💧 Fluid Mechanics
Liquids and gases at rest and in motion: pressure, buoyancy, Bernoulli's equation and viscosity.
What you will learn
- Calculate pressure in fluids
- Apply Archimedes' principle to floating objects
- Use Bernoulli's equation for flowing fluids
- Explain viscosity and drag
Study guide
Introductory College concepts
Bernoulli's Equation — Pressure, Speed and Height in Flowing Fluids
Bernoulli's equation explained term by term: why faster fluid flow means lower pressure, with a worked pipe example and the truth about airplane wings.
Viscosity — Why Honey Flows Slower Than Water
Viscosity explained: internal friction in fluids, temperature effects, laminar vs turbulent flow, Stokes' law, and the Reynolds number.
High School concepts
Buoyancy and Archimedes' Principle — Why Things Float
Archimedes' principle explained: the buoyant force equals the weight of displaced fluid, why ships float, and worked examples.
The Continuity Equation — Why Fluids Speed Up in Narrow Pipes
The continuity equation A₁v₁ = A₂v₂ explained: why fluids speed up in narrow pipes, conservation of mass, and worked examples.
Density and Pressure in Fluids — Definitions, Formulas and Examples
What density and pressure mean in fluids, the formulas ρ = m/V and P = F/A, hydrostatic pressure P = ρgh, and everyday examples.
Fluid Drag — Air Resistance and Terminal Velocity
Fluid drag explained: air resistance, the drag equation F = ½ρv²CdA, terminal velocity, and streamlining.
Fluid Statics — Pressure at Rest, Hydrostatics and Manometers
Pressure in fluids at rest: the hydrostatic equation p = p₀ + ρgh, absolute vs gauge pressure, Pascal's principle, manometers, and why dams are thicker at…
Lift and Drag — The Forces on Wings, Cars and Balls
How wings generate lift, where drag comes from, the lift and drag equations L = ½ρv²SC_L and D = ½ρv²SC_D, angle of attack, stall, and why race cars chase…
Pascal's Principle — How Hydraulic Lifts Multiply Force
Pascal's principle explained: pressure in a confined fluid transmits undiminished, how hydraulic lifts multiply force, and the energy tradeoff.
Reynolds Number — Predicting Laminar vs Turbulent Flow
The Reynolds number predicts whether flow stays smooth or turns turbulent: the formula Re = ρvL/μ, the 2300 pipe-flow threshold, and engineering uses from…
Surface Tension — Why Water Beads Up and Insects Walk on Ponds
Surface tension explained: why water beads up, the molecular origin of cohesion, capillary action, and detergents.
Formulas
Bernoulli's Equation — P + ½ρv² + ρgh = constant
Along a streamline, pressure plus kinetic-energy density plus gravitational-energy density stays constant.
F_b = ρVg — Buoyant Force (Archimedes' Principle)
Buoyant force equals fluid density times displaced volume times g.
A₁v₁ = A₂v₂ — Continuity Equation for Fluids
Cross-sectional area times speed is constant along a pipe.
Pressure — P = F/A
Pressure equals force divided by the area it acts on.
Calculators
Practice
Bernoulli Practice 2
10 problems · 10 practice problems on Bernoulli's equation — pressure-velocity tradeoffs in flowing fluids.…
Buoyancy Practice 2
10 problems · 10 practice problems on buoyancy — Archimedes' principle, floating vs sinking, and apparent weight.…
Fluids Practice — Pressure, Buoyancy and Bernoulli
10 problems · 10 practice problems on fluid mechanics — pressure, buoyancy, continuity and Bernoulli's equation — …
Pressure Practice 2
10 problems · 10 practice problems on pressure — hydrostatic pressure, Pascal's principle and pressure units.…
Viscosity and Flow Practice
10 problems · 10 practice problems on viscosity, laminar vs turbulent flow, and Stokes' law.…