Fluid Mechanics is the branch of physics and engineering concerned with the behaviour of fluids and the forces acting on them. A fluid is a substance that continuously deforms under an applied shear stress, encompassing liquids and gases. Fluid Mechanics examines fluids at rest and in motion and therefore includes the subjects of fluid statics and fluid dynamics. Fundamental quantities include density, pressure, velocity, temperature, viscosity and acceleration, while fundamental principles include conservation of mass, conservation of momentum and conservation of energy. The discipline is applied to pipes, pumps, turbines, aircraft, ships, rivers, oceans, atmospheric systems, biological circulation and countless natural and engineered systems.
Fluids differ from solids primarily in their response to shear stress. A solid can sustain a static shear stress while maintaining a fixed shape, whereas an ordinary fluid continues to deform as long as an appropriate shear stress is applied. Fluids can be described using either continuum or molecular perspectives.
Continuum mechanics treats matter as continuously distributed and allows fields such as pressure and velocity to be defined at points, an approximation that is highly effective when the characteristic length scale is much larger than the molecular scale. Density is mass per unit volume, while specific volume is volume per unit mass. Compressibility describes how density changes in response to pressure and temperature.
The governing equations of Fluid Mechanics arise primarily from conservation laws. Conservation of mass leads to the continuity equation, which relates changes in density and velocity to the transport of mass. Conservation of momentum produces equations such as the Navier Stokes equations, which account for pressure forces, viscous stresses and body forces. Conservation of energy produces an energy equation incorporating kinetic, potential and internal energy and associated heat or work transfer. These equations must be supplemented by appropriate material properties, boundary conditions and initial conditions. Different approximations become possible when particular effects are negligible, allowing complex problems to be simplified.
Fluid Mechanics uses several important classifications. A fluid may be treated as incompressible when density changes are sufficiently small for the problem being considered, although real liquids can be weakly compressible. Flow can be classified as steady or unsteady according to whether flow variables change with time at fixed locations. It can be uniform or nonuniform according to spatial variation along a specified direction. Internal flow occurs within conduits such as pipes, whereas external flow occurs around bodies such as aircraft wings. Rotational and irrotational descriptions depend on the local vorticity of the velocity field. These classifications help determine appropriate mathematical and computational methods.
Viscosity distinguishes idealised inviscid fluid behaviour from real fluid behaviour in which internal friction produces shear stresses. For a Newtonian fluid, shear stress is proportional to the velocity gradient, with dynamic viscosity providing the proportionality coefficient. Water and air are approximately Newtonian over many ordinary conditions, whereas substances such as some polymer solutions, suspensions and pastes can be non Newtonian. Boundary layers arise because viscous fluids satisfy the no slip condition at solid surfaces under ordinary conditions. Viscosity also leads to energy dissipation, pressure losses in pipes and resistance to motion through fluids.
Dimensional analysis is an important tool in Fluid Mechanics because many apparently different systems can be related through dimensionless quantities. The Reynolds number compares inertial effects with viscous effects and is central to distinguishing flow regimes. The Mach number compares flow speed with the speed of sound and becomes important in compressible gas flows. The Froude number compares inertial and gravitational effects and is important in free surface flows. Other dimensionless groups compare effects such as surface tension, pressure, heat transfer and diffusion. Similarity principles allow laboratory experiments and scaled models to provide information about larger systems when the relevant dimensionless relationships are appropriately matched.
Fluid Mechanics has both analytical and computational methods. Simple geometries may permit exact or approximate mathematical solutions, while complex systems often require computational fluid dynamics. Numerical methods discretise governing equations over grids or meshes and calculate approximate pressure, velocity and other fields. Experimental fluid mechanics uses instruments such as pressure sensors, flow meters, particle image velocimetry and wind tunnels to measure real behaviour. Analytical, computational and experimental approaches can complement one another through verification and validation. A computational result is not automatically physically correct simply because a numerical solver converges.
Fluid Mechanics has major practical importance because fluids transport mass, momentum and energy throughout natural and engineered environments. It underpins the design of water networks, heating and cooling systems, combustion equipment, aircraft, marine vehicles, turbines, pumps and medical devices. Atmospheric circulation and ocean currents are also governed by fluid mechanical principles, as are blood flow and airflow through biological systems. The discipline combines fundamental physics with mathematical analysis, experimentation and computation. Its broad scope explains why pressure, viscosity, buoyancy, flow stability, turbulence and thermodynamic properties must often be considered together rather than as isolated phenomena.
