Integration application, force due to fluid pressure

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SUMMARY

The discussion focuses on calculating the differential area (dA) for a triangular prism submerged in water, specifically an equilateral triangle. The user questions the relationship between dA and the dimensions of the prism, noting confusion over the book's assertion that dA equals 2√3ydy. The correct interpretation involves recognizing that the width of the prism at height y is indeed 2y, leading to the conclusion that dA equals 2√3ydy, which accounts for both the height and width of the triangular face.

PREREQUISITES
  • Understanding of fluid mechanics principles, particularly hydrostatic pressure.
  • Familiarity with calculus concepts, specifically integration and differential area calculations.
  • Knowledge of geometric properties of equilateral triangles.
  • Basic proficiency in visualizing three-dimensional shapes and their projections.
NEXT STEPS
  • Study hydrostatic pressure calculations in fluid mechanics.
  • Explore differential area calculations in calculus, focusing on geometric shapes.
  • Learn about the properties of equilateral triangles and their applications in physics.
  • Investigate the integration of area elements in three-dimensional objects.
USEFUL FOR

Students in physics or engineering courses, particularly those studying fluid mechanics, as well as educators seeking to clarify concepts related to pressure forces on submerged objects.

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Homework Statement



I'm working on a particular problem that involves the force on a face of a triangular prism under water. What I am wondering is if someone could explain how to find dA for the prism? If the prism is an equilateral triangle, then dA=\sqrt3dy doesn't it? My book is showing that the area is 2\sqrt3ydy and I really cannot see how...
 
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I understand that the thickness is sqrt(3)dy, but I can't seem to visualize how the width is 2y and thus dA=sqrt(3)2y dy
 

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