How Does Fluid Density Affect Absolute Pressure in a Siphon System?

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SUMMARY

The discussion centers on calculating the absolute pressure at point Y in a siphon system where the fluid density is 800 kg/m³ and atmospheric pressure is 101.3 kPa. The relevant equations include ∆P = density x gravity x ∆height and Archimedes' principle. The user has determined the fluid speed to be 3.429 m/s at points Y and Z but is struggling to apply the height differences correctly to find the absolute pressure at point Y. Clarification on the application of Archimedes' principle is also sought.

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Homework Statement


A flexible tube can be used as a simple siphon to transfer fluid from one container to a lower container. The fluid has a density of 800. kg/m3. See the dimensions given in the figure, and take atmospheric pressure to be 101.3 kPa.
There are three points given:

Pt X is 10cm below the fluid line in tub from which the fluid is draining.
Pt Y is 20cm above the fluid level in the tub.
Pt Z is 60cm below the fluid level in the tub.

What is the absolute pressure at point Y?


Homework Equations


1) ∆P=density x gravity x ∆height
and 2) Archimedes' principle


The Attempt at a Solution


I've already found the speed of the fluid in the siphon to be 3.429m/s at pts Y and Z.
From the book I derived the equation 1 and tried using both .2m and .3m for the ∆h, but to no avail. I didn't forget to add the 101.3kpa to the pressure either, and since neither of the previous two answers are correct, I'm a little lost.
 
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I'm thinking the problem has something to do with Archimedes' Principle, but I don't understand how that applies. Can someone please help?
 

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