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

[jeff.berhow]

The book (Example 13-3):

My attempt:

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.

 

[TSny]

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.]

 

[jeff.berhow]

h = 0.0 meters at the top and h = 1.0 meters at the bottom of the window.

 

[TSny]

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.

 

[jeff.berhow]

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.

 

[TSny]

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.]

 

[jeff.berhow]

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!