column of a fluid = density * g * height
The pressure pushing down at an interface must equal the pressure pushing up if it is stable (ie not moving).
 
So, let me see if I have this right then:

D1 *g* h1 = D2 *g2 * h2

D1 and D2 are given.

My confusion comes from finding h1. Once I have h1, I guess I can find h2, though they gave me the mass of the fluid added in this problem.

How can I use that to help solve this problem? I'm not quite sure what to do with that value.
 
The pressure in the heavy liquid at the interface has gone up by the pressure needed to lift it h1.
This must be equal to the pressure at the bottom of the light liquid.

Another way to look at it is that the light liquid has lifted a weight equal to the extra column of heavy in the left hand side of the tube.
 
Ok, let me approach it this way:

Since I have the mass of the liquid, I can calculate the volume it displaces. From this, using geometry, I can determine how high the dispacement is, equaling h2.

From this, can I plug it into the above formula, and come to the right answer?
 

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