Represent normal stress in a fluid.
Pressure gradients drive flow and transmit forces through static and moving fluids.
Side 142
Fluid Mechanics
Liquids and gases studied as moving continua whose behavior emerges from conservation laws, pressure forces, viscosity, geometry and instability.
forces→conservation→flow field→boundary→regime
04lenses
16working concepts
V0content
SS-1.0standard
Fluids deform continuously under shear.
Pressure, density and viscosity provide the basic material description for continuum flow.
Relate mass to occupied volume.
Density variations can be negligible, important for buoyancy or central to compressible flow.
Measure resistance to shear deformation.
Viscosity controls momentum diffusion and strongly affects near-wall behavior.
Average molecular detail into fields.
Continuum models work when microscopic scales are small relative to the flow geometry.
Flow equations come from conservation laws.
Mass, momentum and energy balances translate physical accounting into differential equations.
Conserve mass through the flow.
Incompressible flow imposes a particularly simple divergence constraint.
Balance acceleration against forces.
The Navier–Stokes equations combine inertia, pressure, viscosity and body forces.
Track mechanical and thermal energy.
Bernoulli-type relations are special-case consequences, not universal rules.
Analyze a region rather than individual particles.
Integral balances are especially useful for engineering systems with inlets and outlets.
Dimensionless ratios reveal which mechanisms dominate.
Similarity parameters let one compare systems of different size, speed and fluid properties.
Compare inertia with viscosity.
Low and high Reynolds-number flows exhibit very different stability and mixing behavior.
Compare flow speed with sound speed.
Compressibility becomes important as the Mach number rises.
Compare inertia with gravity in free-surface flow.
It helps organize waves, open-channel flow and hydraulic transitions.
Match governing dimensionless groups.
Scaled experiments are informative only when the relevant ratios are preserved.
Walls and instabilities create much of real fluid complexity.
Near boundaries, viscosity and geometry shape drag, separation and transition to turbulence.
Concentrate velocity gradients near walls.
Thin viscous layers connect no-slip boundaries to faster outer flow.
Adverse pressure gradients can detach flow.
Separation increases drag and creates large wake structures.
Irregular multiscale motion enhances transport.
Turbulence is deterministic in governing equations but difficult to predict in detail.
Convert flow interaction into resisting force.
Pressure drag and skin friction respond differently to shape and flow regime.
Fluid behavior is governed by competing mechanisms. Pressure, inertia, viscosity, gravity and geometry matter in different ratios, and those ratios determine which approximations are legitimate.