Navier-Stokes Equations and Fluid Mechanics

These flashcards focus on key terms and concepts related to the Navier-Stokes equations and fluid mechanics to aid in exam preparation.

Navier-Stokes Equations

A set of equations that describe the motion of fluid substances, based on the principles of conservation of mass, momentum, and energy.

Conservation of Mass

A principle stating that mass cannot be created or destroyed; in fluid mechanics, it means that the mass of the fluid within a closed system remains constant over time.

Velocity (u)

A vector quantity that refers to the speed of a fluid in a specific direction; it has components in x, y, and z directions.

Nabla (∇)

A mathematical operator used to denote the gradient, indicating how a quantity varies in space, specifically within vector calculus.

Divergence

A mathematical operation that measures the magnitude of a source or sink at a given point in a vector field; in fluid mechanics, it relates to how fluid density changes.

Viscosity

A measure of a fluid's resistance to flow; it describes how thick or sticky a fluid is, affecting its internal friction.

Internal Forces

Forces acting between fluid particles within the fluid, responsible for generating pressure and motion.

External Forces

Forces acting on a fluid from outside, like gravity, that cause it to accelerate or change direction.

Turbulence

A state of fluid flow characterized by chaotic, irregular, and vortical motions, making it complex to model and predict.

Millennium Prize Problem

A set of seven unsolved problems in mathematics, one of which involves proving the existence and smoothness of solutions to the Navier-Stokes equations.

Reynolds Averaging

A statistical method used in fluid mechanics to simplify complex flow problems by averaging fluctuating quantities over time.

Pressure Gradient (∇p)

A vector that represents the rate at which pressure changes in space; it drives fluid motion from areas of high pressure to low pressure.

Gradient

A vector that represents the direction and rate of fastest increase of a scalar quantity; used frequently in calculus to analyze changes in fields.