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Last Rev.: 12 JUL 08Flow Meters Lab : MIME 3470
Page 2
Grading Sheet
~~~~~~~~~~~~~~MIME 3470Thermal Science
Laboratory~~~~~~~~~~~~~~Experiment . 4 Flow Meters Students Names
Section POINTS SCORETOTAL
APPEARANCE10
ORGANIZATION 5
ENGLISH and GRAMMAR 10
MATHCAD
Ordered Data, Dimensions, Physical Properties7
VENTURI METER: COMBINED PLOT: (hflow vs. Qtheo & (hflow vs.
Qact
5
PLOT OF Cv vs. Re 5
ORIFICE METER: COMBINED PLOT: (hflow vs. Qtheo & (hflow vs.
Qact
5
PLOT OF Co vs. Re5
TURBINE METER: PLOT OF Qact vs. Qind5
REGRESSED & PLOTTED CALIBRATION LINE8
ROTAMETER: PLOT OF Qact vs. Qind5
COMBINED PLOT: (h fric vs. Qact FOR THE 4 METERS 5
DISCUSSION OF RESULTS10
CONCLUSIONS10
ORIGINAL DATASHEET 5
TOTAL100
Comments
GRADERd
MIME 3470Thermal Science Laboratory~~~~~~~~~~~~~~Experiment .
4Flow Meters
~~~~~~~~~~~~~~
Lab Partners: Name Name
NameName
NameNameSectionExperiment Time/Date:Time,
date~~~~~~~~~~~~~~ObjectiveThe objective of this experiment is to
familiarize the student with few of the more common types of flow
meters used in engineering applications and to compare
performances. The students will construct calibration curves and
determine meter flow characteristics such as discharge coefficients
and friction drop.IntroductionThere are many different meters used
to measure fluid flow: the turbine-type flow meter, the rotameter,
the orifice meter, and the Venturi meter are only a few. Each meter
works by its ability to alter a certain physical property of the
flowing fluid and then allows this alteration to be measured. The
measured alteration is then related to the flow. The subject of
this experiment is to analyze the features of certain
meters.TheoryThe operating principles of these various meters need
to be developed in order to meaningfully compare their
performance.The Venturi Meter The Venturi meter is constructed as
shown in Figure 1. It has a constriction within itself. When fluid
flows through the constriction, it experiences an increase in
velocity. This increase in velocity causes a decrease in static
pressure at the constriction (throat). The greater the flow, the
greater the pressure drop at the throat. The pressure difference
between the upstream and the downstream flow, hflow, can be found
as a function of the flow rate. Applying Bernoullis equation to
points ( and ( of the Venturi meter and relating the pressure
difference to the flow rate yields
(1)or
.(2)This equation relates the pressure difference, hflow, to the
flow rate Qtheo, and represents the theoretical curve for the
Venturi meter.
To determine Qtheo, first, one needs to find the relationship
between the velocities V1 and V2 using Bernoullis equation.
.
(3)Forandand z1 = z2
(4)Knowing that V = Q/A and Q1 = Q2 = Q
.(5)Thus,
.(6)The Venturi meter is characterized by small pressure losses
due to viscous shear and frictional effects. Thus, for any hflow,
the actual flow rate will be less than the theoretical flow
rate.
(7)where Cv is the Venturi meter discharge coefficient. As flow
increases, the discharge coefficient for a Venturi meter levels off
at about 0.9. Note: Reynolds number for the Venturi meter is based
on the inlet diameter not the throat diameter. The Orifice Meter:
The orifice meter consists of a throttling device (an orifice
plate) inserted in the flow. This orifice plate creates a
measurable pressure difference between its upstream and downstream
sides. This pressure is then related to the flow rate. Like the
Venturi meter, the pressure difference varies directly with the
flow rate. The orifice meter is constructed as shown in Figure
2.
Figure 2Cutaway view of the orifice meter [1]Applying Bernoullis
equation to points and yields
.(8)For any pressure difference, hflow, there will be two
associated flow rates: the theoretical flow rate from the above
equation and the actual flow rate measured in the laboratory. As in
the Venturi meter case, the difference between these flows is
indicated by a discharge coefficient ,Co, defined as
.(9)With increasing flow, values for the discharge coefficient
level off at around Co ( 0.8 for the orifice meter. Referring to
Figure 2, recall that Bernoullis equation was applied to Points and
. However, because it is difficult to place a pressure tap in the
orifice itself, pressure measurements are actually made at and . So
the reader asks: how accurate can such a measurement be? Reference
4 explains that (see Figure 3) the flow at is almost the same as
the slug of flow at and thus the pressures are almost the same.
This is true for a short distance downstream of the orificethen
pressure recovery sets in. With these assumptions, Bernoullis
equation is the same, except pressure measurements are made at
instead of .It should also be noted that the shape of the orifice
is important to the flow quality.
Figure 3(a) The approximate velocity profiles at several planes
near a sharp-edged orifice plate. Note: the jet emerging from the
hole is somewhat smaller than the hole itself; in highly turbulent
flow the jet necks down to a minimum cross section at the vena
contracta. Note that there is some backflow near the wall. (b) It
is assumed that the velocity profile at is given by the approximate
profile shown. It is also assumed that the velocity profile at is
uniform [4]. From boundary layer theory, the pressure of the plug
flow at is transmitted across the (assumed stagnate) interval from
the plug to the pressure port. The Turbine-type Flow Meter: The
turbine-type flow meter consists of a section of pipe into which a
small turbine is placed. As the flow travels through the turbine
blades, the turbine spins at an angular velocity proportional to
the flow rate. After a certain number of revolutions, the turbine
sends an electrical pulse to a preamplifier which, in turn, sends
the pulse to a digital totalizer. The totalizer in effect sums the
pulses and translates them to a digital readout which gives the
volumetric fluid flow that pass through the meter. In addition, the
totalizer will show the actual flow rate of the fluid. Figure 4 is
a schematic of the turbine-type flow meter. The Variable Area Meter
(Rotameter): The variable area meter consists of a tapered metering
tube and a float that is free to move inside the tube. The tube is
mounted vertically with the inlet at the bottom. At any flow rate
within the operating range of the meter, fluid entering the bottom
raises the float and the tube inside diameter increases (because of
the tapering). The flow rate is indicated by the float position
read against the graduated scale.
Figure 5The rotameter and its operation [1] Three common types
of graduated scales are: 1.Percent of maximum flowa meter factor is
given or deter-mined to convert a scale reading to a flow rate.
Many fluids can be used with the meter, the only variable being the
scale factor. 2.Diameter ratio typea calibration curve is
associated with the ratio of the tubes cross-sectional diameter to
the diameter of the float. 3.Direct readinga scale shows actual
flow rate in the desired units. Experimental Procedure: The fluid
meter apparatus is shown in Figure 6. It consists of a centrifugal
pump that draws water from a tank and pumps it to any of the four
meters. In testing any of the four meters, the actual flow, Qact,
is measured by diverting the flow to the collec-tion tank
(volumetric measuring tank) which is graduated in gallons, and
measuring with a stopwatch how long it takes to collect a volume of
water. Strive for collection times in excess of 1 minutea little
extra time spent in collecting good data significantly improves the
quality of the results.
For all four meters, the flow is regulated by the upstream
valve. For several valve positions, record the appropriate meter
data that indicates flow rate, the actual flow rate, and the
pressure drop across the meter, (hfric, which is measured with a
manometer. Be extremely careful that the pressure differences to be
measured by manometers are not so great that the water column on
either side of the manometer goes over the top of the inverted
U-shaped manometer tube. Thus, it is recommended that one
establishes a maximum flow that does not cause this problem by
adjusting the upstream valve. Then subsequent, lesser, flow can be
set by slightly closing the valve. The data particular to
individual meters is discussed next.Venturi MeterSee warning just
above about maxing out the manometers. Two manometers are
associated with this meter. The first manometer measures the total
frictional pressure drop across the entire length of the Venturi
meter, (hfric, as a difference in head pres-sure. The second
manometer measures the head pressure difference, (hflow, between
points and of Figure 1. From (hflow, the theore-tical volumetric
flow rate, Qtheo, can be determined from Equation 6. For your
report, on one graph, plot (hflow vs.
Figure 6Flow Meters ApparatusOrifice MeterUse the procedure and
write up requirements as spe-cified for the Venturi meter. The
expected discharge coefficient is 0.8.Turbine-Type Flow MeterThe
totalizer reading is the measure of indicated or theoretical flow.
The actual flow is still measured using the collection tank and a
stopwatch. For your report, plot the measured flow rate against
(vs.) the flow rate reading and determine and plot a regressed line
of this data all on the same graph. This is a calibration curve.
The Mathcad linear regression function is documented at the right
(source Mathcad Help). RotameterFor the rotameter, record the
position of the float, the pressure drop across the meter, and the
measured flow rate. For your report, plot the measured flow rate
vs. indicated flow rate. Again a calibration curve; but without
regression. Finally, on one graph, plot friction pressure drops,
(hfrict, across each meter vs. the actual flow rate through the
meter. REFERENCES
1.Flowmeters: Introduction, efunda (engineering fundamentals),
http://www.efunda.com/DesignStandards/sensors/flowmeters/flowmeter_intro.cfm
2.Simon & Schuster New Millennium Encyc. & Reference
Library, 2000
3.Prandtl, L., and Tietjens, O.G., Applied Hydro- and
Aeromechanics, Dover Pubs., 1957. [Based on Prandtls Lectures.
Composed by Prandtls student, Tietjens, who turned the lecture
notes into a text. Translated by J.P. Den Hartog. First published
by United Engineering Trustees, Inc., 1934]
4.Bird, R.B., Stewart, W.E., & Lightfoot, E.N., Transport
Phenomena, John-Wiley & Sons, 1960.
5.Ross, S.M. (1998), A First Course in Probability, 5th ed.,
Prentice-HallOrdered Data, Calculations, and Results
DISCUSSION OF RESULTS
CONCLUSIONS
APPENDICES
Appendix AClepsydras (water thief), Ancient Fluid Meters When
one thinks of a fluid meter, they envision a device that ascertains
a flow rate per unit of time. The ancients looked at flow meters
the other way aroundthey used fluid meters to determine a unit of
time per flow rate.
In this experiment, the student used a stopwatch to time a flow
into a catch basin to determine a flow rate. With water clocks, a
known flow rate is used and the tank becomes the stopwatch.
Water Clocks
Source: National Institute of Standards and Technology Physics
Laboratory
Water clocks were among the earliest timekeepers that didn't
depend on the observation of celestial bodies. One of the oldest
was found in the tomb of Amenhotep I, buried around 1500 BC. Later
named clepsydras (water thief) by the Greeks, who began using them
about 325 BC, these were stone vessels with sloping sides that
allowed water to drip at a nearly constant rate from a small hole
near the bottom. Other clepsydras were cylindrical or bowl-shaped
containers designed to slowly fill with water coming in at a
constant rate. Markings on the inside surfaces measured the passage
of hours as the water level reached them. These clocks were used to
determine hours at night, but may have been used in daylight as
well. Another version consisted of a metal bowl with a hole in the
bottom; when placed in a container of water the bowl would fill and
sink in a certain time. These were still in use in North Africa
this century.
More elaborate and impressive mec-hanized water clocks were
develop-ped between 100BC and 500 AD by Greek and Roman horologists
and astronomers. The added complexity was aimed at making the flow
more constant by regulating the pressure, and at providing fancier
displays of the passage of time. Some water clocks rang bells and
gongs, others opened doors and windows to show little figures of
people, or moved pointers, dials, and astrological models of the
universe. A Greek astronomer, Andronikos, supervised the
construction of the Tower of the Winds in Athens in the 1st century
BC. This octagonal struc-ture featured a 24-hour clepsydra and
indicators for the eight winds from which the tower got its name,
and it displayed the seasons of the year and astrological dates and
periods. The Romans also develop-ped mechanized clepsydras, though
their complexity accomplished little improvement over simpler
methods for determining the passage of time. In the Far East,
mechanized astronomical/astrological clock making developed from
200 to 1300 AD. Third-century Chinese clepsydras drove various
mechanisms that illustrated astronomical phenomena. One of the most
elaborate clock towers was built by Su Sung and his associates in
1088 AD. Su Sung's mechanism incorporated a water-driven escapement
invented about 725 AD. The Su Sung clock tower, over 30 feet tall,
possessed a bronze power-driven armillary sphere for observations,
an automatically rotating celestial globe, and five front panels
with doors that permitted the viewing of changing mannikins which
rang bells or gongs, and held tablets indicating the hour or other
special times of the day. Since the rate of flow of water is very
difficult to control accurately, a clock based on that flow can
never achieve excellent accuracy.
http://www.infoplease.com/ipa/A0855491.html
SU-SUNG'S CLOCK
Today, Su-Sung's wonderful clock. The University of Houston's
College of Engineering presents this series about the machines that
make our civilization run, and the people whose ingenuity created
them.
When 16th-century Jesuit missio-naries went to China, they found
time-keeping in a deplorable state. Not even sundials were
reliable! And the clocks they brought as gifts were seen only as
playthings. Timekeeping was hardly on China's radar screen. Of
course, the purpose of all ancient clocks was not so much the
simple telling of time as it was display. Old clocks typically had
bells and dials, and they displayed planetary motions.
In the West, water clocks had evolved from remote antiquity
until mechanical clocks finally replaced them seven hundred years
ago. The Greek name for a water clock was clepsydra. That means "a
stealer of water" because all water clocks depended on a steady
flow of water to meter time. Greco-Egyptian engineers of the 2nd
century BC had added feedback control to regulate the water flow.
That idea was carried forward by Arab artisans until the Moors of
medieval Spain were building the finest clocks in the West.
The Chinese had also built water clocks for millennia, but
without feed-back control. In Western water clocks, a float on the
surface of a stea-dily draining tank drove the displays. But float
indicators exerted scant force for driving extra machinery. The
Chinese, on the other hand, created a new kind of
water-wheel-driven clock during the 8th to 11th centuries. A steady
inflow filled buckets around the rim, one at a time. As each bucket
became heavy enough to trip a mechanism, it fell forward carrying
the bucket behind into place under the water spout. That water
wheel provided power to drive displays of lunar cycles, the
movements of the heavens, and time as well.
Those clocks reached their apogee when the emperor of the Sung
dynasty charged an official, Su-Sung, with creating the grandest
clock that'd ever been built. Su-Sung assembled a team and finished
the clock by 1092. It was hugeforty feet high.
The tick-tock motion of the falling buckets has caused some
historians to call it a mechanical clock. But it had nothing
resembling the inertial escapement that began turning European
clocks into precision instruments by 1300. Neither did it have the
feedback control of Arab water clocks.
Invading Tatars stole the clock when they ended the Sung dynasty
in 1126. They couldn't get it running again, and the high art of
Chinese clockmaking disappeared. Even before the Tatar invasion,
Taoistic reformers had come into power and let the great clock fall
into disrepair. When Jesuits eventually brought Su-Sung's book on
clockmaking back to Europe, it astonished the West -- even though
the escapement clock was then light-years beyond it.
Su-Sung's clock seems to've been pretty accurate. Whether it
reached the fifteen-minute-a-day accuracy of the best Western water
clocks, we don't know. But, for a time, the Chinese were ahead of
the West once again, with the grandest clock in the world.
I'm John Lienhard, at the University of Houston, where we're
interested in the way inventive minds work. Temple, R., The Genius
of China. New York: Simon & Schuster Inc., 1986, pp.
103-110.
The following website provides a great deal of information on
Su-Sung's clock as well as detailed drawings in PDF format:
http://www.lucknow.com/horus/etexts/susung1.html.
by John H. Lienhard, Engines of Our Ingenuity
1580http://www.uh.edu/engines/epi1580.htm The Water Clock
Besides the gnomon or sundial, the Egyptians used the water
clock, which had the advantage over the former of showing time
during the night as well as during the day.
A complete example was found in the Amon Temple of Karnak
(Thebes), 25.5 north of the equator. This water clock dates from
the time of Amenhotep III of the Eighteenth Dynasty, father of
Ikhnaton. The jar has an opening through which water flows out;
marks are incised on the inner surface of the jar to indicate the
time. Since the Egyptian day was divided into hours which changed
in length with the length of the day, the jar has different sets of
markings for the various seasons of the year. Four time points are
prominently important: the autumnal equinox, the winter solstice,
the vernal equinox, and the summer solstice. The equinoxes have
equal days and nights in all latitudes. But on the solstices, when
either the day or the night is the longest of the year, the length
of the daylight varies with the latitude: the farther from the
equator, the greater is the difference between the day and the
night on the day of the solstice. This difference also depends on
the inclination of the equator to the plane of the orbit or
ecliptic, which is at present 23 . Should this inclination change,
or in other words, should the polar axis change its astronomical
position (direction), or should the polar axis change its
geographical position with each pole shifting to another point, the
length of the day and night (on any day except the equinoxes) would
change, too.
The water clock of Amenhotep III presented its investigator with
a very strange time scale. Calculating the length of the day of the
winter sol-stice, he found that the clock was constructed for a day
of 11 hours 18 minutes, whereas the day of the solstice at 25 north
latitude is 10 hours 26 minutes, a difference of fifty-two minutes.
Similarly, the builder of the clock reckoned the night of the
winter solstice to be 12 hours 42 min-utes, where as it is 13 hours
34 minutesfifty-two minutes too short. On the summer solstice, the
longest day, the clock anticipated a day of 12 hours 48 minutes,
where as it is 13 hours and 41 minutes, and a night of 11 hours 12
minutes, where as it is 10 hours 19 minutes.
On the vernal and autumnal equinoxes the day is 11 hours and 56
minutes long, and the clock actually shows 11 hours and 56 minutes;
the night is 12 hours 4 minutes long, and the clock show exactly 12
hours 4 minutes.
The difference between the present values and the values of the
day for which the clock is adjusted is very consistent: on the
winter solstice the day of the clock is fifty-two minutes longer
than the present day of the winter solstice in Karnak, and the
night is fifty-two minutes shorter; on the summer solstice the day
is fifty-three minutes shorter on the clock and the night
fifty-three minutes longer.
The figures on the clock show a smaller difference between the
length of the daylight on the solstices or between the longest and
the shortest days of the year than is observed at Karnak at the
present time. Thus the water clock of Amenhotep III, if it was
correctly built and correctly interpreted, indicates either that
Thebes was closer to the equator or that the inclination of the
equator toward the ecliptic was less than the present angle of 23 .
In either case the climate of the latitudes of Egypt could not have
been the same as it is in our age. As we find from the present
research, the clock of Amenhotep III became obsolete in the middle
of the eighth century; and the clock that might have replaced it at
that time would have been make obsolete in the catastrophes of the
end of the eighth and the beginning of the seventh centuries, when
once more the axis changed its direction in the sky and its
position on the globe as well. Worlds in Collision, Immanuel
Velikovsky,
Delta Book (Dell Publishing Co.), Inc., 1950
In 1952, this was on the New York Times Best Seller list.
Despite this, Velikovsky upset academics in many fieldshistory,
religion, astronomy (including physics), . Those of astronomy [see
below], told Velikovskys then publisher that if they continued to
publish the book that their schools would no longer purchase that
publishers textbooks. The publisher caved. So much for academic
freedom.Most academics and pedestrians having not read this and
subsequent works formed their opinions from hearsay. Einstein was
no different at first. Once Velikovsky, who also lived in
Princeton, got Einsteins atten-tion, Einstein felt that there was
much to Velikovskys interdisciplinary study and his hypotheses
deserved much more research. This does not mean that Einstein fully
agreed with Velikovsky; instead, the weight of evidence more than
justified further investigation. Einstein wrote the following:
Dear Mr. and Mrs. Velikovsky! At the occasion of this
inauspicious birthday [Einsteins], you have presented me once more
with the fruits of an almost eruptive productivity. I look forward
with pleasure to reading the historical book that does not bring
into danger the toes of my guild. How it stands with the toes of
the other faculty [the book, Ages in Chaos, would upset the
historians], I do not know as yet. I think of the touching prayer:
Holy St. Florian, spare my house, put fire to others!
I have already read carefully the first volume of the memoirs to
Worlds in Collisions and have supplied it with a few marginal notes
in pencil that can easily be erased. I admire your dramatic talent
and also the art and the straight forwardness of Thackeray
[Thackrey], who has compelled the roaring astronomical lion
[Shapley] to pull in a little his royal tail, yet not showing
enough respect for the truth. Also, I would feel happy if you could
savor the whole episode for its humorous side.
Unimaginable letter debts and unread manuscripts that were sent
in, force me to be brief. Many thanks to both of you and friendly
wishes.
Your
A. Einstein
Velikovsky Reconsidered, by the editors of Pense
Doubleday and Company, Inc., 1966
If this person has the story correct, Einstein told Velikovsky
that he must make scientific predictions based on his historical
research if his hypothesis of early history was ever to get
scientific attention. One of Vs predictions was that there was an
electromagnetic belt around the earth. At the time, astronomers
considered the mechanisms of the solar system and universe to be
governed simply by Newtonian gravi-tational phenomena. Velikovsky
proposed that electromagnetic attrac-tions / repulsions also were
in play. This greatly incensed astronomers being instructed by
someone outside their field. Yet, early space exploration did
indeed establish the existence of such an electromag-netic beltit
is known to us today as the van Allen radiation belt.
The historical appendices to these labs have been added for a
reason. They exist to help round out the student. Think of them as
brain candy light facts that you will not be tested on. But, there
is a further reason. Velikovskys works were truly
interdisciplinaryincorporating history, astronomy, cosmology,
psychology, geology, and paleontology. With such a broad base, he
was able to advance truly astounding ideas. Maybe one of you might
catch the bug. There is often money to be made where two fields
overlap. More important than money, however, is the excitement of
truly unearthing something new not just developing a better brake
system.
APPENDIX BDATA SHEET FOR FLOW
METERSTime/Date:___________________
Lab Partners____________________________
________________________________________________________
____________________________
________________________________________________________ Venturi
Meter:hflow
inH20hfrictioninH20Water in tank
gal.Times.
d
d
d
d
d
Orifice Meter:hflow
inH20hfrictioninH20Water in tank
gal.Times.
d
d
d
d
d
Turbine Flow Meter:Flow Indicated by Counter,
%hfrictioninH20Water in tank
gal.Times.
100% = _________ gpmd
d
d
d
d
Rotameter:% of FlowhfrictioninH20Water in tank
gal.Times.
100% = _________ gpm
d
d
d
d
d
EMBED Equation.3
EMBED Equation.3
Measure flow at
corner of float
EMBED Equation.3
Figure 4Schematic of the basic operation of the turbine-type
flow meter [1]
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
The Invention of ClocksPart 2:
Sun Clocks, Water Clocks, Obelisks
HYPERLINK
"http://inventors.about.com/library/weekly/aa071401a.htm"
http://inventors.about.com/library/weekly/aa071401a.htm
INCLUDEPICTURE
"http://www.perseus.tufts.edu/GreekScience/Students/Jesse/cleps.gif"
\* MERGEFORMATINET
A Brief History of Clocks:
From Thales to Ptolemy
By: Jesse Weissman
HYPERLINK
"http://www.perseus.tufts.edu/GreekScience/Students/Jesse/CLOCK1A.html"
http://www.perseus.tufts.edu/GreekScience/Students/Jesse/CLOCK1A.html
INCLUDEPICTURE
"http://www.pbs.org/wgbh/nova/galileo/images/expe_inclpln_5stops.gif"
\* MERGEFORMATINET
Using a water clock and an inclined plane, Galileo was able to
determine the rate of acceleration due to gravity. by timing how
long it takes for the ball to roll from the marked distances.
[He found that] it takes one unit of time for the ball to roll
one unit of distance, two units of time to roll four units of
distance, three units of time for the ball to roll nine units of
distance, . NovaGalileos Battle for the Heavens
HYPERLINK
"http://www.pbs.org/wgbh/nova/galileo/expe_inpl_2.html#clock"
http://www.pbs.org/wgbh/nova/galileo/expe_inpl_2.html#clock
Galileo made an amazing contribution to timekeeping, simply by
not paying attention in church. In 1581, Galileo was 17 and he was
standing in the Cathe-dral of Pisa watching a huge chandelier
swinging back and forth from the ceiling. Galileo noticed that no
matter how short or long the arc of the chan-delier was, it took
exactly the same amount of time to complete a full swing.
The chandelier gave Galileo the idea to create a pendulum clock.
While the clock would eventually run of energy, it would keep
accurate time until the pendulum stopped. If the pendulum was set
swinging again before it stopped, there would never be a loss in
accuracy. Because of this, pendulums caught on and are still widely
used today. The History of Time
HYPERLINK
"http://library.thinkquest.org/C008179/historical/basichistory.html#galileo"
http://library.thinkquest.org/C008179/historical/basichistory.html#galileo
EMBED Equation.3
EMBED Equation.3
Fluid enters the tube from the bottom. As it enters, it causes
the float to rise to a position of equilibrium. The position of
equilibrium is at the point where the weight of the float is
balanced by the weight of the fluid it displaces (the buoyant force
exerted on the float by the fluid) and the pressure due to velocity
(dynamic pressure). The higher the float position the greater the
flow rate. Note that as the float rises, the annular area formed
between the float and the tube increases. Maximum flow is at
maximum annular area or when the float is at the top of the tube.
Minimum area, of course, represents minimum flow rate and is when
the float is at the bottom of the tube.
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
Venturi, Giovanni Battista (17461822) Italian physicist,
credited with first observing the phenomenon upon which the
operation of the Venturi tube (later invented by Clemens Herschel)
depends. [2]
Certain difficulties are encountered in attempting to restore
(downstream of the throat) the original pressure by decreasing the
velocity to its original value. In order to do this, it is
necessary to increase the cross section gradually from the
narrowest section to the original cross section. This type of
arrangement, shown in Fig. 208, is called a Venturi meter.
Herschel* first suggested its use for the measurement of delivered
volume in pipe lines. In order to find the relation between the
pressure difference and the mean velocity in the pipe a calibration
curve of a geometrically similar Venturi meter has to be known. In
addition, in cases where the velocity of approach is not very small
with respect to the velocity in the throat this geometrical
similarity has to be extended to the approach as well. For Venturi
tubes of the shape shown in Fig. 208 the velocity coefficient is
approximately 1.00.
* Herschel, Cl., The Venturi Meter, paper read before the Am.
Soc. Civil Eng., December 1887. [3]
BernoulliName of three generations of a family of mathematicians
and scientists of Basel, Switzerland, that started with Jakob I
[aka Jacob, Jacques, Jaques, and James] (16541705); prof. of
mathematics at U. of Basel (from 1687); pioneer in application of
Leibnizian calculus to a variety of problems; introduced term
integral; studied catenaries, and applied calculus to bridge
design. Author of Conamen novi systematis cometarum (1682),
Dissetatio de gravitate aetheris (1683), Ars conjectandi (contains
binomial distribution, pub. posthum. by Nikolaus in 1713), etc. His
brother Johann I (16671748); prof. of mathematics at U. of Basel
(from 1705); was a pioneer in exponential calculus; teacher of
Euler, and collaborator of LHospital. Their nephew Nikolaus
(16871759); prof. of mathematics at Padua (171622), then of law and
logic at U. of Basel; contributed to probability theory and
infinite series. Johanns sons: Daniel (17001782), mathematics prof.
at St. Petersburg (172432), of anatomy, botany, and physics, and
then of philosophy, at U. of Basel; discovered Bernoullis principle
relating fluid velocity and pressure; contributed to probability,
kinetic theory of gases, celestial mechanics; author of
Hydrodynamica (1738) and works on acoustics, astronomy, etc.; and
Johann II (17101790), prof. of eloquence and of mathematics, known
for his contribution to theories of heat and light. Two sons of the
last named: Johann III (17441807), astronomer to the Acad. of
Berlin, author of Recueil pour les astronomes (177276); and Jakob
II (17591789), prof. of mathematics at St. Petersburg. Christoph
(17821863), grandson of Johann II and nephew of Johann III and
Jakob II, was naturalist and prof. at U. of Basel (from 1818);
author of Vademecum des Mechanikers (1829), etc. [2]
Bernoulli may well be the most famous mathematical family of all
time. There were 8-12 Bernoulli mathematiciansthe confusion arises
as the same given names were used in more than one generation
[5].
Bernoullis Equation: applies to incompressible (Mach < 0.3
for gases), inviscid, irrotational fluids. If applying the equation
along a streamline, can drop the irrotational partconstant energy
along a streamline.
Students will often refer to g, the acceleration of gravity, as
the gravitational constant. The gravitational constant is the gc
shown in Bernoullis equation above. In the English Gravitational
System of units, EMBED Equation.3 . In the SI system EMBED
Equation.3 if one wants force expressed as Newtons, N, instead of
EMBED Equation.3 . Many people curse the English Gravitational
System; but, it is ancientvery ancientin many of its units. For
example, the English inch is a smidgen off an ancient inch, found
for example in the Great Pyramid of Giza. This ancient (at least
3500 years old) inch can be found by dividing the polar diameter of
the earth by 500,000,000; e.g., EMBED Equation.3 . Our modern inch
has been maintained to with in 0.001in of its original value. Isaac
Newton was aware of this ancient measure and verified two ancient
cubits based on its length.
While through a Venturi meter the pressure drop is very small
(about 15 to 20 percent of the pressure drop in the throat), its
practical application is limited by its large (long) size.
Therefore standardized orifices as shown in Figs. 209 and 210 are
used more frequently. The pressure diagrams in these two figures
show that with this kind of apparatus, the loss in pressure is from
60 to 70% of the pressure drop in the orifice. The velocity
coefficient has been found to be 0.96 to 0.98 with the standardized
(German) rounded-approach orifice (Fig. 209). For the sharp-edged
orifice shown in Fig. 210 the coefficient depends very much upon
the ratio of the cross sections a/A. For instance, for a/A = 0.15,
we have =0.61, whereas for a/A = 0.75, the velocity coefficient is
= 0.91.
[3]
Remember, to plot A vs. B, B is the independent variable
(horizontal axis) and A is the dependent variable (vertical axis).
Thus, A vs. B could be alternately stated as A as a function of
B.
L. Borchardt, Die altgyptische Zeitrechnung (1920), pp.
6-25.
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