# NOZZLE AND DIFFUSER CLASS NOTES FOR MECHANICAL ENGINEERING

## ENGINEERING

### Case 4

When M< 1 at the ENTRANCE

As area increases, velocity decreases and pressure increases, thus a divergent section becomes a diffuser with M < 1 at entrance.

Thus a nozzle remains a nozzle only if M < 1.

A diffuser remains a diffuser only if M < 1.

Thus flow is SUB-SONIC at entrance.

### NOZZLE

A nozzle is a passage of variable cross-section. In this, pressure of  fluid converts into kinetic energy. The various practical applications of a nozzle are

1. Steam turbines
2. Water turbines
3. Gas Turbines
4. Flow measurements
5. Used in all aircraft’s
6. Jet engines
7. As ejectors for removing air from the condensers
8. As injectors for supplying feed water to boilers
9. Artificial fountains

### DIFFUSER

It is also a passage of varying cross section which converts the kinetic energy of the fluid into pressure energy. It is just reverse of a nozzle.

Applications of a diffuser

1. Centrifugal compressors
2. axial flow compressors
3. Ramming of air in aircraft’s

In one dimensional flow, assume that the velocity and fluid properties change ONLY in the direction of flow. Therefore we can take mean value of velocity and other properties in one direction flow.

### CONVERGENT DIVERGENT NOZZLE

This nozzle is a de Laval nozzle (or CD nozzle). In this, velocity increases in the convergent portion and becomes sonic velocity at the exit (throat). This exit of the of the nozzle has minimum area and maximum velocity. This exit is the THROAT. Now the fluid will enter the divergent portion with supersonic velocity. Here the velocity will further increase. It is necessary to run the turbine at very high speed to generate more power.  Thus, convergent divergent nozzles are used in gas / steam turbines & rocket engines.

Used in steam turbines and all super-sonic aircraft’s.

### COMPARISON OF NOZZLES AND DIFFUSER

Nozzle                                                 DIFFUSER

Boundary layer is thin                      Boundary layer is thick.

Has negligible friction                      Has more friction.

More efficient                                       Less efficient

No shock formation                          Chances of shock formation

### VELOCITY OF STEAM AT ANY SECTION OF THE NOZZLE

v2=C [k(H1– H2)]0.5

Without friction C = 44.72  and k =1

With friction C = 44.72  and k is the friction factor =0.7 to 0.9

k is friction coefficient or nozzle efficiency

### VELOCITY COEFFICIENT

It is the ratio of actual exit velocity to isotropic exit velocity for a certain same pressure drop

cv = Actual velocity/ isotropic velocity

=√actual enthalpy drop/isotropic enthalpy drop

=√η = square root of efficiency√

### EFFICIENCY OF THE NOZZLE

It is a ratio of Actual enthalpy drop to  isotropic enthalpy drop between the same inlet and outlet pressures.

η = Actual enthalpy drop/  isentropic enthalpy drop

### FACTORS ON WHICH THE EFFICIENCY OF A NOZZLE DEPENDS

1. Material of the nozzle
2. Inside surface condition of the nozzle
3. Nature of the fluid flowing through the nozzle
4. Size and shape of the nozzle
5. Reynolds number of the flow
6. Angle of divergence
7. Orientation of the nozzle

### DESIGN OF A STEAM NOZZLE

Data required

1. Inlet pressure and the condition of the steam
2. Back pressure
3. Mass flow rate

### STEPS

(i) Find the back pressure by the standard relation

pb = pi (2/(n+1))(n/(n-1)

(ii) If this calculated back pressure is more than the given back pressure, then the nozzle is a convergent nozzle.

(iii) If this calculated back pressure is less than the given back pressure, then the nozzle is a convergent-divergent

Calculate nozzle dimensions from the

(i)  mass flow rate

(ii) the condition of the steam at inlet, throat and outlet of the nozzle.

Mass flow rate is constant at the inlet, throat and outlet.

Area = m. sp. Volume/velocity

A = π d2/4

26. ### Critical pressure ratio fot

(a) Isentropic process

P*/p = [2/(γ+1)]γ/(γ—1)

(b) Actual process

P*/p = [2/(n+1)]n/(n—1)

27. Mach number

M = actual velocity/sonic velocity

Sonic velocity = 332 m/s

28. Relation between stagnation and static (local ) temperature

T0 /T = 1 + (γ—1) M2/2

### .29. As steam is expanding, velocity at any section of the nozzle

C = 44.72     Without friction

C = 44.72     With friction, k is the friction factor =0.7 to 0.9

30. If the steam expands from pressure p1 and volume v1 to pressure p2

c2 =     2{[(n/(n-1)] [pv1 –p2v2]}0.5

31. Friction reduces the enthalpy drop and hence the velocity at the outlet.

32. Assume no friction in the nozzle. Friction is  in the diffuser only.