Fundamental equations governing viscous fluid motion.
ρ(∂V/∂t+V·∇V)=-∇P+μ∇²V+ρg, with continuity ∇·V=0 for incompressible flow. They govern all Newtonian fluid motion, but analytic solutions exist only for simple cases (Couette, Poiseuille). Their turbulence is a major open mathematical problem.
Poiseuille flow solution gives the parabolic pipe profile.
The Navier-Stokes equations describe viscous fluid motion in full, so they underlie nearly every detailed fluid simulation.
Fundamental equations governing viscous fluid motion.
The Navier-Stokes equations describe viscous fluid motion in full, so they underlie nearly every detailed fluid simulation.
Conservation of mass and momentum for a viscous fluid, with the viscous terms describing friction within the fluid.
They are nonlinear and turbulence adds many scales, so exact solutions exist only for simple cases, and numerical solution is required in practice.
Typical applications include simulating the flow of blood through a stenosed artery, predicting the airflow in a building ventilation design and computing the drag on a car with a computational model.
Study "Normal shock waves" first (topic 79 of 105 in Thermodynamics & Fluids). It covers the groundwork this topic builds on.
Inertia, pressure, viscous and body terms. Non-dimensionalised with Re. Basis for CFD.
Poiseuille flow solution gives the parabolic pipe profile.
The next topic is "Potential flow", which builds directly on this one.
It is classed as Advanced in Thermodynamics & Fluids (topic 80 of 105). It is an advanced topic. It assumes you are comfortable with the intermediate topics in Thermodynamics & Fluids.
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