Post on 27-Feb-2018
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect1
MAE 123 : Mechanical Engineering Laboratory II - Fluids
Laboratory 2: Venturi LabDr. J. M. Meyers | Dr. D. G. Fletcher | Dr. Y. Dubief
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect
Daniel Bernoulli
Bernouli Equation
2
Introduction
• The Bernoulli Equation can be considered to be a
statement of the conservation of energy principle
appropriate for flowing fluids.
• ASSUMPTIONS:
• Steady Flow
• Incompressible flow (� = �����.), M<0.3
• Frictionless flow
• This relation does not account for heat added to or
work done on the flow thus only a conserved
mechanical energy system is valid
• Mechanical energy = working fluid energy that can
be converted entirely to work by an ideal device
Definitions: Mechanical energy (ME 040)
�� =�� +
12�
� + �� = constant
Flow along a single streamline
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect3
Introduction
Giovanni Battista Venturi
Venturi Effect
� ⇒ �
• Assuming constant mechanical energy of a fluid along
a streamline (or within a streamtube) velocity of the
fluid increases as the cross sectional area decreases:
• Static pressure correspondingly decreases:
� ⇒
• According to the Bernouli Equation, fluid velocity
must increase as it passes through a constriction and
static pressure must decrease to satisfy the principle
of continuity and conservation of mechanical energy.
• Thus any gain in kinetic energy a fluid may accrue due
to its increased velocity through a constriction is
negated by a drop in static pressure.
�� =�� +
12�
� + ��
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect4
Streamlines and Streamtubes
Streamline
• A line tangent everywhere to the
velocity vector at a given instant
• A pathline is the actual path traveled by
a particle
• Stream lines and pathlines are identical
in steady flow
Streamtube
• A closed pattern of flow comprised of many
stream lines.
• Fluid within streamtube is confined… no
flow across streamtube boundary!
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect5
Definitions: Mechanical energy (ME 040)
Mechanical energy = working fluid energy that can
be entirely converted to work by an ideal device
This form only valid for incompressible flows. From first law of TD this quantity is a constant and
variations between streamline/streamtube locations are:
This definition comes from ME 040 --
Thermodynamics C&B p. 59
•Neglects frictional effects -- inviscid
•If no energy is exchanged with surroundings then
the first law of TD implies: �� =�� +
12�
� + ��
Compressible Flow
(! ≠ const.const.const.const.)Incompressible Flow
(! = const.const.const.const.)
�� = const.
�� − �$� + 12 �� − �$ � + � �� − �$ = 0
Incompressible Flow
(! = const.const.const.const.)
1
2 1
2streamlinesstreamtubes
Bernoulli Equation Applied Along Streamlines and Streamtubes
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect
•Note the differences in reference point for different pressure
measurements
•Gage pressure is measured relative to atmospheric pressure – very
common and typical of a tire pressure gage
•Vacuum pressure is also measured relative to atmospheric pressure
(typical of many vacuum gages)
•You can avoid mistakes by working in absolute pressure which is
pressure measured from a vacuum reference
6
GAGE AND ABSOLUTE PRESSURE
Pressure is an essential measurement when
dealing experimentally with Bernoulli’s relation
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect7
• Relations do not depend on cross sectional area of tube but must
be large enough to avoid capillary flow
Manometer
Liquid (�&)
∆� = ℎ = ∆��&� =
�) − �*�&�
• Elevation change in fluid at rest is:
• This illustrates how a fluid column can be used to measure
pressure and is the working principle of a manometer
• Pressure is constant in horizontal direction, P1 = P2
• So the pressure of the gas in the tank is found from the force
balance on the liquid column is
MEASUREMING PRESSURE: MANOMETER
+
,
• With a manometer we take advantage of the laws of fluid
statics to measure pressures in fluid dynamic environments
• This is hydrostatic force balance. Note: �* > �) = �*.
�* = �) + �&�ℎ
�& ≡density of
manometer liquid
�* > �)So indeed
• Gravitational affect on gases is very small (thus gas in the tank is
all at Pa )
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect8
MEASUREMING PRESSURE: ELECTRONIC TRANSDUCER
A transducer is a device that converts input energy of one
form into output energy of another through some physical
process that is to be measured.
These include , piezoelectric crystals, microphones,
photoelectric cells, thermocouples, and pressure transducers.
A pressure transducer is a transducer that converts pressure
into an analog electrical signal that can be recorded by
electrical DAQ systems.
Strain Gage
Pressure Transducer
Capacitive
Pressure Transducer
Piezoelectric
Pressure Transducer
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect9
Definitions: Total Pressure: the sum of the static pressure and dynamic pressures
�.0.*1 = �2.*.3� + �456*3� = �2.*.3� +12��
�
Static Pressure, Velocity Pressure, and Total Press ure
Static Pressure
Measurement
StaticAtmospheric
Atmospheric Static
Total Total
Total Pressure
Measurement
Dynamic Pressure
Measurement
This part of the
illustration is wrong…
can you see why?
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect10
•A wind tunnel starts with atmospheric air drawn in from the room
•In the room, the velocity is zero, the air is at rest from a macroscopic view (although there is
microscopic motion, and that is how pressure is measured
•This room measured air static pressure is equal to the tunnel total pressure!!
•The relation is derived from the Bernoulli equation for horizontal flow (∆ℎ = 0) between two
points in the flow that follow the same streamline are:
which can also be written as:
�.0.*1 = �2.*.3� +12��
� = constant
�� − �$� + 12 �� − �$ � = 0
�$ +12��$
� = �� +12���
�
Static Pressure, Velocity Pressure, and Total Press ure
Incompressible Flow
(! = const.const.const.const.)
1
2
streamlines
Definitions: Total Pressure: the sum of the static pressure and dynamic pressures
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect11
•The Pitot probe is a common instrument used to measure dynamic pressure and
so to find the flow velocity
•The central tube measures the total pressure of the flow (�2.*.3� + �456*3�)
•The outer tube functions in the same way that the pressure taps in the wall
function and senses the static pressure only as there is no velocity component
normal to the wall
Pitot Probe
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect12
� = 2 7�.0.*1 − �2.*.3�8�
Total
pressure
Static
pressure
We’re measuring the total pressure
and static pressure in this region
�.0.*1 = �2.*.3� +12��
� = constant
•So knowing that total pressure is constant, we can use
the static pressure distribution to infer the velocity
distribution
•As we said earlier, we assume that the flow is inviscid --
we ignore viscosity and we also make use of the fact that
at our low speeds, density is constant. The flow is
incompressible.
Pitot Probe: Calculating Velocity
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect13
Velocity from Mass Conservation of a Fluid
9: ≡ massflowrate
Simply stated, the mass flow rate of a fluid is defined as the
amount of travelling through an area per unit time.
Standard notation for mass flow rate is:
The mass flow rate at any location in the flow can be
determined from locally determined properties as:
9: = �AB
� ≡ density, A = area, andB = velocity
A$
A�
Incompressible Flow
(! = const.const.const.const.)
1
2
streamtubes
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect14
Velocity from Mass Conservation of a Fluid
A$
A�
Incompressible Flow
(! = const.const.const.const.)
1
2
streamtubes
If no mass of fluid is being removed or added across the
stream tube walls, then the mass flow rate of the fluid is
conserved and constant:
9$: = 9�:9: = constant �$A$B$ = ��A�B�
9: = �$A$B$ = ��A�B�B$ =
9:�$A$
B� =9:��A�
Keep in mind that for our low speed incompressible flow
applications we can assume density to be constant and
calculated from atmospheric conditions.
This means that if the mass flow rate can be determined at
any region in the streamtube, then the velocity at any
other point along the streamtube through knowledge of
local density and local area
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect15
UVM Low Speed 12”x12” Wind Tunnel (Flowtek 1440)
Plastic
Honeycomb Flow
Straightener
Test
Section
(12”x12”x36”)
2 HP Motor and
Fan Section
Diffuser
Section
Contraction
Cone
Data
Acquisition
Manometer
Tunnel
Controls
Flow Direction
(0-90MPH)
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect16
Venturi Experiment
A Venturi experiment is a good laboratory exercise to help understand the basic principles of Bernouli
equation and mass flow conservation.
Already installed in the test section is are two inserts with 10 or so static pressure taps along the surface
to create a Venturi effect.
A Pitot probe is also installed to measure the total pressure.
A static pressure measurement at the test section inlet will also be required.
You will be given the height of each tap location to estimate the area at each measurement location.
Pitot-static
probe
Inlet static
pressure port
HI
Test Section
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect17
(1) From room temperature and atmospheric pressure, calculate density
(2) Operate wind tunnel at two speeds. At each speed record:
a) 10 (or so) static pressure readings over Venturi from manometer
b) Inlet static pressure reading from manometer
c) Pitot pressure reading from manometer
d) Static pressure reading of Pitot-static probe from manometer (careful to take not
WHERE the measured location is in “H”.
c) Record the atmospheric pressure level of the manometer as this is needed for
reference.
Venturi Experiment: Measurements
At least 3 measurements for all the above are needed to calculate both a mean and a standard
deviation… but more are better, time permitting.
Test Section
Pitot-static
probe
Inlet static
pressure port
HI
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect18
Venturi Experiment: Data Reduction and Analysis
Determine a velocity profile along the Venturi installation at each measurement port using two
methods: conservation of mechanical energy and conservation of mass.
Method 1: Conservation of Fluid Mechanical Energy (Bernoulli relation)
• The total pressure acquired is constant.
• Measure the static pressure at each pressure tap location along the Venturi.
• Extract the dynamic pressure at each location from the Bernouli relation.
• Use dynamic pressure to calculate the velocity at respective pressure tap location.
Keep in mind you are recording differential pressures. You must record atmospheric pressure on the
manometer to extract an effective ∆J to relate toward your KL,LMN and OPQ,RMN measurements
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect19
Venturi Experiment: Data Reduction and Analysis
Method 2: Conservation of Mass
• Envision the flow through the tunnel as one large streamtube.
• Measured total and static pressure yield the dynamic pressure upstream of the Venturi.
• Calculate velocity in this region.
• Calculate density in this region from temperature and static pressure.
• Calculate mass flow which is constant throughout the Venturi.
• Using the supplied thickness of Venturi at each station and calculate respective area.
• Calculate velocity at each pressure tap location with calculated area, density, and area.
Determine a velocity profile along the Venturi installation at each measurement port using two
methods: conservation of mechanical energy and conservation of mass.
ME 123: Mechanical Engineering Lab II: Fluids
Laboratory 2: Venturi Effect
ST = SUV�WAWH$
�+ SUX�
WAWH�
�+ SUY�
WAWHZ
�+⋯+ SU\�
WAWH6
� General Form for
the Expression of
Uncertainty
H̅6 =1^_ H6 3
3
SU\� =1
^ − 1_ H6 3 − H̅6 �`
3a$
Practically, the variances are expressed as:
Recall general expression for propagation of error:
Evaluating this is simply based on finding the mean value:
20
Venturi Experiment: Data Reduction and Analysis
• Which method, did you find, to be the most accurate and precise in your analysis?
• Perform a sensitivity analysis to identify the most significant contributors to overall uncertainty.
• Provide suggestions to improve upon said uncertainties
• Estimate uncertainty for both methods