MAE 123 : Mechanical Engineering Laboratory II -Fluids ...jmmeyers/ME123/Lectures/ME123 Lecture...

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


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



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�

� + ��



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!



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


1

2 1

2streamlinesstreamtubes

Bernoulli Equation Applied Along Streamlines and Streamtubes



•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



• 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 )



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



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?



•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


1

2

streamlines

Definitions: Total Pressure: the sum of the static pressure and dynamic pressures



•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



� = 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



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


1

2

streamtubes



Velocity from Mass Conservation of a Fluid

A$

A�

Incompressible Flow


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



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)



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



(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



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




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.



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


• 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

MAE 123 : Mechanical Engineering Laboratory II -Fluids ...jmmeyers/ME123/Lectures/ME123 Lecture...

Documents

Transcript of MAE 123 : Mechanical Engineering Laboratory II -Fluids ...jmmeyers/ME123/Lectures/ME123 Lecture...