Fluid Dynamics

Advanced

Watch fluid particles flow around obstacles and observe how velocity, pressure, and viscosity interact. Explore Bernoulli's principle and see how flow patterns change with Reynolds number.

Key Formulas

Bernoulli's Equation

P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}

Conservation of energy along a streamline in an inviscid, incompressible flow.

Continuity Equation

A_1 v_1 = A_2 v_2

Mass conservation for incompressible flow: the product of cross-sectional area and velocity is constant.

Reynolds Number

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

Dimensionless ratio of inertial to viscous forces, predicting laminar vs turbulent flow.

Navier-Stokes (simplified)

\rho \frac{D\vec{v}}{Dt} = -\nabla P + \mu \nabla^2 \vec{v} + \rho \vec{g}

Fundamental equation of viscous fluid motion (incompressible form).

Viscous Drag

F_d = 6\pi \mu r v

Stokes drag force on a sphere in a viscous fluid at low Reynolds number.

Key Concepts

Laminar vs turbulent flow
Bernoulli's principle and pressure-velocity tradeoff
Viscosity and shear stress
Streamlines and flow visualization
Reynolds number as flow regime indicator

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