Exercise
https://texercises.com/exercise/aquarium-3/
Question
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The following quantities appear in the problem: Länge \(\ell\) / Kraft \(F\) / Druck \(p\) / Fläche \(A\) / Ortsfaktor \(g\) / Höhe \(h\) / Dichte \(\varrho\) / Breite \(b\) /
The following formulas must be used to solve the exercise: \(p = \dfrac{F}{A} \quad \) \(A = ab \quad \) \(p = \varrho g h \quad \)
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Exercise:
The glass pane of a large zoo aquarium is lO long and hO high. The water level reaches dO above the upper edge of the glass pane. What is the total force that the water exerts on the pane?

Solution:
Geg l lO l b bO b h hO  h % GesForceF siN % The everage pressure on the glass pane is equal to the pressure in the middle of the glass pane i.e. in al bar h fracb + h h + fracb hp depth. The water pressure in this depth equals al p rho g bar h rho g leftfracb + hright r ncg hp p The total area of the glass pane is al A lb l b A hence the total force the water exerts is: al F pA rho g leftfracb + hright lb p A F. % F rho g leftfracb + hright lb F
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Exercise:
The glass pane of a large zoo aquarium is lO long and hO high. The water level reaches dO above the upper edge of the glass pane. What is the total force that the water exerts on the pane?

Solution:
Geg l lO l b bO b h hO  h % GesForceF siN % The everage pressure on the glass pane is equal to the pressure in the middle of the glass pane i.e. in al bar h fracb + h h + fracb hp depth. The water pressure in this depth equals al p rho g bar h rho g leftfracb + hright r ncg hp p The total area of the glass pane is al A lb l b A hence the total force the water exerts is: al F pA rho g leftfracb + hright lb p A F. % F rho g leftfracb + hright lb F
Contained in these collections:
  1. Aquarium by TeXercises
    10 | 12
  2. 8 | 11


Attributes & Decorations
Branches
Hydrostatics
Tags
aquarium, hydrostatics, mechanics, physics, pressure, water
Content image
Difficulty
(3, default)
Points
3 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator uz
Decoration
File
Link