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Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. [ 1 ] : 3 It has applications in a wide range of disciplines, including mechanical , aerospace , civil , chemical , and biomedical engineering , as well as geophysics , oceanography , meteorology , astrophysics ...
where is the Young's modulus of the material, is the surface energy per unit area of the crack, and is the crack length for edge cracks or is the crack length for plane cracks. The quantity σ π a {\displaystyle \sigma {\sqrt {\pi a}}} is postulated as a material parameter called the fracture toughness .
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of water and other liquids in motion).
First law of thermodynamics (fluid mechanics) Flow conditioning; Flow in partially full conduits; Flow net; Flow, Turbulence and Combustion; Flowability; Fluid dynamic gauge; Fluid flow through porous media; Fluid kinematics; Fluid–structure interaction; FluoroPOSS; Free surface; Free surface effect; Friction loss
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
The J-integral represents a way to calculate the strain energy release rate, or work per unit fracture surface area, in a material. [1] The theoretical concept of J-integral was developed in 1967 by G. P. Cherepanov [2] and independently in 1968 by James R. Rice, [3] who showed that an energetic contour path integral (called J) was independent of the path around a crack.
Fluid motion is governed by the Navier–Stokes equations, a set of coupled and nonlinear partial differential equations derived from the basic laws of conservation of mass, momentum and energy. The unknowns are usually the flow velocity , the pressure and density and temperature .
ΔE is the fluid's mechanical energy loss, ξ is an empirical loss coefficient, which is dimensionless and has a value between zero and one, 0 ≤ ξ ≤ 1, ρ is the fluid density, v 1 and v 2 are the mean flow velocities before and after the expansion. In case of an abrupt and wide expansion, the loss coefficient is equal to one. [1]