VENTURI LABORATORY
ME 123: Mechanical Engineering Laboratory II: Fluids
Dr. J. M. Meyers | Dr. D. G. Fletcher | Dr. Y. Dubief
1. Introduction
In this experiment, we will study the laws of mechanical energy and mass conservation of an inviscid,
incompressible fluid through Venturi flow. This will be done using pressure measurements made along
Venturi apparatus inserted into the test section of a low-speed wind tunnel. A Venturi is a simple, yet
elegant device that illustrates many fundamental fluid dynamic phenomena. We saw in class how the
flow rate and velocity through a Venturi can be related to pressure measurements, using Bernoulli’s
equation. Here we will explore the use of Bernoulli’s equation over a range of flow conditions, paying
particular attention to the validity of the assumptions behind the derivation of Bernoulli’s equation. In
particular, in deriving Bernoulli’s equation we assume that the flow in question is (A) inviscid, (B) steady,
and (C) incompressible.
The main objectives of this lab are to:
• Learn how to perform standard air flow measurement using a wind tunnel.
• Experimentally understand the concepts of mechanical energy conservation and mass flow
conservation.
• Compare reduced velocities for various area changes along the flow path of a Venturi insert
using both Bernoulli and mass flow conservation relations.
• Perform uncertainty analysis of reduced data and comment on the fidelity of both methods.
2. Experimental Arrangement
The UVM Low Speed Wind Tunnel (Model Flotek 1440) will be the main experimental facility in this
experiment. The test section cross section is listed at 12 in. x 12 in. but upon measuring, the values are
actually closer to 11 7/8 in. x 11 7/8 in. (±1/8 in.). The wind tunnel uses a suction effect generated by the
fan at the downstream end of the wind tunnel. Upstream of the test section, a honeycomb screen and a
three-dimensional contraction attenuate any turbulence that is sucked in the wind tunnel. The flow
upstream of the test section is assumed to be very close to laminar.
Two inserts placed at the top and bottom of the test section are used to create a Venturi effect (Figure
1). Pressure taps are located on the bottom insert and labeled from 1 to 12. Each pressure port location
has a pre-measured value of respective test-section height as indicated in Table 1. Also given in Table 1
is the surface length location along the Venturi where these taps are located. It is recommended to plot
your results with these values on the x-axis. An additional pressure tap is normally located on the wall
upstream of the insert at the test section inlet to assist in inlet velocity and mass flow calculations.
However, this tap is located slightly into the Venturi section. Use a height of 10.7±0.1 in. at this location
to calculate your mass flow. A Pitot-static probe is also installed to monitor total pressure at the location
of insertion. All pressure taps are connected to a manometer rack.
Be sure to write a concise, yet sufficiently detailed, explanation of how the different components of the
experiment work as this information will be used to describe your experiment in your report.
Figure 1: Venturi apparatus in UVM 12 in. x 12 in. Wind Tunnel test section.
Table 1: Venturi height at pressure port location
Port #
1
2
3
4
5
6
7
8
9
10
11
12
Tunnel Section Height
±0.15 [in.]
9.18
8.33
7.92
8.04
8.33
8.75
9.125
9.42
9.92
10.46
10.985
11.51
Venturi Location s-direction
±0.1 [cm.]
7.0
10.7
14.6
18.6
26.2
33.8
41.4
49.1
56.7
64.4
72.0
79.6
3. Measurements
Each group will get about 20 minutes max to perform measurements and afterward, if time allows
after, groups needing/wanting more time may continue with measurements. Measure as best you can
with the equipment and instrumentation at hand the locations of the Venturi ports in the x-direction
with respect to the inlet of the Venturi. Adjusting the rheostat adjusts the test section wind velocity. For
this lab you will run two speeds. The two speeds you choose should show noticeable level changes in
manometer tube heights. A setting close to 60 and subsequent setting between 80 and 90, for example,
would suffice. Note that you need to let the flow settle before taking any measurement after changing
the speed. Use hand pump to CAREFULLY (small quick pumps) check which pressure port coincides with
which manometer tube. Set up data record sheet similar to the following (Do not throw this away.
Retain your original data sheet and add it to your report!):
Venturi Lab Raw Data Sheet (Date)
Group#: Section#:
Group Members:
Lab Monitor:
Room Conditions: P = ???±σP, T = ???±σT
Ruler Used:
Tunnel Condition 1:
Tunnel Condition 2:
Manometer
Tube
ATM
ATM
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
Measured
Item
atm
atm
Ps inlet
V 01
V 02
V 03
V 04
V 05
V 06
V 07
V 08
V 09
V 10
V 11
V 12
Ps probe
Pt probe
atm
atm
atm
Man. Height
[mm] ±σh
Tunnel Setting 1
Tunnel Setting 2
1
2
3
1
2
3
Figure 2: Example data record sheet
A manometer will be used to measure pressure along the Venturi and at other relevant locations during
the experiment. At each rheostat setting, cycle through the manometer measurements AT LEAST 3
times. More data will not lead to extra effort in data reduction. For each cycle, one person will read the
manometer level with a single transparent ruler (1, 2 or 3). Measure the manometer level of each tube
with a common base location for each tube. The fluid in the manometer will have a slight meniscus
owing to capillary effects. Be sure to measure your manometer height at the same meniscus location for
each reading. Make note of which ruler and stick with it and don’t change as each ruler has a slightly
different offset. Another person will record what the manometer reader measures to the raw data
record. Third person can oversee tunnel (monitor Pitot-static probe orientation, for example). Students
will rotate tasks once so that each has an opportunity to read the manometer. Compare the total
pressure reading with that of the atmospheric pressure reading. What can you ascertain from this
comparison? Retain original measured units on raw data sheet. Ultimately, all measured units will be
put into common units of [kg], [m], and [s] in another column. Keep this original hand written data sheet
(if used… laptop recording of data is OK) as it will be added to final report.
Figure 3: Illustration manometer heights at various pressure locations.
4. Reduction of Data
Lecture notes covering material for this laboratory have already been introduced. These notes along
with literature and notes from ME 143 Fluids contain ample information regarding how to reduce your
measured values of manometer heights and room density to velocity and mass flow.
4.1. Velocity Reduction Method 1: Bernoulli equation
Using the Bernoulli equation (a relation of mechanical energy conservation acting on the fluid) for the
upstream pressure tap and the 12 pressure taps distributed along the bottom wall, determine the
relation between the velocity inside the tunnel, the densities of air and water, and the height of water in
the manometer. You will assume pressure variations in the vertical direction are negligible. Density
calculated at atmospheric pressure (given to you) and ambient temperature (given to you as well) is
constant throughout the tunnel- thus, an incompressible flow field. Manometer tubes that are not
connected to any pressure tap are measuring the room’s ambient pressure. Bear in mind that the
manometer measurement is a gage pressure measurement, where:
=
−
For these measurements,
is atmospheric pressure, because the liquid reservoir is open to room
atmospheric pressure. The pressure taps are connected to the top of the manometer bank, and the
bottom of each tube has liquid from the reservoir that is open to atmosphere. Since the static pressure
values are all less than atmospheric pressure, the liquid in each tube that is attached to a pressure tap in
the Venturi section is displaced upward. Please make sure that you explain this in your report.
Velocity at each Venturi port can be calculated using Bernoulli relation:
=
+
1
2
Static pressure at each port location can be determined from respective manometer height:
−
=
|ℎ − ℎ
|
Manometer fluid is water whose density ( ) is standard water density of 1000 kg/m3 even with red food
coloring.
You are asked to derive the velocity at each pressure tap location from the static pressure
distribution, which means that you need to solve for velocity in terms of the pressure difference, and
then write the pressure difference in terms of the manometer measurement. This should give a formula
relating velocity to measured parameters (which include manometer height difference):
=
2
|ℎ − ℎ
|
What are all relevant measured parameters for this velocity relation? At this point it is good practice to
check if your calculations are more or less in the ballpark of the wind tunnel’s capabilities. Compare your
reduced inlet velocity with respective rheostat setting and manufacturer listed tunnel velocity range of
0-90 MPH. If your reduction is correct, the values should be close to this factory inlet velocity estimate.
4.2. Velocity Reduction Method 2: Conservation of Mass
For the second part of the lab, students are given the local dimension (height and width) at each of
the pressure tap locations and asked to find the velocity at each station from conservation of mass. We
will assume that the flow is uniform and unidirectional. Using the conservation of mass, determine the
velocity at the centerline location of the sections corresponding to port 1 to 12. The conservation of
mass states that:
̅∙
= constant
for any cross section A of the wind tunnel and ̅ and are the velocity vector and vector normal to A, at
any point on A. This can be reduced to a common form of mass flow:
'( =
)*
= const.
)*
Initially, calculate inlet mass flow, '(, which is constant through the tunnel via inlet conditions. Use
Bernoulli relation at inlet to calculate inlet velocity:
)*
=
2
−
)*
2
=
|ℎ − ℎ
)*
|
With constant mass flow determined, calculate velocity at each Venturi port using a relation
incorporating all relevant measured parameters:
=
'(
What are all relevant measured parameters for this velocity relation? In order to develop a relevant
uncertainty model for velocity, each measured quantity used to determine velocity must have with it a
corresponding error recorded.
5. Analysis and Discussion for Report
Both methods rely on the measurement of velocity by a pressure tap. You will be required to
compare the magnitudes of both methods for the two velocity settings. Student lab reports need to
show how velocities were obtained from both methods using the measured static pressure distributions.
The formulas used should be in the body of the report in a clear presentation. They need to include the
data, which are comprised of the measured values and the calculated results from the measurements.
Also explain:
•
•
•
why all the static pressure values are all less than atmospheric pressure in terms of a conserved
analysis quantity of the Bernoulli equation.
why atmospheric pressure and total pressure are identical.
how a flow boundary layer would theoretically affect your pressure measurements, Bernoulli
equation analysis, and the mass flow conservation analysis even though we are assuming an
inviscid flow.
You are also required to ascertain the uncertainty on velocity measurements for both velocities. To
compare uncertainty of both methods, you are required to develop a velocity uncertainty equation
derived from all measured parameters for both methods. Recall the general expression for uncertainty
as explained in your notes:
,- =
1
1
1
1
,./ 0
4 + ,.5 0
4 + ,.6 0
4 + ⋯ + ,.9 0
4
123
12
127
12)
Using a measured parameter sensitivity analysis (described in Lecture 1), determine which measured
values affect the precision of your measurements the most (and least).
When presenting your results graphically, think about what is important to show and how can you
most efficiently and effectively communicate you results in a single figure of representative data. One
suggested means to graphically portray your results is as follows:
In a first plot:
• Plot all static pressures and dynamic pressures in Venturi for both tunnel settings vs. s-direction
distribution of venture locations on a single plot.
• In a plot just below and lined up coincidentally with x-direction distribution values of your Venturi
port locations, show the area distribution along the Venturi.
• Be sure to show error/uncertainty bars where applicable on the plot.
In a second plot:
• Plot all reduced velocities for both cases and both tunnel settings vs. s-direction distribution of
venture locations on a single plot.
• In a plot just below and lined up coincidentally with s-direction distribution values of your Venturi
port locations, show the area distribution along the Venturi.
• Be sure to show error/uncertainty bars where applicable on the plot.
Adhere to the standard lab write-up template supplied to you.