When should we use p = ρ.g.h and p = ρ.g.hcg for hydrostatic pressure?

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SUMMARY

The discussion clarifies the appropriate use of the hydrostatic pressure equations p = ρ.g.h and p = ρ.g.hcg. The first equation is used when measuring pressure at a specific depth, where h represents the height of the water column. The second equation is applicable when calculating pressure at the center of gravity of a submerged body, where hcg denotes the distance from the water surface to the center of gravity. Understanding the distinction between 'height' and 'center of pressure' is crucial for accurate hydrostatic calculations.

PREREQUISITES
  • Understanding of hydrostatic pressure principles
  • Familiarity with fluid mechanics terminology
  • Knowledge of density (ρ) and acceleration due to gravity (g)
  • Concept of center of gravity (hcg) in submerged bodies
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  • Study the derivation and applications of the hydrostatic pressure equations
  • Learn about the concept of center of pressure in fluid mechanics
  • Explore the implications of varying density in hydrostatic calculations
  • Investigate real-world applications of hydrostatic pressure in engineering
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Students and professionals in engineering, particularly those specializing in fluid mechanics, civil engineering, and hydraulic systems, will benefit from this discussion.

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For the hydrostatic pressure, when do we use [ p = ρ.g.h ] and [ p = ρ.g.hcg ]

where:
ρ = density
g = acc of gravity
h = height of water column
hcg = the distance to the center of gravity from the surface of water downward
 
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It depends. h should actually be measured from the surface to the 'center of pressure', which is not always located at the c.g. of a submerged body.

http://www.nptel.iitm.ac.in/courses/Webcourse-contents/IIT-KANPUR/FLUID-MECHANICS/lecture-5/5-2_hydro_thrust_plane_surf.htm
 
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