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Next: Nozzle Flow With External Up: Normal Shock in Variable Previous: Nozzle efficiency   Index

# Diffuser Efficiency

The efficiency of the diffuser is defined as the ratio of the enthalpy change that occurred between the entrance to exit stagnation pressure to the kinetic energy.

For perfect gas equation (6.6) can be converted to

And further expanding equation (6.7) results in

Solution

The condition at is summarized in following table

 3.0000 0.35714 0.07623 4.2346 0.02722 0.11528 0.65326
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The nozzle area can be calculated by

In this case, is constant (constant mass flow). First the stagnation behind the shock will be

 3.0000 0.47519 2.6790 3.8571 10.3333 0.32834
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Solution

This is a case of completely and suddenly open valve with the shock velocity, temperature and pressure upstream'' known. In this case Potto-GDC provides the following table

 5.5346 0.37554 0.0 1.989 5.479 34.50 0.021717
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The calculations were carried as following: First calculate the as

Then calculate the by using Potto-GDC or utilize the Tables. For example Potto-GDC (this code was produce by the program)

 5.5346 0.37554 5.4789 6.2963 34.4968 0.02172
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The calculation of the temperature and pressure ratio also can be obtain by the same manner. The downstream'' shock number is

Finally utilizing the equation to calculate the following

Solution

This is an open valve case in which the pressure ratio is given. For this pressure ratio of the following table can be obtained or by using Potto-GDC
 1.3628 0.75593 1.2308 1.6250 2.0000 0.96697
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The temperature ratio and the Mach numbers for the velocity of the air (and the piston) can be calculated. The temperature at downstream'' (close to the piston) is

The velocity of the piston is then

Solution

This is the case of a close valve in which mass flow rate with the area given. Thus, the upstream'' Mach is given.

Thus the static Mach number, is

With this value for the Mach number Potto-GDC provides

 2.9222 0.47996 2.1500 0.0 2.589 9.796 0.35101
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This table was obtained by using the procedure described in this book. The iteration of the procedure are

 0 3.1500 0.46689 2.8598 11.4096 0.0 1 2.940 0.47886 2.609 9.914 0.0 2 2.923 0.47988 2.590 9.804 0.0 3 2.922 0.47995 2.589 9.796 0.0 4 2.922 0.47996 2.589 9.796 0.0 5 2.922 0.47996 2.589 9.796 0.0
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Next: Nozzle Flow With External Up: Normal Shock in Variable Previous: Nozzle efficiency   Index
Created by:Genick Bar-Meir, Ph.D.
On: 2007-11-21