Fluid Statics, U-Tubes & Hydrometry
Hydrostatic pressure (P = hρg), Pascal’s principle, Archimedes’ upthrust, law of flotation, U-tube manometers, Hare’s apparatus, and loaded test tube hydrometers.
Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.
Learning Objectives
- Calculate hydrostatic head pressure and understand the hydrostatic paradox.
- Apply equilibrium conditions to U-tube immiscible manometers and Hare’s apparatus slope analysis.
Core Theory & Concepts
Fluid statics governs fluids at rest. The weight of fluid columns exerts pressure uniformly in all directions at a given depth. Immersed objects experience an upward buoyant upthrust equal to the weight of fluid displaced.
Hydrostatic Pressure & Datum Line
Pressure at depth h in liquid of density ρ is P = P₀ + hρg. In a U-tube, equal pressure across a horizontal plane through the lower interface gives h₁ ρ₁ = h₂ ρ₂.
Law of Flotation
A freely floating body displaces its own weight of fluid: M_body · g = (A · h) · ρ_liquid · g ⇒ M = (A · ρ) · h.
Common Misconceptions
Believing pressure at the bottom of a container depends on the total volume or shape of the container.
Syllabus Topic Outline
- 1Hydrostatic pressure P = h · ρ · g and atmospheric pressure P₀
- 2Pascal’s Principle: hydraulic lift multiplication F₁/A₁ = F₂/A₂
- 3Archimedes’ principle and upthrust U = V_disp · ρ_fluid · g
- 4Law of flotation and hydrometer calibration