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The fundamental equations governing fluid dynamics are the Navier-Stokes equations. These equations describe the conservation of momentum and mass for a fluid. However, solving the Navier-Stokes equations analytically is often challenging, and numerical methods are commonly used for practical applications.

Fluid flow can be described by several characteristics, including velocity (speed and direction of motion), pressure (force exerted by the fluid per unit area), density (mass per unit volume), and viscosity (the resistance of the fluid to flow).

In fluid dynamics, the continuum hypothesis is often employed, treating fluids as continuous and homogeneous substances, rather than considering them as composed of individual molecules. This simplification allows for the use of differential equations to describe fluid motion.