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Newton's First Law (Inertia)

\sum F = 0 \Rightarrow v = \text{const}

An object stays at rest or in uniform motion unless acted on by a net force.

Newton's Second Law

F = ma = \frac{dp}{dt}

Net force equals mass times acceleration (rate of change of momentum).

Newton First Law

\sum F = 0 \Rightarrow \text{constant } v

An object stays at rest or in uniform motion unless acted upon.

Newton Third Law

F_{AB} = -F_{BA}

Every action has an equal and opposite reaction.

Fluid Pressure

P = \rho g h

Pressure at depth in a fluid.

Pressure

P = \frac{F}{A}

Force per unit area.

Archimedes' Principle

F_b = \rho g V

Buoyant force equals weight of displaced fluid.

Continuity Equation

A_1 v_1 = A_2 v_2

Conservation of flow in an incompressible fluid.

Bernoulli's Equation

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

Energy conservation along a streamline.

Volumetric Flow Rate

Q = Av

Volume of fluid passing per unit time.

Reynolds Number

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

Predicts laminar vs turbulent flow.

Poiseuille's Law

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

Laminar flow rate through a pipe.

Stokes' Drag

F = 6\pi\mu r v

Drag on a small sphere in viscous flow.

Surface Tension

\gamma = \frac{F}{L}

Force per unit length along a liquid surface.

Hydraulic Press (Pascal)

\frac{F_1}{A_1} = \frac{F_2}{A_2}

Pressure transmits equally in a hydraulic system.

Torricelli's Law

v = \sqrt{2gh}

Speed of fluid leaving a hole at depth h.

Drag Force

F_D = \tfrac{1}{2}\rho v^2 C_D A

Aerodynamic drag on a moving body.