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The gas flow is along a straight line from gas inlet to exhaust gas exit. The gas flow behavior is compressible. There are numerous applications where a steady, uniform, isentropic flow is a good approximation to the flow in conduits. These include the flow through a jet engine, through the nozzle of a rocket, from a broken gas line, and past ...
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]
In fluid dynamics, an isentropic flow is a fluid flow that is both adiabatic and reversible. That is, no heat is added to the flow, and no energy transformations occur due to friction or dissipative effects. For an isentropic flow of a perfect gas, several relations can be derived to define the pressure, density and temperature along a streamline.
For isentropic flow, density can be expressed as a function only of enthalpy = (), which in turn using Bernoulli's equation can be written as = (). Since the flow is irrotational, a velocity potential ϕ {\displaystyle \phi } exists and its differential is simply d ϕ = v x d x + v y d y {\displaystyle d\phi =v_{x}dx+v_{y}dy} .
In the classical regime, expansions are smooth isentropic processes, while compressions occur through shock waves, which are discontinuities in the flow. If gas-dynamics is inverted, the opposite occurs, namely rarefaction shock waves are physically admissible and compressions occur through smooth isentropic processes. [24]
The two points of interest are 1) in the freestream flow at relative speed where the pressure is called the "static" pressure, (for example well away from an airplane moving at speed ); and 2) at a "stagnation" point where the fluid is at rest with respect to the measuring apparatus (for example at the end of a pitot tube in an airplane).
If a near supersonic flow experiences an area contraction, the velocity of the flow will decrease until it reaches the local speed of sound, and the flow will be choked. This is the principle behind the Kantrowitz limit: it is the maximum amount of contraction a flow can experience before the flow chokes, and the flow speed can no longer be ...
Point 3 labels the transition from isentropic to Fanno flow. Points 4 and 5 give the pre- and post-shock wave conditions, and point E is the exit from the duct. Figure 4 The H-S diagram is depicted for the conditions of Figure 3. Entropy is constant for isentropic flow, so the conditions at point 1 move down vertically to point 3.