Fluid Mechanics

Bernoulli, viscosity · 6 formulas

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Continuity Equation

A1v1=A2v2A_1 v_1 = A_2 v_2

What flows in must flow out — narrow pipes force faster flow.

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Bernoulli's Equation

P+12ρv2+ρgh=constP + \tfrac{1}{2}\rho v^2 + \rho g h = \text{const}

Pressure, kinetic, and potential energy per unit volume sum to a constant along a streamline.

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Hydrostatic Pressure

P=P0+ρghP = P_0 + \rho g h

Pressure grows linearly with depth because of the weight of fluid above.

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Archimedes' Principle

Fb=ρVgF_b = \rho V g

Buoyant force equals the weight of fluid displaced.

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Torricelli's Law

v=2ghv = \sqrt{2 g h}

Falling fluid trades height for speed, just like a dropped ball.

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Reynolds Number

Re=ρvLμRe = \frac{\rho v L}{\mu}

Ratio of inertial to viscous forces — high Re means inertia wins, turbulence reigns.