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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 ...
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.
The analysis of gas flow through de Laval nozzles involves a number of concepts and assumptions: For simplicity, the gas is assumed to be an ideal gas. The gas flow is isentropic (i.e., at constant entropy). As a result, the flow is reversible (frictionless and no dissipative losses), and adiabatic (i.e., no heat enters or leaves the system).
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} .
For isentropic processes, the Cauchy number may be expressed in terms of Mach number. The isentropic bulk modulus K s = γ p {\displaystyle K_{s}=\gamma p} , where γ {\displaystyle \gamma } is the specific heat capacity ratio and p is the fluid pressure.
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.
The Bernoulli equation applicable to incompressible flow shows that the stagnation pressure is equal to the dynamic pressure and static pressure combined. [1]: § 3.5 In compressible flows, stagnation pressure is also equal to total pressure as well, provided that the fluid entering the stagnation point is brought to rest isentropically.
In aerodynamics, the Prandtl–Meyer function describes the angle through which a flow turns isentropically from sonic velocity (M=1) to a Mach (M) number greater than 1. The maximum angle through which a sonic ( M = 1) flow can be turned around a convex corner is calculated for M = ∞ {\displaystyle \infty } .