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Advanced4 equations~10 hours

Fluid Mechanics and CFD

Flow, pressure, Reynolds numbers, and the Navier-Stokes frontier.

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  1. 1

    Bernoulli Equation

    Intermediate
    P+12ρv2+ρgh=constantP + \frac{1}{2}\rho v^2 + \rho g h = \text{constant}

    Along a streamline, pressure, kinetic energy, and potential energy per unit volume sum to a constant.

    Physical Sciences
    Fluid Mechanics
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  2. 2

    Navier-Stokes Equation

    Research
    ρ(∂v∂t+v⋅∇v)=−∇P+μ∇2v+f\rho\left(\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v}\cdot\nabla\mathbf{v}\right) = -\nabla P + \mu\nabla^2\mathbf{v} + \mathbf{f}

    The master equation of fluid motion—balancing inertia, pressure, viscosity, and external forces.

    Physical Sciences
    Fluid Mechanics
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  3. 3

    Reynolds Number

    Intermediate
    Re=ρvLμRe = \frac{\rho v L}{\mu}

    Ratio of inertial to viscous forces—predicts laminar vs turbulent flow.

    Engineering Sciences
    Mechanical Engineering
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  4. 4

    Mach Number

    Intermediate
    M=vcM = \frac{v}{c}

    Flow speed divided by speed of sound—classifies compressibility effects.

    Engineering Sciences
    Aerospace Engineering
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