Discrepancy between my work and book's [Static Fluid/Pressure]

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The discussion revolves around a discrepancy in calculating fluid pressure related to a submerged window in an aquarium. The original confusion stems from the starting height of 1.0 meters above the water surface, leading to an incorrect value compared to the book's example. Clarifications indicate that the depth variable 'h' should be defined correctly based on the window's position, with 'h' being 0.0 meters at the top and 1.0 meters at the bottom of the window. The participant realizes the need to adjust their integration bounds and origin for accurate calculations. Ultimately, after reevaluating the problem with the correct approach, they achieve the correct result.
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The book (Example 13-3):
XmnYGsI.jpg


My attempt:
GgSrM7Q.jpg


My confusion is in why they are starting their height at 1.0 meters above the surface of the water and then getting a y_2 value of 2.0 meters. That's the discrepancy that's giving me a different value than the book's. It never says in the question to do that, and I'm baffled as to how I am supposed to know.

Thanks in advance for the help.
 
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Hello.

In P = ρgh, h denotes the depth below the surface of the water. h is also your integration variable. What is the value of h at the top of the window? At the bottom of the window?

[EDIT: Note that the window is submerged below the surface of the water.]
 
h = 0.0 meters at the top and h = 1.0 meters at the bottom of the window.
 
The widow is embedded in the side of the aquarium with the top of the window 1.0 m below the surface of the water.
 
Ah, I see. I wish they would explicitly state these things in the question as it seems I am unable to derive them from the pictures, haha. Well, they don't write the books for me!

Thanks TSny! I will approach this problem again. Do you think I can keep my origin at the top of the window and change my bounds to -1m to +1m? It seems this will still give me an incorrect value and I may have to change my origin to the top of the water tank.
 
Suppose you introduce a y-axis going vertically downward. You can certainly choose the origin of y to be at the top of the window. Then you would need to think about how to express the depth h in terms of y.

[EDIT: You could then integrate from y = 0 to y = 1.]
 
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Alright, it seems you have nailed the source of confusion on the head. I will have to redraw my diagram and rewrite my integral thinking about the relation of h and y.

edit: I was way overthinking this. I reintegrated with new bounds and it comes out perfectly. Thanks a bunch, TSny!
 
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