MEASUREMENTS IN FLUID MECHANICS
LABORATORY SESSION NR.9.:
Measuring the characteristics of the diffuser
Location of measurement: Department of Fluid Mechanics, Laboratory
1. The aim of measurement:
The efficiencies (  diff ) of diffusers 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 (qv). Three different angles (6°, 15°, 30°) and a Borda-Carnot element can be
built into the measuring device. The 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 standardized orifice plate (6) by the use of the upper, socalled 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.
2
6
5
7
2
Figure 1. Calibration
Device
6
2
2
3
2
5
4
2
3
5
7
4
5
Figure 2. Measuring device to determine efficiency
INLET ORIFICE PLATE CALIBRATION
The air 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 determine
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 be 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.
DIFFUSER 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 taps before and after the diffuser with an inclined micromanometer. There are more
pressure taps 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 always 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 it mean, and how do we 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 diameter (a Borda-Carnot element) with greater separation
loss, or the other extreme, a high wall friction, infinite, expanding tube. With regard 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
180
Borda–Carnot
component
REASON FOR PRESSURE
LOSS IN THE SYSTEM
separation
Wall friction
RATE OF
EFFICIENCY
BIG
-
BAD
LITTLE
-
LITTLE
BIG
MAXIMUM
BAD
(sudden increase in diameter)
Diffuser
Infinite expanding tube
section

~ 0
Table 1.
For the characteristics of a diffuser in numbers, we define the rate of efficiency of a diffuser:
 diff 
 p2  p1 val .

2

 v v
2
1
2
2

,
that relates the actual increase in pressure
 p 2  p1 id . ,
 p2  p1 val to
the ideal increase in pressure
where there is no loss and which can be calculated with a simple Bernoulli
equation:
 p2  p1 id .    v12  v 22 ,
2
The diffuser efficiency grade is the ratio of the actual (measured) and the ideal pressure
increase.
The other characteristic, which is used to characterize components (valves, angles, etc) is the
 loss factor, which can be determined in case of a diffuser with following quotation:
 diff . 
p' diff  p2  p1 id .   p2  p1 val .
.

 2
 2
2
 v1
2
 v1
The pressure loss in the diffuser 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 v1  A1  v 2  A2 continuity.)
 diff .
  v 2 
  A 2 
2
 1   diff  1      1   diff  1   1  
  v1  
  A2  
4. The process of measuring
Calibration of the inlet orifice plate
The equation of the flow rate to the inlet orifice plate is following:
d 2 2
qv   b
p
4
1 b
where

flow number
db
inner diameter of inlet orifice plate
1
density of air
pb
pressure drop measured on the inlet orifice plate
The flow number of the inlet orifice plate can be determined with a calibration tube (figure 1).
The 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 inlet 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
factor 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:
C
d 2 2
qv 

p
1
4
1
1  4
where
C


d
p
Flow component
Measure brim relation to diameter (here =0,6587)
Compressibility factor (=1, since change in the pressure of the medium is low)
Hole diameter of measure brim (here d=38.8mm)
Pressure drop on measure brim
Formula to calculate flow component C:
 10 6  

C  0,5961  0,0261  0,216   0,000521
 Re D 
D 

 0,0110,75    2,8 

0,0254 

where
2
8
0,7
 (0,0188  0,0063 A) 
3, 5
 10 6 


 Re D 
0,3

ReD the Reynolds number calculated with the diameter before the measure brim (here
D=58,9mm)
0 ,8
 19000  

A  
 Re D 
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 actual 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
v1 and v 2 velocities can be calculated with the volumetric air flow measured with the help of
the inlet orifice plate:
,
v1 
4  qv
d in2  
v2 
4  qv
2
d out

We have to measure the pressure drops between the pressure tap before the diffusor (p1) and
the pressure taps of the so called measuring section (p2). From the pressure drop and the
velocity we can calculate the efficiency (  diff ).
5. Checking and comparing the results with data from the literature:
The geometrical data of the diffusers have to be recorded during the measurement. The
measured velocities and pressure values have to be shown in diagrams. After the
measurements the efficiency (  diff ) 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 units 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 manometers 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 manometer, to attach the rubber tube
extremely carefully 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 help 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 transmitting 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 connected to the instruments.