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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.
Isentropic is the combination of the Greek word "iso" (which means - same) and entropy. When the change in flow variables is small and gradual, isentropic flows occur. The generation of sound waves is an isentropic process. A supersonic flow that is turned while there is an
Note that before and after the shock the isentropic relations are valid and connect static and total quantities. That means, p t o t a l ≠ p s t a t i c + p d y n a m i c {\displaystyle p_{total}\neq p_{static}+p_{dynamic}} (comes from Bernoulli, assumes incompressible flow) because the flow is for Mach numbers greater than unity always ...
However, the definition of dynamic pressure can be extended to include compressible flows. [ 2 ] [ 3 ] For compressible flow the isentropic relations can be used (also valid for incompressible flow):
For isentropic compression, ν ( M 2 ) = ν ( M 1 ) − θ {\displaystyle \nu (M_{2})=\nu (M_{1})-\theta \,} where, θ {\displaystyle \theta } is the absolute value of the angle through which the flow turns, M {\displaystyle M} is the flow Mach number and the suffixes "1" and "2" denote the initial and final conditions respectively.
See relations between specific heats for the derivation of the thermodynamic relations between the heat capacities. The above definition is the approach used to develop rigorous expressions from equations of state (such as Peng–Robinson ), which match experimental values so closely that there is little need to develop a database of ratios or ...
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.
The area and mass flow rate are held constant for Rayleigh flow. Unlike Fanno flow, the Fanning friction factor, f, remains constant.These relations are shown below with the * symbol representing the throat location where choking can occur.