Two points A and B are located in the same stationary
PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids
Problem
Two points A and B are located in the same stationary, incompressible fluid. Point B is exactly h meters vertically below point A. Neglect viscosity and assume the fluid is at rest relative to the container.
(a) Starting from fundamental principles of mechanics applied to a small fluid element, derive an expression for the pressure difference PB−PA between the two points in terms of the fluid density ρ, the gravitational field strength g, and the separation distance h.
(b) Clearly state every assumption you made in the derivation and explain why each assumption is necessary.
(c) Discuss qualitatively how the derived relationship would be expected to change if the fluid were appreciably compressible (for example, if the fluid were air rather than water).