MCG 3330 FLUID MECHANICS I
LABORATORY SESSIONS
Professor S. Tavoularis
Department of Mechanical Engineering
University of Ottawa
September 2008
© Copyright Stavros Tavoularis, 2008
MCG 3330 FLUID MECHANICS I / Laboratory Instructions / Prof. S. Tavoularis
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JET IMPACT - MOMENTUM EQUATION
1. Objective
The objective of this laboratory session is to measure the force of a water jet impacting on objects
and to compare it to an estimate based on the momentum equation.
2. Apparatus and Instrumentation
The experiment is performed using a hydraulics apparatus manufactured by TecQuipment Ltd.
Water is supplied in closed loop by a pump. The flow rate is determined with the use of a weighing
tank and a stopwatch. The water issues vertically upwards into the air, through a nozzle with a
diameter of 9.5 mm. Two objects are available: a flat plate and a hemispherical cup. Each object
can be mounted on a horizontal lever above the water jet and receive its impact. The force on the
object can be determined with the use of weights that can be hanged at different positions on the
lever. Notice that the water jet is under atmospheric pressure; then, one may neglect friction to use
Bernoulli’s equation, which shows that the water velocity would be approximately constant along
its path, which is tangential to the object surface. A force balance on the zeroed lever is performed
on the following page.
3. Instructions for the Experiments
Additional details for the use of the apparatus and specifications for the experiments to be conducted
will be provided by the instructor.
a) Study carefully the layout and components of the apparatus and familiarize yourselves with all
controls and measuring instrumentation. Identify the measured properties and their units.
b) Conduct the Jet Impact experiment:
• level the apparatus and set the lever at its balance position
• attach the hemispherical cup and centre the jet by adjusting the three screws at the base to
produce axisymmetric flow on the cup
• adjust the mass flow rate of water and then measure it; start by adding a certain weight and
fill the tank until the lever arm lifts off its cradle; at this time, quickly add another weight
and measure the time that it takes for the lever to lift from its cradle for a second time; note
that the value given on the weights is the actual weight (in lbf) of water added to the tank
• measure the force on the cup by properly positioning the weight (see procedure below)
• repeat the test for a second flow rate, as specified
• replace the cup by the flat plate and repeat the tests
c) Prepare a brief report of your measurements and calculations. All results should be presented
in clear tables and graphs, when necessary. Solve the momentum equation for both the cup and
the plate, and compare these estimates with the measured forces. Discuss any differences,
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MCG 3330 FLUID MECHANICS I / Laboratory Instructions / Prof. S. Tavoularis
explain possible reasons for them, and list the percent differences in a table.
Procedure for measuring the impact force
First balance the lever without the jet (Figure 1a) by moving the weight left or right. Balance of
moments about the pivot point gives
LsFs = LfFw
Next activate the jet (Figure 2a) and balance the lever once again. Note that, in both cases, the spring
has been stretched by exactly the same amount, so that the spring force and the corresponding
moment about the pivot point are the same in both cases. A moment balance on the new system
yields
LsFs = (Lf + ΔX) Fw - LfFj
Equating the right-hand sides of the two equations above gives
Fj = Fw ΔX/Lf
where Fj and Fw are measured in lbf and ΔX, Lf are measured in inches. It is given that Lf = 6 in and
Fw = 1.20 lbf.
Figure 1 Sketch of the jet impact force measurement apparatus a) without the
jet and b) with the jet.
MCG 3330 FLUID MECHANICS I / Laboratory Instructions / Prof. S. Tavoularis
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CHANNEL FLOW - BERNOULLI’S EQUATION
1. Objective
The objective of this laboratory session is to measure the static pressure variation in water flow
along a converging-diverging channel and to compare it to estimates based on Bernoulli’s equation.
2. Apparatus and Instrumentation
The experiment is conducted in a variable cross-section (convergent-divergent) channel system,
manufactured by Armfield Engineering Ltd. The water flow is maintained by a pump and its flow
rate is measured by timing the discharge. The channel width is 38 mm. Pressure taps, connected
to vertical tubes acting as manometers, are located along the upper wall of the channel as follows
(x is the axial distance from the inlet plane of the channel).
Tap
a
b
c
d
e
f
g
h
x [mm]
25.4
63.5
88.9
114.3
139.7
165.1
190.5
215.9
Tap
i
j
k
l
m
n
o
x [mm]
241.3
266.7
292.1
317.5
342.9
368.3
406.4
3. Instructions for the Experiments
Additional details for the use of the apparatus and specifications for the experiments to be conducted
will be provided by the instructor.
a) Study carefully the layout and components of the apparatus and familiarize yourselves with all
controls and measuring instrumentation. Identify the measured properties and their units.
b) Conduct the Channel Flow experiment:
•
measure and tabulate the elevation of the top wall of the channel at the locations of the
pressure taps; use the flat plate base as a datum
•
measure and tabulate the corresponding elevations of the bottom wall of the channel
•
calculate the channel cross sectional areas at the locations of the taps
•
adjust the flow rate of water and then measure it; start by adding a certain weight and fill the
tank until the lever arm lifts off its cradle; at this time, quickly add another weight and
measure the time that it takes for the lever to lift from its cradle for a second time; note that
the value given on the weights is the actual weight (in lbf) of water added to the tank
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MCG 3330 FLUID MECHANICS I / Laboratory Instructions / Prof. S. Tavoularis
•
estimate the average flow velocity and the dynamic pressure at the cross-section of each tap
•
measure the static pressure at each tap by measuring the height of the water in the
corresponding standpipe
•
apply Bernoulli’s equation along a streamline coinciding with the top wall of the channel to
estimate the static pressure pest at the location of each tap, assuming negligible pressure
losses in the channel and uniform velocity across each cross-section; use tap “a” as a
reference
•
compare the measured and estimated values of the static pressure at each tap
•
compute the sum of the total pressure: pmeas + ½DV 2 + Dgz at the locations of the taps, and
plot it vs. x
•
repeat above steps for a different flow rate
c) Prepare a brief report of your measurements and calculations. All results should be presented
in clear tables and graphs, when necessary. Discuss your findings, identify any differences
between measured and estimated values, explain possible reasons for such differences, and list
the % differences in a table.
MCG 3330 FLUID MECHANICS I / Laboratory Instructions / Prof. S. Tavoularis
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PRESSURE LOSSES IN INTERNAL FLOWS
1. Objective
The objective of this laboratory session is to measure frictional pressure losses in pipes, valves,
fittings and simple flow measuring devices.
2. Apparatus and Instrumentation
The tests are conducted in a "Fluid Friction Apparatus", manufactured by Armfield Engineering
Limited. The geometric specifications for the devices contained in this apparatus are listed in Table
1. Water flow is produced in a closed loop system by a pump. The main water line is divided into
several branches, the flow rate in each of which is controlled by individual valves. The flow rate can
be measured by timing the filling of a measuring tank. The pressure losses in the 6 mm pipe, which
is used for laminar flow tests, is measured using a pressurized water manometer. Pressure
differences for all other devices are measured with a mercury manometer.
3. Instructions for the Experiments
Further explanations for the use of the apparatus and specifications for the experiments to be
conducted will be provided by the instructor. Among the required tasks are the following.
a) Study carefully the layout and components of the apparatus and familiarize yourselves with all
controls and measuring instrumentation. Identify the appropriate taps to be used (see Table 2)
and the direction of flow in each of the pipes. Sketch the apparatus.
b) Start the pump. Measure the water flow rate using the stopwatch and one of the two tanks with
graduated scales at the system outlet. Note that the scales do not measure the absolute volume
in the tank, therefore it is necessary to measure a change in water level. Use the smaller or larger
tank, depending on the flow rate. For the laminar flow experiment, measure the flow rate from
tap #2 using the 500 ml plastic graduated cylinder.
c) Measure the friction coefficients for the specified pipes at the specified flow rate(s), according
to Table 2. Verify whether the flow between the two pressure taps used each time is fully
developed. Use the format of Table 3 to record your measurements and calculations. Compare
your results with values available in your fluid mechanics textbook.
d) Measure the loss coefficients and the equivalent pipe lengths for the specified fittings and
valves, according to Table 2. Use the format of Table 3 to record your measurements and
calculations. Compare your results with values available in your fluid mechanics textbook or
other sources.
e) Prepare a brief report of your measurements and calculations. All results should be presented
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MCG 3330 FLUID MECHANICS I / Laboratory Instructions / Prof. S. Tavoularis
in clear tables and graphs, when necessary. Determine the percent differences between measured
and estimated friction and loss coefficients and explain the possible reasons for such differences.
Table 1: Geometrical Specifications for the Different Devices
Device
Specifications
Pipes
Smooth pipe (topmost)
ID: 22 mm
Roughened pipe
ID: 19 mm; average roughness height: 0.5 mm
Smooth pipe
ID: 18 mm
Smooth pipe
ID: 6 mm
All pipes have a length of 2.40 m and are equipped with three pressure taps spaced at 1.00 m
Fittings
Bend (right angle)
ID = 28.5 mm; radius = 106 mm; z39 - z36 = 218 mm
Elbow (right angle)
ID = 28.5 mm; z37 - z38 = 104 mm
Elbow (45)
ID = 28.5 mm; z28 - z23 = 64 mm
Elbow (45)
ID = 28.5 mm; z23 - z20 = 56 mm
Valves
Globe valve
pipe ID = 28.5 mm
Gate valve
pipe ID = 28.5 mm
Butterfly valve
(from tables, Le/D•20)
pipe ID = 28.5 mm
Table 2: Measurements to be Conducted
Device(s)
Flow Rate(s)
Manometer
6 mm pipe
Maximum and two others
Water
22 mm pipe
Maximum and two others
90° bend
90° elbow
Both 45° elbows
The three valves,
fully open
Maximum
Mercury
MCG 3330 FLUID MECHANICS I / Laboratory Instructions / Prof. S. Tavoularis
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Table 3: Measurements and Calculations
Manometer Readings Pressure
Hg H2O hA
hB
PA-PB
f, K, or
Le/D
From
Textbook
Friction Coefficient etc.
Measured
Tap B #
Pressure Drop
Tap A #
Re
Q
Volume
Time
Device
Area
Flow Rate / Reynolds No.