Last Rev.: 12 JUL 08
Flow Meters Lab : MIME 3470
Page 1
Grading Sheet
~~~~~~~~~~~~~~
MIME 3470—Thermal Science Laboratory
~~~~~~~~~~~~~~
Experiment №. 4
FLOW METERS
Students’ Names  Section №
APPEARANCE
ORGANIZATION
ENGLISH and GRAMMAR
MATHCAD
ORDERED DATA, DIMENSIONS, PHYSICAL PROPERTIES
VENTURI METER: COMBINED PLOT: hflow vs. Qtheo & hflow vs. Qact
PLOT OF Cv vs. Re
ORIFICE METER: COMBINED PLOT: hflow vs. Qtheo & hflow vs. Qact
PLOT OF Co vs. Re
TURBINE METER: PLOT OF Qact vs. Qind
REGRESSED & PLOTTED CALIBRATION LINE
ROTAMETER:
PLOT OF Qact vs. Qind
COMBINED PLOT: h fric vs. Qact FOR THE 4 METERS
DISCUSSION OF RESULTS
CONCLUSIONS
ORIGINAL DATASHEET
TOTAL
Comments
d
GRADER—
POINTS
10
5
10
7
5
5
5
5
5
8
5
5
10
10
5
100
SCORE
TOTAL
Last Rev.: 12 JUL 08
Flow Meters Lab : MIME 3470
Page 2
MIME 3470—Thermal Science Laboratory
~~~~~~~~~~~~~~
Experiment №. 4
FLOW METERS
NAME
NAME
NAME
 1
1 


.
(2)
 A2 A2 
2 
 1
This equation relates the pressure difference, Δhflow, to the flow rate
Qtheo, and represents the theoretical curve for the Venturi meter.
TIME, DATE
~~~~~~~~~~~~~~
OBJECTIVE—The 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.
INTRODUCTION—There 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.
THEORY—The operating principles of these various meters need
to be developed in order to meaningfully compare their performance.
The Venturi Meter The Venturi1 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, Δhflow, can be found as a function of the flow rate.
Applying Bernoulli’s2 equation3 to points  and  of the Venturi
meter and relating the pressure difference to the flow rate yields
1
Venturi, Giovanni Battista (1746–1822) 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.,
2
(1)
2
1
 p 2  p1   h flow g  Qtheo

gc
2g c
or
~~~~~~~~~~~~~~
LAB PARTNERS: NAME
NAME
NAME
SECTION
№
EXPERIMENT TIME/DATE:
p2  p1 V12  V22


2 gc
December 1887. [3]
Bernoulli—Name of three generations of a family of mathematicians and scientists of
Basel, Switzerland, that started with Jakob I [aka Jacob, Jacques, Jaques, and James]
(1654–1705); 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
(1667–1748); prof. of mathematics at U. of Basel (from 1705); was a pioneer in
exponential calculus; teacher of Euler, and collaborator of L’Hospital. Their nephew
Nikolaus (1687–1759); prof. of mathematics at Padua (1716–22), then of law and logic
h flow
1
2
Figure 1—Schematic of the Venturi meter [1]
To determine Qtheo, first, one needs to find the relationship between
the velocities V1 and V2 using Bernoulli’s equation.
p1
V2
p
V2
g
g
 z1
 1  2  z2
 2 .4
1
gc 2gc 2
gc 2gc
(3)
For 1   2   and p1  p2  gh flow and z1 = z2
p1  p2 gh flow
V 2  V12

 gh flow  2


2
(4)
Knowing that V = Q/A and Q1 = Q2 = Q
2
2
 1
Q  Q 
1 
2 gh flow  V22  V12   2    1   Q 2  2  2  .
A

 A2   A1 
 2 A1 
Thus,
Q
2 gh flow
 1
1 


2
A
A12 
 2
 Qtheo .
(5)
(6)
at U. of Basel; contributed to probability theory and infinite series. Johann’s sons:
Daniel (1700–1782), mathematics prof. at St. Petersburg (1724–32), of anatomy,
botany, and physics, and then of philosophy, at U. of Basel; discovered Bernoulli’s
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 (1710–1790), prof. of eloquence and of
mathematics, known for his contribution to theories of heat and light. Two sons of the
last named: Johann III (1744–1807), astronomer to the Acad. of Berlin, author of
Recueil pour les astronomes (1772–76); and Jakob II (1759–1789), prof. of
mathematics at St. Petersburg. Christoph (1782–1863), 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 mathematicians—the confusion arises as the same given
names were used in more than one generation [5].
3 Bernoulli’s Equation: applies to incompressible (Mach < 0.3 for gases), inviscid,
irrotational fluids. If applying the equation along a streamline, can drop the
irrotational part—constant energy along a streamline.
4 Students will often refer to g, the acceleration of gravity, as the gravitational constant.
The gravitational constant is the gc shown in Bernoulli’s equation above. In the
lbm  ft
English Gravitational System of units, g c  1
. In the SI system
lbf  s 2
kg  m
kg  m
if one wants force expressed as Newtons, N, instead of
. Many
N  s2
s2
people curse the English Gravitational System; but, it is ancient—very ancient—in
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.,
(7899.83mi  5280 ft / mi  12in / ft) 500,000,000  1.00107in . 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.
gc  1
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Flow Meters Lab : MIME 3470
The Venturi meter is characterized by small pressure losses due to
viscous shear and frictional effects. Thus, for any Δhflow, the actual
flow rate will be less than the theoretical flow rate.
Qact
(7)
 Cv
Qtheo
Page 3
2
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.
1
2
1
2
2
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 2 is given by the approximate profile shown. It is also
assumed that the velocity profile at 1 is uniform [4]. From boundary
layer theory, the pressure of the plug flow at 2 is transmitted across
the (assumed stagnate) interval from the plug to the pressure port.
2
Figure 2—Cutaway view of the orifice meter [1]
Applying Bernoulli’s equation to points
1
and 2 yields
2 

(8)
 p2  p1   h flow g  Q  12  12  .
gc
2 g c  A1
A2 
For any pressure difference, Δhflow, 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
Co 
Qact
.
Qtheo
(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 Bernoulli’s equation was applied
to Points 1 and 2 . However, because it is difficult to place a
pressure tap in the orifice itself, pressure measurements are
actually made at 1 and 2 . So the reader asks: how accurate can
such a measurement be? Reference 4 explains that (see Figure 3)
the flow at 2 is almost the same as the slug of flow at 2 and thus
the pressures are almost the same. This is true for a short distance
downstream of the orifice—then pressure recovery sets in. With
these assumptions, Bernoulli’s equation is the same, except
pressure measurements are made at 2 instead of 2 .
It should also be noted that the shape of the orifice is important to
the flow quality.5
5
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 α 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 α =0.61, whereas for a/A =
0.75, the velocity coefficient is α = 0.91.
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
Figure 4—Schematic of the basic
pass through the meter. In
operation of the turbine-type
addition, the totalizer will
flow meter [1]
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.
[3]
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Flow Meters Lab : MIME 3470
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.
Page 4
On a separate graph, plot Cv vs. React, (Reynolds number based Qact). In
making this second plot, use an absolute (starting at zero) scale on
the vertical axis. Using a marker, plot the expected discharge
coefficient of 0.9.
Valve
Manometer (Typ)
For both venturi and orifice:
Inlet ID:
1.025in
Throat Diam.: 0.625in
Venturi
Orifice Meter
Collection Tank
Turbine Meter
Rotameter
Sump Tank
P
Measure flow at
corner of float
Figure 5—The rotameter and its operation [1]
Three common types of graduated scales are:
1. Percent of maximum flow—a meter factor is given or determined 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 type—a calibration curve is associated with the ratio
of the tube’s cross-sectional diameter to the diameter of the float.
3. Direct reading—a 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 collection 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 minute—a 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 Meter—See 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 pressure. The second manometer measures the head pressure difference,
hflow, between points 1 and 2 of Figure 1. From hflow, the theoretical volumetric flow rate, Qtheo, can be determined from Equation 6.
For your report, on one graph, plot hflow vs. 6 Qact and hflow vs. Qtheo.
6
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.
Figure 6—Flow Meters Apparatus
Orifice Meter—Use the procedure and write up requirements as specified for the Venturi meter. The expected discharge coefficient is 0.8.
Turbine-Type Flow Meter—The 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).
Rotameter—For 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 Prandtl’s Lectures. Composed by Prandtl’s
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-Hall
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ORDERED DATA, CALCULATIONS, AND RESULTS
MATHCAD OBJECT--DOUBLE CLICK TO OPEN
Flow Meters Lab : MIME 3470
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DISCUSSION OF RESULTS
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CONCLUSIONS
Page 6
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APPENDICES
Appendix A—Clepsydras (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 around—they 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 strucA Brief History of Clocks:
ture featured a 24-hour clepsydra
From Thales to Ptolemy
By: Jesse Weissman
and indicators for the eight winds
http://www.perseus.tufts.edu/Gre
from which the tower got its name,
ekScience/Students/Jesse/CLOC
and it displayed the seasons of the
K1A.html
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 waterdriven 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 missionaries 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 Invention of Clocks—Part 2:
the simple telling of time as it was
Sun Clocks, Water Clocks, Obelisks
display. Old clocks typically had
http://inventors.about.com/library/wee
bells and dials, and they
kly/aa071401a.htm
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 feedback control. In Western water clocks, a float on the surface of a steadily 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 huge–forty 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 № 1580
http://www.uh.edu/engines/epi1580.htm
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Flow Meters Lab : MIME 3470
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), 25.5º 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 23½ º. 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.7 Calculating the length of the day of the winter solstice, he found that the clock was constructed for a day of 11 hours 18
minutes, whereas the day of the solstice at 25º 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 minutes, where as it is 13 hours 34 minutes—fifty-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 23½ º. 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 fields—history, religion,
astronomy (including physics), …. Those of astronomy [see below],
told Velikovsky’s then publisher that if they continued to publish the
book that their schools would no longer purchase that publisher’s
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
7 L. Borchardt, Die altägyptische Zeitrechnung (1920), pp. 6-25.
Page 8
first. Once Velikovsky, who also lived in Princeton, got Einstein’s attention, Einstein felt that there was much to Velikovsky’s 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 [Einstein’s], 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 Pensée
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
V’s 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 gravitational phenomena. Velikovsky proposed that electromagnetic attractions / 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 electromagnetic belt—it 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.
Velikovsky’s works were truly interdisciplinary—incorporating 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.
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, ….
Nova—Galileo’s Battle for the Heavens
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 Cathedral 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 chandelier 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
http://library.thinkquest.org/C008179/historical/basichistory.html#galileo
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Flow Meters Lab : MIME 3470
Page 9
APPENDIX B—DATA SHEET FOR FLOW METERS
Time/Date:
___________________
Lab Partners
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
Δhflow
Δhfriction
inH20
inH20
Δhflow
Δhfriction
inH20
inH20
Flow Indicated
by Counter, %
Δhfriction
Venturi Meter:
Water in tank
gal.
Time
s.
Water in tank
gal.
Time
s.
Water in tank
gal.
Time
s.
Water in tank
gal.
Time
s.
d
d
d
d
d
Orifice Meter:
d
d
d
d
d
Turbine Flow Meter:
100% = _________ gpm
d
d
d
d
d
Rotameter:
100% = _________ gpm
inH20
% of Flow
d
d
d
d
d
Δhfriction
inH20
Last Rev.: 12 JUL 08
Flow Meters Lab : MIME 3470
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