04 Flow Meters

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<p>xcvsv</p> <p>Last Rev.: 12 JUL 08Flow Meters Lab : MIME 3470 </p> <p>Page 2</p> <p>Grading Sheet</p> <p>~~~~~~~~~~~~~~MIME 3470Thermal Science Laboratory~~~~~~~~~~~~~~Experiment . 4 Flow Meters Students Names Section POINTS SCORETOTAL</p> <p>APPEARANCE10</p> <p>ORGANIZATION 5</p> <p>ENGLISH and GRAMMAR 10</p> <p>MATHCAD</p> <p> Ordered Data, Dimensions, Physical Properties7</p> <p> VENTURI METER: COMBINED PLOT: (hflow vs. Qtheo &amp; (hflow vs. Qact</p> <p>5</p> <p> PLOT OF Cv vs. Re 5</p> <p> ORIFICE METER: COMBINED PLOT: (hflow vs. Qtheo &amp; (hflow vs. Qact</p> <p>5</p> <p> PLOT OF Co vs. Re5</p> <p> TURBINE METER: PLOT OF Qact vs. Qind5</p> <p> REGRESSED &amp; PLOTTED CALIBRATION LINE8</p> <p> ROTAMETER: PLOT OF Qact vs. Qind5</p> <p> COMBINED PLOT: (h fric vs. Qact FOR THE 4 METERS 5</p> <p>DISCUSSION OF RESULTS10</p> <p>CONCLUSIONS10</p> <p>ORIGINAL DATASHEET 5</p> <p> TOTAL100 </p> <p>Comments </p> <p>GRADERd</p> <p>MIME 3470Thermal Science Laboratory~~~~~~~~~~~~~~Experiment . 4Flow Meters</p> <p>~~~~~~~~~~~~~~</p> <p>Lab Partners: Name Name</p> <p>NameName</p> <p>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 </p> <p>(1)or</p> <p>.(2)This equation relates the pressure difference, hflow, to the flow rate Qtheo, and represents the theoretical curve for the Venturi meter. </p> <p>To determine Qtheo, first, one needs to find the relationship between the velocities V1 and V2 using Bernoullis equation. </p> <p>.</p> <p>(3)Forandand z1 = z2 </p> <p>(4)Knowing that V = Q/A and Q1 = Q2 = Q</p> <p>.(5)Thus,</p> <p>.(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. </p> <p>(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.</p> <p>Figure 2Cutaway view of the orifice meter [1]Applying Bernoullis equation to points and yields</p> <p>.(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</p> <p>.(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. </p> <p>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. </p> <p>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. </p> <p>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. </p> <p>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 </p> <p>1.Flowmeters: Introduction, efunda (engineering fundamentals), http://www.efunda.com/DesignStandards/sensors/flowmeters/flowmeter_intro.cfm </p> <p>2.Simon &amp; Schuster New Millennium Encyc. &amp; Reference Library, 2000</p> <p>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] </p> <p>4.Bird, R.B., Stewart, W.E., &amp; Lightfoot, E.N., Transport Phenomena, John-Wiley &amp; Sons, 1960. </p> <p>5.Ross, S.M. (1998), A First Course in Probability, 5th ed., Prentice-HallOrdered Data, Calculations, and Results </p> <p>DISCUSSION OF RESULTS</p> <p>CONCLUSIONS</p> <p>APPENDICES</p> <p>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. </p> <p>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. </p> <p>Water Clocks</p> <p>Source: National Institute of Standards and Technology Physics Laboratory</p> <p>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. </p> <p>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.</p> <p>http://www.infoplease.com/ipa/A0855491.html </p> <p>SU-SUNG'S CLOCK</p> <p>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. </p> <p>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...</p>

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