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The pressure of a fluid varies with depth h as P = P₀ + pgh, where ρ i

June 1, 2025 by rawan239

The pressure of a fluid varies with depth h as P = P₀ + pgh, where ρ is the fluid density. This expression is associated with

Pascal's law

Newton's law

Bernoulli's principle

Archimedes' principle

This question was previously asked in

UPSC CDS-1 – 2018

Download PDF Attempt Online

The expression P = P₀ + ρgh gives the total pressure at a depth h in a fluid. P₀ is the pressure at the surface (e.g., atmospheric pressure), ρ is the fluid density, g is the acceleration due to gravity, and h is the depth. This formula describes the hydrostatic pressure at a given depth. This concept and formula are fundamental to hydrostatics, a field significantly contributed to by Blaise Pascal. While the formula is derived from basic principles of force and pressure (considering the weight of the fluid column), it is most directly associated with Pascal’s principles of hydrostatics, which deal with the pressure exerted by fluids at rest and its transmission.

– The formula P = P₀ + ρgh quantifies hydrostatic pressure variation with depth.
– Pascal’s contributions were foundational to understanding fluid pressure at rest and its transmission.

Newton’s laws relate to motion and force. Bernoulli’s principle relates pressure, velocity, and height in fluid flow (fluid dynamics). Archimedes’ principle relates to buoyancy and displaced fluid. While all are important concepts in fluid mechanics, the specific formula for pressure variation with depth in a static fluid is most closely linked to the principles and studies of hydrostatics pioneered by Pascal.

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