Physics / advanced
Flow, pressure, and conservation
Develop fluid equations from mass and momentum balance, then solve representative inviscid and viscous flows with clear boundary conditions.
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Module 01 advanced
Flow, pressure, and conservation
Develop fluid equations from mass and momentum balance, then solve representative inviscid and viscous flows with clear boundary conditions.
- 01
Watching a flow and following its material
Translate between a velocity field and particle paths, and distinguish streamlines from the histories recorded by tracers.
34 min - 02
Conservation of mass along a moving element
Derive the material derivative and continuity equation, then separate incompressibility from constant density and steady flow.
34 min - 03
Pressure forces and Bernoulli’s qualified constant
Derive an inviscid momentum balance and use Bernoulli only along the paths and under the assumptions that support it.
34 min - 04
Local rotation and circulation carried by material
Relate curl to circulation and apply Kelvin’s theorem without confusing a moving loop, a fixed contour, and a constant vorticity.
34 min - 05
Potential flow and inertia in the surrounding fluid
Reduce irrotational incompressible flow to a boundary problem and calculate the added inertia of an ideal accelerating sphere.
34 min - 06
Navier–Stokes stress and viscosity
Build the Newtonian constitutive law, keep shear and bulk viscosity distinct, and connect stress gradients with momentum transport.
29 min - 07
Reynolds number and flow similarity
Nondimensionalize fluid momentum balance, design matched-scale experiments, and identify what Reynolds similarity does and does not establish.
27 min - 08
Couette and Poiseuille solutions
Solve fully developed flow between parallel plates, distinguish wall-driven and pressure-driven motion, and check stress and flow-rate balances.
29 min - 09
Boundary Layers and Flow Separation
Resolve thin viscous regions, estimate laminar wall shear, and distinguish steady separation from a universal zero-shear rule.
29 min - 10
Compressible Flow and Mach Number
Connect acoustic information speed to thermodynamic closure, Mach number, choking, and the branches of ideal nozzle flow.
30 min