1. Area, Mass Flow Functions
C-D Nozzles

2. Compressible Flow Relationships
Mass Flow parameter

3. Compressible Flow Relationships
Area-Mach number differential relation
Area-Mach number integral relation
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4. Compressible Flow Relationships
What does subscript * mean?
For all flow variables it means when that variable when M=1 [sonic]
For area A* this is reference area for choking flow [M=1]
Note this area is a minimum or throat
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5. Compressible Flow Relations

11. Compressible Flow Examples

12. Compressible Flow Examples

13. Compressible Flow
Mass Flow Parameters:

14. Compressible Flow Relationships
Mass flow parameters
Note:
FPo, FPs are similar,
but different f[M] powers

15. Compressible Flow Relationships
Mass flow parameters
How to get more mass flow, i.e. greater thrust, more power?

16. Compressible Flow Examples

17. Example

18. Static Pressure Mass Flow Parameter
Defining: FP = Flow parameter=f(M)
For Air

19. Static Pressure Mass Flow Parameter
Remember that
can be inverted:

20. Total Pressure Mass Flow Parameter
Introducing P0:
No explicit solution for M
FPs is single valued, FPo is not

21. Total Pressure Mass Flow Parameter
FP0 is double valued
FP0 maximizes at M = 1.0
Maximum FP0 is for  = 1.4

22. Mass Flow Parameters
Be careful: FPs single valued, FPo double values

23. Other Parameters Example: m = 50 lb/sec A = 200 sq.in.
P0 = 14.7 psia  = 30
T0 = 519 R

24. Example Solution to Mass Flow Parameter
Rearrange FP0 equation: