Total hydrostatic force on submerged observation pod windows

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Gon
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Homework Statement


A marine biology observation pod is being designed. It will be submerged, with vertical windows of various sizes and shapes. Calculate the total force being exerted on each of the windows described below. Density of water is 1000 kg/m^3

Three labelled diagrams of window shapes: A) rectangle 8m tall by 4m wide, top edge marked 7m depth; B) rectangle 7m tall by 3m wide, top edge marked 5m depth; C) circle of radius 2m, top marked 6m depth.

Three labelled hand-drawn window shapes: D) semi-circle with radius 1.5m and top height 2.5m; E) right triangle with vertical side 6m, horizontal side 5m, and 2m marked at the top; F) equilateral triangle with base 0.5m and 1m marked at the top.

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[h2]Homework Equations[/h2][h2]The Attempt at a Solution[/h2]
I'm not sure if I'm doing it in right way, do I need to use integration to calculate the total force?
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Attachments
  • Handwritten sketches of three vertical window shapes with dimensions: a rectangle labelled 4 m wide and 8 m tall, a rectangle labelled 3 m wide and 7 m tall with a 5 m mark above, and a circle of radius 2 m with a 6 m mark above it.
    upload_2016-11-29_23-18-13.png
    7.1 KB · Views: 527
  • Three labelled sketches of window shapes with dimensions: A) rectangle 4 m wide by 8 m tall, with 2 m marked above its top edge; B) rectangle 7 m tall, 3 m wide at the bottom, with 5 m marked above its top edge; C) circle of radius 2 m, with 6 m marked above its top edge.
    upload_2016-11-29_23-20-32.png
    11.2 KB · Views: 514
  • Three labelled handwritten sketches: D) a semi-circle with radius 1.5 m marked along its diameter, E) a right triangle with vertical side 6 m, horizontal side 5 m and a right-angle mark, F) an equilateral triangle with base 0.5 m, each with a brace marking a depth of 2 m or 1 m.
    upload_2016-11-29_23-22-27.png
    14.2 KB · Views: 502
  • Three diagrams of window shapes labelled a) rectangle, b) rectangle, c) circle, each with dimension labels such as h and w and a radius marked on the circle.
    url].jpg
    2 KB · Views: 232
  • Handwritten-style worked solution in monospaced text for a rectangular window: height H = 3 + 8 = 11, area = (8)(4) = 32, force = (1000)(9.8)(11)(32) = 3,449,600 N.
    20Force%20exerted%20%3D%7D%281000%29%289.8%29%2811%29%2832%29%3D3%2C449%2C600%5Ctexttt%7B%20N%7D.gif
    3.4 KB · Views: 214
  • Worked calculation for a rectangular window: Height H = 5 + 7 = 12, Area = (7)(3) = 21, Force = (1000)(9.8)(12)(21) = 2,469,600 N, in monospaced text.
    20Force%20exerted%20%3D%7D%281000%29%289.8%29%2812%29%2821%29%3D2%2C469%2C600%5Ctexttt%7B%20N%7D.gif
    3.4 KB · Views: 230
  • Worked solution for a circular window: height H = 6 + 4 = 10, area = π(2)² = 4π, force = (1000)(9.8)(10)(4π) = 3,920,000π N.
    ed%20%3D%7D%281000%29%289.8%29%2810%29%284%5Cpi%20%29%3D3%2C920%2C000%5Cpi%20%5Ctexttt%7B%20N%7D.gif
    3.3 KB · Views: 245
  • Handwritten-style worked solution for a semicircular window: height H = 2.5 + 1.5 = 4, area = π(1.5)²/2 = 2.25π/2, and force = (1000)(9.8)(4)(2.25π/2) = 44,100π N.
    9%289.8%29%284%29%28%5Cfrac%7B2.25%5Cpi%7D%7B2%7D%20%29%3D%2044%2C100%5Cpi%20%5Ctexttt%7B%20N%7D.gif
    3.6 KB · Views: 211
  • Handwritten-style worked solution for a right triangle window: height H = 2 + 6 = 8, area = (1/2)(6)(5) = 15, force = (1000)(9.8)(8)(15) = 1,176,000 N.
    ce%20exerted%20%3D%7D%281000%29%289.8%29%288%29%2815%29%3D%201%2C176%2C000%20%5Ctexttt%7B%20N%7D.gif
    3.5 KB · Views: 236
  • Handwritten-style worked solution in monospace text for an equilateral triangle window: height H = 1 + sqrt(3)/4 = (4 + sqrt(3))/4, area = sqrt(3)/4 (0.5)^2 = sqrt(3)/16, force = (1000)(9.8)((4 + sqrt(3))/4)(sqrt(3)/16) = 1520.198 N.
    %7D%7B4%7D%29%28%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B16%7D%29%20%3D%201520.198%20%5Ctexttt%7B%20N%7D.gif
    4.4 KB · Views: 244
Last edited by a moderator:

Discussion

How does the water pressure vary with depth ?

Is the water pressure acting on the windows varying with depth ?
 
Last edited:
Nidum said:
How does the water pressure vary with depth ?

Is the water pressure acting on the windows varying with depth ?
YES
 
I solve all of them except F and the professor said the final answer should be 11099.9N but I didn't get that
 
Gon said:
I solve all of them except F and the professor said the final answer should be 11099.9N but I didn't get that
You mean you that think your answer to (a) is correct?
 
Chestermiller said:
You mean you that think your answer to (a) is correct?
No, I use integration to solve them.
 
Gon said:
No, I use integration to solve them.
So please show us what you did using integration to solve F (so we can see where to help).
 

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