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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]
Because the energy per unit mass of liquid in a well-mixed reservoir is uniform throughout, Bernoulli's equation can be used to analyze the fluid flow everywhere in that reservoir (including pipes or flow fields that the reservoir feeds) except where viscous forces dominate and erode the energy per unit mass. [6]: Example 3.5 and p.116
The equation above is a vector equation in a three-dimensional flow, but it can be expressed as three scalar equations in three coordinate directions. The conservation of momentum equations for the compressible, viscous flow case is called the Navier–Stokes equations. [2] Conservation of energy
Also, temperature variations for compressible flows are usually significant and thus the energy equation is important. Curious phenomena can occur with compressible flows. For simplicity, the gas is assumed to be an ideal gas. The gas flow is isentropic. The gas flow is constant. The gas flow is along a straight line from gas inlet to exhaust ...
When the density is allowed to vary, the flow is called compressible. In air, compressibility effects are usually ignored when the Mach number in the flow does not exceed 0.3 (about 335 feet (102 m) per second or 228 miles (366 km) per hour at 60 °F (16 °C)). Above Mach 0.3, the problem flow should be described using compressible aerodynamics.
Then for an ideal gas the compressible Euler equations can be simply expressed in the mechanical or primitive variables specific volume, flow velocity and pressure, by taking the set of the equations for a thermodynamic system and modifying the energy equation into a pressure equation through this mechanical equation of state. At last, in ...
is the flow velocity. and is the heat flux vector. Because it expresses conservation of total energy, this is sometimes referred to as the energy balance equation of continuous media. The first law is used to derive the non-conservation form of the Navier–Stokes equations. [3]
The above equation can be used to plot the Rayleigh line on a Mach number versus ΔS graph, but the dimensionless enthalpy, H, versus ΔS diagram, is more often used. The dimensionless enthalpy equation is shown below with an equation relating the static temperature with its value at the choke location for a calorically perfect gas where the ...