Total pressure is a force exerted by a fluid when static mass of the fluid comes in contact with a plane or curved surface. The point of application of total pressure on the surface is known as ____.
Try it first: pick an option, then read the explanation.
Asked in SSC JE 16.11.2022
Detailed Explanation
As depth increases, hydrostatic pressure increases linearly. Because pressure is distributed non-uniformly across a submerged vertical or inclined area, the single point where the resultant force acts is shifted downward from the area's geometric centroid.
Hydrostatic force definition and moment balance:
1. Total pressure (resultant thrust):
\[ P = \int_A p \, dA = \int_A \rho g h \, dA = \rho g A \bar{h} \]
2. By Varignon's principle of moments, the moment of the resultant force about the free surface axis equals the sum of moments of individual pressure forces:
\[ P \cdot h^* = \int_A h \cdot (p \, dA) = \int_A \rho g h^2 \, dA = \rho g I_{O-O} \]
3. Solving for the depth of this point of application (\(h^*\)):
\[ h^* = \frac{I_{O-O}}{A \bar{h}} = \bar{h} + \frac{I_G}{A \bar{h}} \]
This point of application is formally defined as the centre of pressure.
Why “centre of pressure” Is Correct
By definition in fluid mechanics, the point on a submerged plane or curved boundary through which the entire resultant hydrostatic thrust is assumed to act is known as the centre of pressure.
Why the Other Options Are Wrong
- A. centroid: Centroid is the purely geometric centre of area (x̄, ȳ) where first moments of area vanish.
- B. centre of point: 'Centre of point' is a fictitious term with no meaning in physics or mechanics.
- C. centre of gravity: Centre of gravity is the point through which the resultant gravitational weight of a physical body acts.
Key Point
Centre of pressure is the point of application of the resultant hydrostatic thrust on a submerged surface.
Key Concepts for Students
- Centre of pressure h* always lies strictly below the centroid h̄ for inclined and vertical plane surfaces.
- As depth of submersion h̄ increases indefinitely, h* approaches h̄ asymptotically (h* − h̄ → 0).
- For a horizontal surface, pressure is uniform and the centre of pressure coincides with the centroid.
Practice more: this is question 7 in Hydrostatic Pressure MCQs – Part 1. Try the whole set and check every answer instantly.