Fluid Dynamics
Introduction
Fluid dynamics is a sub-discipline of fluid mechanics that deals with the study of the motion of fluids - both liquids and gases. It has several sub-disciplines itself, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and reportedly modeling fission in nuclear reactors.
Governing Equations
The foundational axioms of fluid dynamics are the conservation laws, specifically, conservation of mass, conservation of linear momentum (or Newton's Second Law of Motion), and conservation of energy. These are based on the differential equations that describe how these quantities change with time and position in the fluid. The equations are simplified by applying the assumptions of fluid dynamics - that the fluid is a continuum and not made up of individual particles. These equations are called the Navier-Stokes equations.
The Navier-Stokes equations are the fundamental partial differential equations of fluid dynamics. They are based on the assumption that the fluid, at the scale of interest, is a continuum - a continuous substance rather than discrete particles. The equations are named after Claude-Louis Navier and George Gabriel Stokes.
The Navier-Stokes equations are a set of nonlinear partial differential equations that describe the motion of fluid substances. These equations establish that changes in momentum in infinitesimal volumes of fluid are simply the product of changes in pressure and dissipative viscous forces (similar to friction) acting inside those volumes.
Incompressible Flow
In fluid dynamics, incompressible flow refers to a flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves with the flow velocity. Incompressible flow does not imply that the fluid itself is incompressible; indeed, the density of the fluid can change significantly along a streamline. Rather, the term "incompressible flow" means that the divergence of the flow velocity is zero, which in fluid dynamics is expressed mathematically as ∇•v = 0, where v is the flow velocity vector.
Compressible Flow
Compressible flow (gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressible, flows are usually treated as being incompressible when the Mach number (the ratio of the speed of the flow to the speed of sound) is less than 0.3 (since the density change due to velocity is about 5% in that case).
Laminar and Turbulent Flow
Flow can be either laminar or turbulent and is characterized by the Reynolds number. Laminar flow occurs at lower Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion; while turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, causing the fluid to form eddies, vortices, and other flow instabilities.
Boundary Layers
In fluid dynamics, a boundary layer is the layer of fluid in the immediate vicinity of a bounding surface where the effects of viscosity are significant. In the Earth's atmosphere, the atmospheric boundary layer is the air layer near the ground affected by diurnal heat, moisture or momentum transfer to or from the surface.
Computational Fluid Dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid (liquids and gases) with surfaces defined by boundary conditions.