Fluid Mechanics – Pressure, Buoyancy & Flow Explained | Chapter 12 of University Physics

Chapter 12 of University Physics explores how fluids behave at rest and in motion. You’ll learn how density defines fluid mass, how pressure varies with depth, why objects float or sink, and how incompressible fluids obey continuity and Bernoulli’s equations. These principles underpin applications from submarines to blood flow.

Watch the full video summary for real-world examples and problem walkthroughs.

Fluid Properties & Density

Fluids include liquids and gases, distinguished by their ability to flow and conform to containers. Density (ρ = m/V) measures mass per unit volume and varies with temperature and pressure. Specific gravity compares a fluid’s density to water, offering a dimensionless way to gauge buoyancy potential.

Pressure in a Fluid

Pressure (p = F/A) quantifies force per area in pascals (Pa). In a static fluid, pressure increases with depth: p = p₀ + ρgh. Pascal’s Law states that applied pressure is transmitted undiminished in all directions, enabling devices like hydraulic lifts and presses. Instruments such as manometers and barometers measure gauge and atmospheric pressures respectively.

Buoyancy & Archimedes’ Principle

An object immersed in a fluid experiences a buoyant force equal to the weight of the displaced fluid: B = ρVg. When object density is less than fluid density, it floats; if greater, it sinks. Neutral buoyancy occurs when densities match. Hydrometers exploit this principle to determine liquid densities by observing floatation level.

Fluid Flow & Continuity

In ideal (incompressible, non-viscous) fluids, steady flow means the velocity at each point remains constant. The continuity equation (A₁v₁ = A₂v₂) expresses mass conservation: when a pipe narrows, fluid speed increases proportionally to maintain constant volume flow rate.

Bernoulli’s Equation

Bernoulli’s principle applies energy conservation to flowing fluids:

p + ρgy + ½ρv² = constant

This implies that where fluid speed is high, pressure is low, and vice versa. Applications include the Venturi meter for measuring flow speed and lift generation over an airplane wing.

Viscosity & Turbulence

Viscosity measures internal friction resisting fluid motion—critical in blood flow, lubrication, and pipeline transport. Laminar flow features smooth, layered motion, while turbulent flow is chaotic with eddies, arising at high velocities or around obstacles.

Conclusion

Mastering fluid mechanics principles—density, pressure variation, buoyancy, continuity, and Bernoulli’s equation—enables you to predict and engineer fluid behavior in diverse contexts, from hydraulic systems to aerodynamics and biological flows.

For detailed derivations and worked examples, watch the full video summary here.

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