Fluid Mechanics

Pressure, buoyancy, flow and the behaviour of fluids

Fluid Mechanics brings together the core formulas used to describe how liquids and gases behave, from pressure and buoyancy to flow rate, drag, and surface tension. It’s a valuable reference for students, exam preparation, and anyone working with pipes, pumps, aerodynamics, or hydraulics, because these equations help predict and control real-world fluid systems with accuracy.

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.

Specific Gravity

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

Density relative to water.