1. BY Dr. P M V Subbarao Mechanical Engineering Department I I T Delhi
Theory of Nozzles BY
Dr. P M V Subbarao
Mechanical Engineering Department
I I T Delhi
A primitive machine to create motive power from Fluid Power.

2. Role of Nozzles in Generation of Motive Power

3. Simple Straight Nozzle in an Impulse Turbine

4. Analysis of Simple Moving Nozzle
Vai
Vri
Vre
Vae U
Change in velocity :
Motive Power Generated:

5. Kinetic energy of the jet in the nozzle increases at the cost of enthalpy.
This leads to increase in exit relative velocity (Vre) the jet.
The total power lost by the jet is equals to the kinetic power gained by the nozzle.
Power lost by the jet:

6. Simple Impulse-Reaction Nozzle
Vre
Vae
Vri
Vai
Jet will lose power both by Impulse and Reaction.
One important and essential element in all these cases is a nozzle.

7. Theory of Nozzles
Nozzle is a variable shape tube which can accelerate a fluid.
The cross section of the nozzle can be circular / rectangular / elliptical.
An externally imposed pressure conditions at the ends will drive the flow through the nozzle.
An adiabatic and frictionless flow through nozzle will convert maximum enthalpy of fluid to its kinetic energy.
An appropriate cross-sectional area should be provided along the flow direction.
The length of the nozzle is immaterial if the flow is reversible.
However, an irreversible flow will restrict the minimum and maximum allowed lengths of a nozzle.

8. Isentropic Flow Through a Nozzle
Assume SSSF.
Consider an infinitesimal control volume dv in the flow dv
State 1
State 2
u : Velocity
e : Specific Internal Energy x2 x1

9. Conservation of Mass: x2 x1

10. Conservation of Momentum:
Rate of Change in Inertial force = Rate of Change in Static Force + Rate of Change in Geometric force

12. First Law Analysis :SSSF
First Laws for nozzle in SSSF Mode:

13. No change in elevation, z.or

14. Conservation of mass
Conservation of Momentum
Conservation of Energy

15. Velocity of sound in an Ideal Gas,
Recall first Law of Thermodynamics for a reversible Process.
For an isentropic process:
Velocity of sound in an Ideal Gas,

16. Transfer of Message through A Fluid
Valve Fully closed, no flow.
pamb c c c c
pfluid c
Role of Sonic Velocity in Engineering

17. Transfer of Message through A Fluid
Valve Partially opened, low flow.
pamb c u
c-u
c+u
pfluid
Role of Sonic Velocity in Engineering

18. Transfer of Message through A Fluid
Valve more opened, more flow.
pamb c u
c-u
c+u
pfluid
Role of Sonic Velocity in Engineering

19. Transfer of Message through A Fluid
Valve opened such that u=c.
pamb c u
c-u=0
pfluid
c+u=2c
Role of Sonic Velocity in Engineering

20. Fluid starting form Rest
After Countdown
                                                                                                                                                                      
Before Countdown

21. Fluid starting form Rest
Valve Fully closed, no flow.
pamb c c c c
pfluid c
From Stagnation to Flow………..

22. Integrating from stagnation:
First Law for nozzle :
Integrating from stagnation:

23. Let
M : Mach Number

24. For an isentropic process

25. Conservation of Momentum
Conservation of mass

28. Subsonic Nozzle
Subsonic Diffuser
dA < 0 & M <1
So, du > 0 & dp <0
dA > 0 & M <1
So, du < 0 & dp>0

29. Supersonic Diffuser
Supersonic Nozzle
dA < 0 & M >1
So, du < 0 & dp >0
dA > 0 & M >1
So, du >0 & dp<0

30. Generation of Supersonic Velocity from Rest

31. Generation of High Pressure from Supersonic velocity

32. RAMJET Engine

33. Isentropic Nozzle:
On Integration:

34. Nozzle at Design Exit Pressure
pthroat
p2d p1 p1 p p*
p2d

35. At Throat: M=1
Minimum Area = A*

37. Irreversible Adiabatic Nozzle:p2 p1

38. For Isentropic flow through Nozzle:
For irreversible flow through Adiabatic Nozzle:

40. Nozzle at Off Design Exit Pressure
pthroat
p2d p1
p2a > p2d

41. Nozzle at Off Design Exit Pressure
pthroat p1
p1 > p2a > pthroat p1
p2a p
P*2a p*
p2d

45. Vai
Vri U
Vre