Solving Fluid Statics Problem: Centre of Pressure

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SUMMARY

The discussion addresses the calculation of the center of pressure for a semicircular plane submerged vertically in a homogeneous liquid. The correct formula for determining the depth \( s \) of the center of pressure is established as \( s = \frac{3\pi d}{32} \). Participants suggest avoiding complex integration methods and refer to equation 11-7b from a specific fluid statics textbook for a more straightforward solution. The link provided leads to a resource that elaborates on this equation.

PREREQUISITES
  • Understanding of fluid statics principles
  • Familiarity with the concept of center of pressure
  • Basic knowledge of integration techniques
  • Access to fluid mechanics textbooks or resources
NEXT STEPS
  • Review the derivation of the center of pressure in fluid statics
  • Study equation 11-7b from the referenced textbook for clarity
  • Explore applications of the center of pressure in engineering design
  • Learn about the implications of fluid density and depth on pressure calculations
USEFUL FOR

Students and professionals in engineering, particularly those specializing in fluid mechanics, as well as anyone involved in hydraulic design and analysis.

AppleBite
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Ok, I've come across this problem in fluid statics, but seem to be getting the integration wrong:

"A semicircular plane is submerged vertically in a homogeneous liquid with its diameter d at the free surface. At what depth s is the centre of pressure?"

The answer should be

s = (3*pi*d) / 32

Any ideas?
 
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