The concept which defines 'the pressure at a certain horizontal level in a static fluid is proportional to the vertical distance to the surface of the fluid' is called
Try it first: pick an option, then read the explanation.
Asked in SSC JE 28-10-2020 (Evening)
Detailed Explanation
The hydrostatic pressure at any point on the bottom of a container depends exclusively on the vertical height of liquid above it and its density. It does not depend on the cross-sectional shape, volume, or weight of the liquid contained.
1. Hydrostatic law equation:
\[ p = \rho g h = \gamma h \]
2. Consider vessels of completely different geometries (conical, inverted cone, stepped, cylindrical) with identical base area \(A\) and identical liquid depth \(h\):
- Hydrostatic pressure intensity at base: \(p = \gamma h\) (identical in all vessels)
- Total downward hydrostatic force on base: \(F = p \cdot A = \gamma h A\) (identical in all vessels)
3. In an expanding conical vessel, the total weight of liquid exceeds \(\gamma h A\); the excess weight is supported by upward reaction components from the sloping side walls.
4. In a converging conical vessel, the total weight of liquid is less than \(\gamma h A\); the additional bottom thrust is supplied by downward reaction components from the overhang walls.
This seeming contradiction between total liquid weight and bottom force is termed the hydrostatic paradox.
Why “Hydrostatic paradox” Is Correct
The statement describes the hydrostatic paradox, which clarifies that local hydrostatic pressure is governed strictly by vertical depth (\(p \propto h\)) and is completely decoupled from container geometry.
Why the Other Options Are Wrong
- A. D'alembert's paradox: D'Alembert's paradox states that zero drag force acts on a body moving at constant velocity through an inviscid fluid.
- B. Magnus effect: Magnus effect refers to the lateral aerodynamic lift force generated on a spinning cylinder or sphere in a crossflow.
- D. Archimedes effect: Archimedes effect refers to upward buoyancy resulting from the net vertical hydrostatic pressure difference.
Key Point
Hydrostatic paradox: Bottom pressure p = γh depends solely on vertical liquid depth, not vessel shape.
Key Concepts for Students
- Vessel side walls carry the difference between liquid weight and bottom hydrostatic force via reaction forces.
- Bottom thrust equals the weight of an imaginary liquid column of base area A and height h.
- Pascal demonstrated this dramatically by bursting a sturdy barrel with just a thin tube of water filled to high altitude.
Practice more: this is question 12 in Hydrostatic Pressure MCQs – Part 1. Try the whole set and check every answer instantly.