Reversible adiabatic, isentropic flow

Response time constant 403 Rkster. S. 6-13,655 Return bends, heat exchanger 505 Reversed flow 668 Reversibility, isothermal flow 143 Reversible adiabatic, isentropic flow 148... 

Putting k = y gives an approximate equation for adiabatic flow. The result is only approximate because it implies an isentropic change, ie a reversible adiabatic change, but this is not the case owing to friction. A rigorous solution for adiabatic flow is given in Section 6.5. 

These inviscid flows are said to be reversible adiabatic or isentropic. ... 

A very important special case of the polytropic flow equation (5.25) is that describing a reversible, adiabatic expansion, where no heat is exchanged with the surroundings, i.e. an isentropic expansion. In this case, the ratio of specific heats, y, is substituted for n in the mass-flow equation ... 

The maximum flow is obtained for the reversible adiabatic, that is, isentropic state change. However, for the calculation of this process, the speed of sound has to be evaluated at the conditions in the cross-flow area (index 1) of the valve. For this purpose, an iterative procedure is necessary. The necessary steps are as follows ... 

Figure 21.2 Schematic diagram showing the flow from a supersonic nozzle into a low-pressure region. Inside the isentropic core, the flux is a reversible adiabatic expansion. Adapted from Hudson,SoffoceSc7C/7ce, 1998, with permission of John Wiley Sons Ltd...

Formally, a flow which is both adiabatic and reversible, and hence entropy remains constant. In practice, this is a flow in which sources of irreversibility (e.g., friction, thermal diffusion, chemical nonequilibrium) are considered negligible. Shock-free compressible flows are typically modeled as isentropic. 

Discharge Coefficient. Because the assumption of adiabatic and reversible (isentropic) flow is seldom the case, the actual rate of flow through a differential pressure meter is very seldom, if ever, exactly equal to the rate of flow indicated by the particular theoretical equation used. In general, the actual rate of flow is less than the indicated theoretical rate. Hence, to obtain the actual flow from the theoretical equation, an additional factor, called the discharge coefficient, must be introduced. This coefficient is represented by C and defined by the equation... 

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