AE 334 EXPERIMENT : DETERMINATION OF NOZZLE ...

Introduction:
AE 334
EXPERIMENT : DETERMINATION OF NOZZLE EFFICIENCY
Nozzles are suitably shaped passages in which a fluid accelerates as its pressure decreases.
Nozzles are vital components in a wide variety of engineering applications: turbines, jet
propulsion, rockets, ejectors.
The high velocity jet of fluid leaving a nozzle may be used in several ways:
• In a turbine, the kinetic energy stored in the fluid forms the energy available to the blades or the
rotor for conversion to shaft work.
• In rockets and jet propulsion, the change of momentum associated with the velocity changes in
the nozzle provides most of the propulsion force.
• In ejectors and injectors, the changes of momentum of the jet, with its entrained fluid, is used to
bring about the desired pressure changes.
In the ideal nozzle, flow through a perfect nozzle would be reversible, (i.e. without heat
transfer and without frictional effects, shocks, etc.) and will therefore be isentropic.
Objective:
The aim of this experiment is to determine the effect of back pressure on the mass flow rate with a
constant inlet pressure and compare the mass flow rate with the theoretical value for a perfect gas
flowing isentropically and calculate the nozzle efficiency.

Experimental setup:
Theory:
Due to the effects of friction, uncontrolled expansion, shocks etc., the velocity of the jet of
fluid leaving a nozzle will be lower than that from an ideal nozzle.
The efficiency of a nozzle as a kinetic energy producer is the ratio:
Kinetic energy increase across the nozzle
Kinetic energy increase in an isentropic nozzle
Since the kinetic energy of the fluid before the nozzle is usually insignificant,
Kinetic energy of jet leaving the nozzle
Nozzle Efficiency =
Isentropic enthalpy change across the nozzle

For reversible and adiabatic one-dimensional expansion through a passage, the following
relationships apply at any section XX.
2
V
ht = h + = constant
2
2
2
V1
Vx
h1 + = hx
+
2 2
assuming that V = 0 then
V = 2( h − h )
x 1 x
A
x
.
mν
x =
V
x
1
where .
h = total enthalpy
t
h = enthalpy
V = velocity
m = mass flow rate
A = Area
ν = specific volume
If it is assumed the relationship between p and ν in such an expansion is pν γ = constant.
1 2s
2s
h − h = ν dp
1
γ −1
γ p γ
2
1 − 2s = 1ν ⎢
1 1−
⎥
γ −1 ⎢ p1
⎥
⎣ ⎦
h h p
pν = RT
1 1 1
∫
⎡ ⎤
To calculate mass flow rate per unit area m/A in a nozzle from the contunuity equation
we proceed as follows:
(1)
(2)

.
m PV γTt
= ρV
=
A RT γT
.
=
PV
γ RT
γ Tt
1
R T T
t
t
PM γ γ −1 2 Pt
⎡ γ −1
2 ⎤
= 1+ M where = 1 M
T R 2 P ⎢
+
2 ⎥
⎣ ⎦
t
m
=
A
(3)
Pt
Tt
γ M
R
⎡ γ −1
2 ⎤
⎢
1+
M
⎣ 2 ⎥
⎦
γ + 1
2( γ −1)
For choked condition Mach number equals to one, then :
At
.
P1
theoretical = 0.404 t where P1
m A T
1
: throat area
: Inlet Pressure
γ
γ −1
D = throat diameter = 0.00202m
The theoretical value of the jet velocity leaving the nozzle can be found from Equation1
and the actual jet velocity can be found from V=F/m where F is the force which will be found
from F/Δ graph.
(4)

Experimental Procedure:
1. Close the air inlet valve and open the chamber pressure control valve.
2. Check that the micrometer dial has been correctly zeroed.
3. Adjust the air inlet control valve to give a constant air inlet pressure of about 500-600 kN.m -2
gauge with the chamber pressure control valve fully open.
4. Then rotate the micrometer adjustment screw until the voltmeter and lamb indicates
that the contact is just made.
5. Observe the pressures, temperatures, airflow rate and the dial reading.
6. Increase the chamber pressure and with the original inlet pressure repeat the test.
P1(kN/m 2 ) P2(kN/m 2 ) mmeasured(g/s) Δ(dial) T1(C°) T2(C°)
500 150
500 200
500 250
500 300
500 350
500 400

Calculations and Results:
Do the steps below for the given pressure adjustments:
1. Calculate the theoretical mass flow rate.
2. Calculate the jet velocity.
3. Calculate the specific kinetic energy, V2/2.
4. Calculate the isentropic enthalpy change.
5. Calculate the nozzle efficiency.
6. Tabulate all the results for each pressure adjustment.
7. Plot m_ theoretical/rp.
8. Plot m_ measured/rp.
Note: Be careful on the units !
Discussions and Conclusion:
Make comment on the graph. Write your own opinions about the results. What might be the
possible causes of errors in this experiment? Discuss about whether the results are acceptable or
not? Make comment on the efficiency of the nozzle.