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Compressible flow (or 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 smaller than 0.3 (since the density change due to velocity is about 5% in that case). [1]
ρ f = Mass density of the fluid; V imm = Immersed volume of body in fluid; ... ρ = fluid mass density; u is the flow velocity vector; E = total volume energy density;
Mass flow rate is defined by the limit [3] [4] ˙ = =, i.e., the flow of mass m through a surface per unit time t. The overdot on the m is Newton's notation for a time derivative . Since mass is a scalar quantity, the mass flow rate (the time derivative of mass) is also a scalar quantity.
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.
In fluid measurement, the fluid's flow conditions (or flowing conditions) refer to quantities like temperature and static pressure of the metered substance.The flowing conditions are required data in order to calculate the density of the fluid at flowing conditions.
q is the dynamic pressure in pascals (i.e., N/m 2, ρ (Greek letter rho) is the fluid mass density (e.g. in kg/m 3), and; u is the flow speed in m/s. It can be thought of as the fluid's kinetic energy per unit volume. For incompressible flow, the dynamic pressure of a fluid is the difference between its total pressure and static pressure.
Enthalpy-Entropy diagram of stagnation state. In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero. The isentropic stagnation state is the state a flowing fluid would attain if it underwent a reversible adiabatic deceleration to zero velocity.
In the Boussinesq approximation, variations in fluid properties other than density ρ are ignored, and density only appears when it is multiplied by g, the gravitational acceleration. [ 2 ] : 127–128 If u is the local velocity of a parcel of fluid, the continuity equation for conservation of mass is [ 2 ] : 52