MEASUREMENTS IN FLUID MECHANICS
L
ABORATORY
SESSION
N
R
.
9
.:
Measuring
the characteristics of the diffuser
Location
of measur
ement
:
Department of Fluid Mechanics
,
Laboratory
1. The aim of measurement
:
The efficiencies
(
) of diffus
ers with circular cross section
are
to be defined. The
efficiency has to be measured and illustrated
as a function of
the angle of the diffuser (
) and
the flow rate (
q
v
). Three different angles (6°, 15°, 3
0°) and a Borda

Carnot element
can be
built into t
he measuring device.
T
he flow rate of the diffuser is adjustable.
2. Description of the measuring device
The sketch of the measuring device can be seen in Figure 1. We calibrate the
inlet
orifice
plate (5) by the help of a built in
standard
ized
orifice
p
late
(6)
by the use
of the upper, so

called calibration line (7). After the calibration of the
inlet orifice plate
(5) it has to be built in
the lower measurement section and the actual measuring can begin.
Figure 1. Calibration Device
Figure 2. M
eas
uring device
to determine efficiency
INLET ORIFICE PLATE
CALIBRATION
The
a
ir is delivered into the device via a radial ventilator
built into the table (1) which is
connected to the calibration tube(7).
By the use of the calibration line (6), we can det
ermine
the flow number of the inlet orifice plate, by measuring the pressure difference on the
standard built

in orifice plate and the inlet orifice plate simultaneously. Volume flow rate can
be calculated based on the standard orifice plate, then it can b
e substituted into the equation
describing the inlet orifice plate, where the only unknown variable will be the flow number. A
calibration diagram can be constructed if the corresponding pressure differences are recorded
and displayed in a diagram.
DIFF
USER EFFICIENCY MEASUREMENT
The suction tube of the ventilator and the
inlet orifice plate
has to be
connected
to
the
measurement section (3). We attach the diffusers to be measured (4) between the
measurement section and the
inlet orifice plate
. The flow
rate can be calculated based on the
pressure differences, with the help of the calibration diagram recorded previously.
The efficiency of the diffuser can be calculated from the increase of pressure measured on the
pressure tap
s before and after the diffu
ser with an inclined micromanometer. There are more
pressure tap
s on the measurement section after the diffuser to evade pressure measurement in
the separated flow.
3. The theory of the measuring
The
variables
in the next theoretical definitions are alw
ays average
variables
applied to
pressures and velocities in whole cross sections. Cross section ‘1’ is the diffuser entry cross
section while cross section ‘2’ is the diffuser exit cross section (the cross section to the
measurement section).
What does i
t mean, and ho
w do w
e define that a diffuser is good?
We use a diffuser if we want to establish a cross section expansion between two sections with
two different cross sections, that is an A1/A2 cross

section expansion. The expansion should
be established
with the lowest possible loss of
total
pressure.
The diameter expansion could be
achieved with sudden increase in di
ameter (a Borda

Carnot element
) with greater separation
loss, or the other extreme, a high wall friction, infinite, expanding tube. With reg
ard to the
given flow, the best possible solution seems between the two, a diffuser with
the lowest loss
(
an optimal opening angle,
best efficiency) see table 1 below.
DIAMTER
EXPANSION
SOLUTION
Diffuser
opening
angle
REASON FOR PRESSURE
LOSS IN THE SYS
TEM
RATE OF
EFFICIENCY
separation
Wall friction
Borda
–
Carn潴
c潭灯pent
(sudden increase in diameter)
180
BIG

BA
iffuser
LITTL
LITTL
AXI
Infi湩te e灡n摩湧 tu扥
secti潮
~‰

BIG
BA
Ta扬eㄮ1
F潲⁴hecharacteristics 潦a
iffuser innum扥rsⰠ we摥fine therate潦efficiency 潦affuser
:
,
that relates the actual increase in pressure
to the ideal increase in pressure
, where there is no loss and which can be calc
ulated with a simple Bernoulli
equation
:
,
The diffuser
efficiency grade is the ratio
of the actual (measured) and the ideal pressure
increase.
The other characteristic, which is us
ed to characterize components (
valves, angles, etc)
is the
loss factor, which can be determined in case of a diffuser with following quotation:
.
The pressure loss
in the dif
fuser is by the entrance
dynamic pressure. Of course, between the
efficiency and the loss
factor is a close relationship, which is following: (on the right side of
the equation using the
continuity.)
4. The process of measuring
Calibration of the
inlet orifice plate
The equation of the flow rate to th
e
inlet orifice plate
is following:
where
flow number
d
b
inner diameter of
inlet orifice plate
1
density of air
p
b
pressure drop measured on the
inlet orifice plate
The flow number of the
inlet orifice plate
can be determined w
ith a calibration tube (figure 1).
T
he calibration tube contains a
standardized
orifice plate
, on which we can measure the flow
rate with the standard method. During calibration we have to measure the pressure drop of the
standard orifice plate
and the
inl
et orifice plate
at different flow rates. The flow rate can be
deduced from the pressure drop of the
standard orifice plate
, which compared to the pressure
drop of the
inlet orifice plate
determines the flow rate in the equation. (In lack of time flow
fact
or of the
inlet orifice plate
can be changed to 1, so the pressure drop on the component
will be nearly identical with the local dynamic pressure.)
The formula to calculate the flow rate of the
standard orifice plate
:
where
C
Flow co
mponent
Measure brim relation to diameter (here
=0,6587)
Compressibility factor (
=1, since change in the pressure of the medium is low)
d
Hole diameter of measure brim (here d=38.8mm)
p
Pressure drop on measure brim
Formula to calculate flow component C:
where
Re
D
the Reynolds number calculated with the diameter before the measure brim (here
D=58,9mm)
Since the Reynolds number is
dependent of the
velocity, and velocity is
dependent of the
flow
component, which is
again
dependent of the
Reynolds number, it is advisable to use iteration
to do the task. The flow number in the first iteration cycle shall be C=0,6. We shall determine
flow rate at the given flow number, the velocity before the
standard orifice plate
, the
Reynolds
number, and finally we shall determine the flow number. From here the cycle starts all over
again, we calculate flow rate with the new flow number, the velocity, etc. The results
converge swiftly and after 2 or 3 iteration cycles we get the actua
l results
(we can consider the
solution final, if the relative difference of substituted C and the calculated C value is below
5%)
.
Pressure drop and velocity
and
velocities can be calculated with the volumetric a
ir flow measured with the help of
the
inlet orifice plate
:
,
We have to measure the pressure
drops between the
pressure tap
before the diffusor (p1) and
the
pressure tap
s of the so called measuring
section (p2). From the pressure drop and th
e
velocity we can calculate
the
efficiency (
)
.
5. Checking and
comparing the results with data
from the literature:
The geometrical data
of
the diffusers have to be recorded
during the meas
urement. The
measured velocities and pressure values have to be shown in diagrams. After the
measurements
the efficiency (
)
has to be determined.
You can find the requirements of the report at the homepage of the Department of Fluid
Mechanics.
Keep in mind while
measuring
While evaluation we have to determine measuring mistakes resulting from
imprecise measurement. These affect the results.
Before turning on the measuring device and while operating it, we must make sure
that all
conditions of safe operation are fulfilled. Nearby colleagues should be
warned before turning on the device or if there are modifications in function.
The temperature and atmospheric pressure needs to be recorded in every case.
Recording the figures and u
nits on the measuring devices as well as factors that
affect them.
Record the type and the serial number of measuring devices, and the density of
fluid used in them.
Compare the units of the measured data and the data used in calculations.
U

tube manomet
ers can only be used if they are leveled properly.
When connecting the manometer, we must be precautious with selecting the
measurement limits and the + and
–
ends of the terminals. We must be careful with
all manometers
–
especially with the inclined mano
meter, to attach the rubber tube
extremely car
efully to the manometer, constantly checking the measurement fluid
for changes or unusual activity. If the level of measurement fluid approaches the
maximum deflection before the tubes are secured, the measurement limit has to be
reset. If this does not he
lp either, another device has to be used that is suitable for
measurements with higher pressure. If we ignore the problem, fluid might flow
into the connecting tube adulterating the results or making the entire measuring
impossible.
The pressure transmitt
ing rubber or silicone tubes have to be checked before and
while working with them, because if these tubes should rip, all results will be lost.
Checking can be made by surveying or pressure testing. Critical points are the
places where the tubes are conne
cted to the instruments.
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