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Fluid Mechanics

Pressure, buoyancy, flow and the behaviour of fluids

Fluid Pressure

Basic
P=ρghP = \rho g h

Pressure at depth in a fluid.

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Pressure

Basic
P=FAP = \frac{F}{A}

Force per unit area.

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Archimedes' Principle

Intermediate
Fb=ρgVF_b = \rho g V

Buoyant force equals weight of displaced fluid.

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Continuity Equation

Intermediate
A1v1=A2v2A_1 v_1 = A_2 v_2

Conservation of flow in an incompressible fluid.

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Bernoulli's Equation

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

Energy conservation along a streamline.

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Volumetric Flow Rate

Basic
Q=AvQ = Av

Volume of fluid passing per unit time.

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Reynolds Number

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

Predicts laminar vs turbulent flow.

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Poiseuille's Law

Advanced
Q=πr4ΔP8μLQ = \frac{\pi r^4 \Delta P}{8\mu L}

Laminar flow rate through a pipe.

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Stokes' Drag

Advanced
F=6πμrvF = 6\pi\mu r v

Drag on a small sphere in viscous flow.

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Surface Tension

Intermediate
γ=FL\gamma = \frac{F}{L}

Force per unit length along a liquid surface.

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Hydraulic Press (Pascal)

Intermediate
F1A1=F2A2\frac{F_1}{A_1} = \frac{F_2}{A_2}

Pressure transmits equally in a hydraulic system.

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Torricelli's Law

Advanced
v=2ghv = \sqrt{2gh}

Speed of fluid leaving a hole at depth h.

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Drag Force

Advanced
FD=12ρv2CDAF_D = \tfrac{1}{2}\rho v^2 C_D A

Aerodynamic drag on a moving body.

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Specific Gravity

Basic
SG=ρρwaterSG = \frac{\rho}{\rho_{water}}

Density relative to water.

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