Vortex Shedding on Combined Bodies at Incidence to a Uniform Air Stream T. Yavuz x, Y. E. Akansu xx, M. Sarıo lu xxx, and M.
|
|
- Shawn Parsons
- 6 years ago
- Views:
Transcription
1 Vorte Sheing on Combine Boies at Incience to a Uniform Air Stream T. Yavuz, Y. E. Akansu, M. Sarıo lu, an M. Özmert. Ba kent Universit, : Nige Universit,, : Karaeniz Technical Universit,Turke Abstract Vorte-sheing phenomenon of the flow aroun combine two boies having various geometries an sizes has been investigate eperimentall in the Renols number range between an To see the effect of the rotation of the boies on the vorte sheing, the combine boies were rotate from 0 to 180. The combine moels have a cross section composing of a main circular cliner an an attache circular or square cliner. Results have shown that s for two cases were change consierabl with the angle of incience, while it was foun to be largel inepenent of Renols number at 150. Characteristics of the vorte formation region an location of flow attachments, reattachments, an separations were observe b means of the flow visualizations. epening on the inclination angle the effects of flow attachment, separation an reattachment on vorte-sheing phenomenon have been iscusse. Kewors Bluff bo, vorte sheing, flow separation, flow reattachment. F I. INTROUCTION LOWS aroun circular cliner an square prism as basic geometries, have been investigate b man workers for a long time. Such bluff boies often applie in the form of groups in man cases of engineering practices. In these cases, flow characteristics of such objects in contact or in close proimit show major ifferences, because of the interactions with each other, accoring to those of single applications. Therefore, numerous investigators have been intereste in flow past two boies which have same or ifferent shapes. Fleck [1] investigate the flow past a combine bo, compose of a circular cliner an a rectangular prism, in the Renols number range from to It was foun that the observe is inepenent of Renols number for the range of angle of attack In effect, the sharp corners of the rectangular portion ominate the vorte sheing mechanism for the majorit of the range of the angle of attack. The onl range where there is Renols number epenence is 45 90, when the rectangular bo is largel in the wake of the circular bo. In this case, the presence of the rectangular bo on the ownstream sie : Corresponing autor of the circular cliner consierabl affects the location of the separation point. Wei an Chang [2] stuie flow characteristic of wake an base-blee flow ownstream of two bluff boies, with ifferent geometries, arrange sie b sie. The two-bo arrangements are comprise of flat plate-square cliner, flat plate-circular cliner, an square cliner-circular cliner. In this stu, the use two sets of moels, these being bluff boies with the same cross sectional imension but with ifferent vorte sheing frequencies, an bluff boies with ifferent cross sectional imension but with the same vorte sheing frequencies. It is suggeste that when the gap istance is small, the vorte sheing frequenc ownstream of the two bo arrangement is about half of the average of the sheing frequencies that correspon to each single bluff bo. Luo an Gan [3] investigate the structure associate with flow past two tanem circular cliners with a iameter ratio of 0.33 an with the smaller cliner upstream. Just like the case of flow past two equal size cliners, a critical spacing was foun to eist. For spacing less than the critical value, share laers that separate from the upstream cliner reattach onto the ownstream cliner whereas for spacing larger than the critical value both cliners she vortices. In the stu of Igarashi [4], eperimental investigations on the characteristics of a flow aroun two circular cliners of ifferent iameters with the ratio 2 / 1 =0.68 arrange in tanem were carrie out. The flow patterns var with an increasing of the spacing of the aes of the cliners in the same manner as in the case of equal iameters. The pattern in which the spacing of the aes of the cliners was the smallest (this case is closest to our present case) is a complete separation tpe in which the separate shear laer from the first cliner oes not reattach onto the secon one. Tsutsui et al. [5] stuie eperimentall an numericall the behavior of an interactive flow aroun two circular cliners with ifferent iameters (/=0.45) at close proimit. In particular, the reattachment that the separate share laer from the main cliner reattaches on the rear surface b Coana effect was mentione. In the stu of Gu an Sun [6], the interference between two ientical circular cliners arrange in staggere configurations has been investigate at high subcritical Renols numbers. In general, three ifferent pressure 673
2 istribution patterns on the ownstream cliner an two switching processes were observe for the win angle varing from 0 (in tanem) to 90 (in sie b sie). The corresponing flow patterns were classifie as wake, share laer an neighbourhoo interference respectivel. For ifferent forebo sections, vorte sheings from bluff boies with emphasis on fining the effects of afterbo shape were eperimentall investigate b Nakamura [7]. It was foun that the of a bluff bo with afterbo ecreases initiall with increasing sie ratio in which one of the most important shape parameters for controlling the is the ratio of afterbo length to cross-flow imension of the bluff bo. This is in sharp contrast to the base suction that is sensitivel epenent of afterbo shape. Nakamura [8] also eperimentall stuie the effect of the etene splitter plates on the bluff boies with forebo shapes. These forebo shapes eamine inclue a circular shape, a semi-circular section with an without a rectangular block an a normal flat plate. It was shown that vorte sheing from bluff boies with etene splitter plates is characterize b the impinging-shear-laer instabilit, where the in terms of splitter plate length increases with increasing splitter plate length. Akansu et al. [9] investigate eperimentall the behavior of a stationar circular cliner with an attache plate, uner conitions where the entire cliner-plate bo was to rotate about the cliner ais, in the Renols number of The results inicate that the sheing frequenc was nearl constant in the range of the plate angle of an as farther increasing the angle from 120 to 160, it strikingl increases an then again ecreases at the angles bigger than 160 eg. The plate also causes important changes in pressures on the surface of the cliner epening on the flow separation an reattachment as increasing the inclination angle. A similar stu for a square prism with an attache plate was mae b Sarioglu et al. [10]. Their results inicate that the base on, the sie length of the square cliner, has a strong peak at = 12 an rag coefficient of the square cliner has minimum an maimum values at approimatel = 20 an 80 respectivel. Base on the results summarize above, it can be conclue that flow aroun two ajacent bluff boies epens strongl on the geometries an the angle of incience. Therefore, the present stu focuse on the investigation of the flow aroun combine bluff boies with ifferent cross-sectional geometries at incience. Two combine moels use as a main circular cliner (=9.5 mm) with an attache small cliner having circular cliner (=6 mm) or square prism (=6 mm). II. EXPERIMENTAL APPARATUS AN PROCEURE The eperiments were conucte in the test section of a blower tpe open jet TE 44 subsonic win tunnel having working cross section of 457 mm 457 mm. Bounar laer correction is achieve b corner fillets etening the length of the contraction cone an the working section, proportione to ensure a uniform longituinal pressure in the working section. At the maimum tunnel spee of about 30 m/s, the free stream turbulence intensit was about 0.5%; the turbulence intensit was higher at low tunnel spees, about 1.5% at 4 m/s, which is the lowest spee in the tunnel. The Renols number base on the iameter of the main cliner,, was range between an The tunnel an test section are shown in Fig. 1. VALVE VENTILATOR ELECTRIC MOTOR 1200 TEST REGION STATIC PRESSURE TAPS Fig. 1 Blower tpe open jet subsonic win tunnel an test section. The test moels consiste of two configurations are shown in Fig. 2. As shown in the figure, the upstream cliners having circular an square cross sections were combine with the main circular cliner in a line contact at the center ais. The sie length of the square cliner (=6 mm) an the iameter of the main circular cliner (=9.5 mm) were chosen to ensure the vorte sheing frequencies of both square an circular cliners to be same when the sta isolate in the flow. All moels were mae from stainless steel an the square prism was machine sharp eges. The lengths of the boies are same with the with of the tunnel test section an the spanne the entire with of the test section. Flow Flow Combine Moel-I Combine Moel-II Fig. 2 Two ifferent combine moel geometries an coorinate sstem. The combine moels were centere on the mi-height of the test section an the were positione at an angle of incience to the free-stream flow irection an turne in the range of with an increment of 3, with an accurac of 0.5. Maimum soli blockage ratios of the combine moels are, 3.48 % for the Moel-I at = 75 an 674
3 105, an 3.39 % for the Moel-II at = 90. As the blockage ratios are smaller than 6.0 %, no correction was mae for the blockage effects [11]. Minimum aspect ratios base on the projecte cross stream imension of the moels are 29.5 for the Moel-I an II. It can be sai that these aspect ratios are satisfactor for a bluff bo to be treate as two imensional [2]. Vorte sheings from the test moels were etecte b using a TSI IFA 100 moel constant temperature anemometer with two hot-film probes. The s for the vorte sheing from the moels were etermine from the frequenc analsis of the velocit fluctuations. The probes were locate at the position of / = 5 an 15, / = 2.5, where / an / are the ownstream an vertical istances respectivel, in the ownstream of the bo. The hot-film probes were calibrate using a TSI Moel 1125 calibrator. The frequenc response for the hot-film probes were foun to be about 20 khz b using a square wave test. The velocit measurements were carrie out using a computer controlle ata acquisition sstem. For velocit measurements at each measurement point, 4096 ata were acquire at a sampling rate of 4 khz using a low-pass filter setting of 2000 Hz. So the measuring time correspone to s. TSI Thermal-Pro Software was use to acquire signals with a 12 bit A/ converter an to obtain the statistical an spectral analze of these measurement signals. Flow visualization eperiments were conucte b using a smoke-wire metho in the ifferent win tunnel for Renols number of In these eperiments, three times bigger test moel imensions have been use to obtain a Renols number to be in the range of Renols number use in the velocit measurements. The eperimental uncertaint in the measurement of velocit was etermine to be less than 3%, whereas those of the an the frequenc spectra calculate from the eperimental measurements were etermine to be less than 3.3% an 0.5%, respectivel. III. EXPERIMENTAL RESULTS AN ISCUSSION The vorte sheings from the moels were eamine in the Renols number between an A sample velocit spectra istribution obtaine for the Moel-I, at the Renols number is given in Fig. 3. It is quite clear that, with increasing from 0, there is a sharpl ecrease in vorte sheing frequenc up to =24, then this ecrease in sheing frequenc slightl continues up to 48. After 84, it grauall increases up to 168 an then it ecreases again. Using vorte-sheing frequencies obtaine from spectral istributions, the s, St base on an St base on, calculate for the Moels I an II at the three Renols number , an are shown in Figs. 4 an 5. As shown in Fig. 4, at = 0 the value of St is about 0.25 an this value is above of that of the single circular cliner. This inicates that the shear laers separate from the leaing eges of the square cliner goes ver near main cliner of the Moel-I an causes to narrow wake than that of the single circular cliner. The ecreases sharpl from 0 to 15. Because, the shear laers separate from the corner A an B roll rear of the moel without a reattachments on the cliner an with a more wie wake. The increases grauall with the rotation of the Moel-I in the range between This increase in St quietl epens on the reattachment of the separate shear laer from corner B on the face AB. As the angle approaches 69, this reattachment point closes to the corner A an, so it is seen a peak in the. After this angle, the separate shear laer from the corner B oes not reattach on the face AB anmore an causes a suen increase in the with of the wake an consequentl the ecreases. This phenomenon implies the eistence of a ecrease in the. This ecrease procees until about 90 in which the with of the wake reaches its maimum value. As the angle farther increases, the Strouhal number increases grauall up to 168 in which the Strouhal number shows a peak for the Renols numbers an Approaching this angle, a reattachment occurs again on the square cliner. After 168, there is a suen ecrease in ue to giving up this reattachment an also reucing the with of the wake. For Re= , the peak in the occurs at 174. This is associate with the variation of the separation point on the circular cliner with the Renols number. As a matter of fact, in the stu of Fleck [1], changes with the Renols number strikingl especiall in the case where the circular cliner is upstream. Spectral ensit (arbitrar scale) Frequenc, Hz =0 Fig. 3 Spectra measure at / = 15, / = 2.5 in the wake of the Moel-I ( ). 675
4 FLOW A B 0.1 St = f/u St ' = f'/u Re = Re = C [ ] To eamine the flow fiel about the Moel-II arrangement, flow visualization eperiments were conucte b using a smoke-wire metho in the win tunnel for Re= In Fig. 6, the positions of flow attachment, separation, an reattachment on the two combine circular cliners ue to the inclination of the bo can be clearl seen. The variation of vorte formation region behin the boies can be also seen in this figure. When the flow pattern of the Moel-II at =0 is compare with the case of =180, there are consierable changes in the wake, an the istance require for vorte formation behin the boies varies. Narrow wake causes more small vortices an higher vorte sheing frequencies. Fig. 4 vs rotation angle, for the Moel-I. s for the Moel-II are presente in Fig. 5. In this case, as the smaller bo has circular shape, the Renols number effects are notice in the range of, 0 12, unlike the other moel. At = 0, the value of the Strouhal Number for the Re= is above of those for the Re= an For the case of Re= , at the beginning ( = 0 ), the shear laer separate from the small cliner reattaches on the ownstream cliner an this reattachment continues, with the small change in the location of the separation point on the big cliner, until = 12. After 12, a suen ecrease in the occurs b ening the reattachment. For the case of Re= , there is no reattachment at the beginning. With increasing the angle of incience up to 12, the increases because of the reattachment occurring on the lower sie of the Moel-II. Here, also after = 12, the reattachments give up an the ecreases suenl. In the range of = , unlike the Moel-I having sharp eges, there is no peak in. After 150, the variation of the Strouhal number is similar to those of the Moel-I because of changing the position of the main cliner from ownstream to upstream, an consequentl the flow uner consieration is in the influence of the main circular cliner FLOW 0.1 Sr = f/u Sr ' = f'/u Re = Re = [ ] Fig. 5 vs incience angle for the Moel-II = 0 = 30 = 90 = 155 = 15 = 60 = 120 = 180 Fig. 6 Smoke-wire visualization of the flow aroun test Moel-II for Re = Fig. 7 shows as a function of Renols number for various angles of incience consiere for the Moel-I. It can be sai that the was foun to be largel inepenent of Renols number up to 100. In the range of , has an unstable variation with Renols number in Re< This situation was also seen in Fig
5 = 0 = 5 = 30 = 70 = 100 = 160 = 165 = 170 =1 75 it was foun to be largel inepenent of Renols number at 150 eg. For both of the moels, the increase at the angles of incience in which reattachments occur. B the en of reattachments, the with of the wake increases an ecreases suenl. The peak appeare in at about = 60 in the case of sharp ege square moel have not seen in the case of Moel- II which is compose of two circular cliners. Probe position : /=5; /= Renols number Fig. 7 istribution of of the Moel-I vs Renols number for ifferent angles of incience. A summarize classification of the flow regimes of the two combine test moels is shown in Fig. 8. The flow structures mentione above are presente schematicall in this figure. Here, flow attachments, separations an reattachments an their behaviors accoring to the angle of incience are shown. = 0 = 10 = 30 = 69 =9 0 = 120 = 168 = 180 (a) = 0 = 10 = 30 = 69 = 90 = 120 = 165 =180 (b) Fig. 7 Assume flow patterns aroun the combine moels for Re= a) Moel-I, b) Moel-II IV. CONCLUSION Vorte-sheing phenomenon in the flow aroun two ifferent combine moels at incience has been investigate eperimentall in the Renols number range of an The following conclusions were obtaine: The s for two combine moels consiere were change strikingl with the angle of incience, whereas Smbol Quantit NOMENCLATURE iameter of the bigger circular cliner the projecte cross stream imension of the combine boies small imension of the upstream boies f vorte-sheing frequenc R Renols number base on, U/ St, f /U St, f /U U freestream velocit w the length of the big sie of the rectangular bo, streamwise an lateral coorinates inclination angle of the combine moels kinematic viscosit of flui ensit of air REFERENCES [1] B. A. Fleck, Strouhal Numbers for Flow past a Combine Circular- Rectangular Prism, Journal of Win Engineering an Inustrial Aeronamics, vol. 89, 2001, pp [2] Y. C. Wei an J. R. Chang, Wake an Base-Blee Flow ownstream of Bluff Boies with ifferent Geometr, Eperimental Thermal an Flui Science, vol. 26, 2002, pp [3] S. C. Luo an T. L. Gan, Flow past 2 Tanem Circular-Cliners of Unequal iameter, Aeronautical Journal, vol. 6, No. 953, 1992, pp [4] T. Igarashi, Characteristics of a Flow aroun Two Circular Cliners of ifferent iameters Arrange in Tanem, Bulletin of the JSME, vol. 25, No. 201, 1982, pp [5] T. Tsutsui, T. Igarashi, an K. Kamemoto, Interactive Flow aroun two Circular Cliners of ifferent iameters at Close Proimit. Eperiment an Numerical Analsis b Vorte Metho, Journal of Win Engineering an Inustrial Aeronamics, vol. 69, no. 71, 1997, pp [6] Z. Gu an T. Sun, On Interference between two Circular Cliners in Staggere Arrangement at High Subcritical Renols Numbers, Journal of Win Engineering an Inustrial Aeronamics, vol. 80, 1999, pp [7] Y. Nakamura, Vorte Sheing From Bluff Boies an a Universal Strouhal Number, Journal of Fluis an Structures, vol. 10, 1996, pp [8] Y. Nakamura, Vorte Sheing From Bluff Boies with Splitter Plates, Journal of Fluis an Structures, vol. 10, 1996, pp [9] Y. E. Akansu, M. Sarioglu, an T. Yavuz, Flow Aroun a Rotatable Circular Cliner Plate Bo at Subcritical Renols Numbers, AIAA Journal, vol. 42, no. 6, June 2004, pp [10] M. Sarioglu, Y. E. Akansu, an T. Yavuz, Flow Aroun a Rotatable Square Cliner Plate Bo, AIAA Journal, vol. 44, no. 5, Ma 2006, pp [11] G. S. West an C. J. Apelt, The Effects of Tunnel Blockage an Aspect Ratio on the Mean Flow Past a Circular Cliner with Renols Numbers between 10 4 an 10 5, J. Flui Mech., vol. 114, 1982, pp
6. Friction and viscosity in gasses
IR2 6. Friction an viscosity in gasses 6.1 Introuction Similar to fluis, also for laminar flowing gases Newtons s friction law hols true (see experiment IR1). Using Newton s law the viscosity of air uner
More informationMagnetic field generated by current filaments
Journal of Phsics: Conference Series OPEN ACCESS Magnetic fiel generate b current filaments To cite this article: Y Kimura 2014 J. Phs.: Conf. Ser. 544 012004 View the article online for upates an enhancements.
More informationA Finite volume simulation of a supersonic laminar Flow: Application to a compression corner
Journal of Materials an Environmental Sciences ISSN : 08-508 opright 07, Universit of Mohamme Premier Ouja Morocco JMES, 07 Volume 8, Issue, Page 3993-400 http://www.jmaterenvironsci.com/. Introuction
More information1. The electron volt is a measure of (A) charge (B) energy (C) impulse (D) momentum (E) velocity
AP Physics Multiple Choice Practice Electrostatics 1. The electron volt is a measure of (A) charge (B) energy (C) impulse (D) momentum (E) velocity. A soli conucting sphere is given a positive charge Q.
More informationPhysics 2212 K Quiz #2 Solutions Summer 2016
Physics 1 K Quiz # Solutions Summer 016 I. (18 points) A positron has the same mass as an electron, but has opposite charge. Consier a positron an an electron at rest, separate by a istance = 1.0 nm. What
More informationPREPARATION OF THE NATIONAL MAGNETIC FIELD STANDARD IN CROATIA
n IMEKO TC 11 International Symposium METROLOGICAL INFRASTRUCTURE June 15-17, 11, Cavtat, Dubrovni Riviera, Croatia PREPARATION OF THE NATIONAL MAGNETIC FIELD STANDARD IN CROATIA A. Pavić 1, L.Ferović,
More informationA New Approach in Analytical Analysis of Eddy Currents in Laminated Core
J. Basic. Appl. Sci. Res., (7)741-745, 1 1, TextRoa Publication ISSN 9-434 Journal of Basic an Applie Scientific Research www.textroa.com A New Approach in Analtical Analsis of E Currents in Laminate Core
More informationInfluence the Nozzle Shape on Local Heat Transfer in Impinging Jet
Issue 6, Volume 6, 12 Influence the Nozzle Shape on Local Heat Transfer in Impinging Jet M. Attalla an M. S. Ahme 1 Abstract The local Nusselt number istributions of circular nozzle on a heate flat plate
More informationEFFECTS OF SWEEP ANGLES AND ANGLES OF ATTACK ON JUNCTION-FLOW PATTERNS
4 Journal of Marine Science and Technolog, Vol., No., pp. 4- (4) DOI:.69/JMST-3-35- EFFECTS OF SWEEP ANGLES AND ANGLES OF ATTACK ON JUNCTION-FLOW PATTERNS Kuo-Ching San, Ying-Zong Lin, and Shun-Chang Yen
More informationCE2253- APPLIED HYDRAULIC ENGINEERING (FOR IV SEMESTER)
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW CE5- APPLIED HYDRAULIC ENGINEERING (FOR IV SEMESTER) UNIT II- UNIFORM FLOW CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW CE5- APPLIED HYDRAULIC
More informationTime-of-Arrival Estimation in Non-Line-Of-Sight Environments
2 Conference on Information Sciences an Systems, The Johns Hopkins University, March 2, 2 Time-of-Arrival Estimation in Non-Line-Of-Sight Environments Sinan Gezici, Hisashi Kobayashi an H. Vincent Poor
More informationCALCULATION OF 2D-THERMOMAGNETIC CURRENT AND ITS FLUCTUATIONS USING THE METHOD OF EFFECTIVE HAMILTONIAN. R. G. Aghayeva
CALCULATION OF D-THERMOMAGNETIC CURRENT AND ITS FLUCTUATIONS USING THE METHOD OF EFFECTIVE HAMILTONIAN H. M. Abullaev Institute of Phsics, National Acaem of Sciences of Azerbaijan, H. Javi ave. 33, Baku,
More informationDESIGN, CONSTRUCTION AND TEST OF A TWO-STAGE PLANETARY TRACTION SPEED REDUCER
DEIGN, CONTRUCTION AND TET OF A TWO-TAGE LANETARY TRACTION EED REDUCER Euaro Lobo Lustosa Cabral Escola olitécnica a Universiae e ão aulo Departamento e Engenharia Mecatrônica e istemas Mecânicos Av. Mello
More informationEnhancement of Critical Heat Flux in Tight Rod Bundle with Wire Spacer
Journal of Energy an Power Engineering 10 (2016) 109-115 oi: 10.17265/1934-8975/2016.02.005 D DAVID PUBLISHING Enhancement of Critical Heat Flux in Tight Ro Bunle with Wire Spacer Dan Tri Le 1 an Minoru
More informationAIR BUBBLE ENTRAINMENT IN HYDRAULIC JUMPS: PHYSICAL MODELING AND SCALE EFFECTS
AIR BUBBLE ENTRAINMENT IN HYDRAULIC JUMPS: PHYSICAL MODELING AND SCALE EFFECTS Hubert CHANSON Professor in Civil Engineering The University of Queenslan Brisbane QLD 4072 Australia Ph.: (6 7) 3365 463
More informationNumerical Investigation of Non-Stationary Parameters on Effective Phenomena of a Pitching Airfoil at Low Reynolds Number
Journal of Applie Flui Mechanics, Vol. 9, No. 2, pp. 643-651, 2016. Available online at www.jafmonline.net, ISSN 1735-3572, EISSN 1735-3645. Numerical Investigation of Non-Stationary Parameters on Effective
More informationPARALLEL-PLATE CAPACITATOR
Physics Department Electric an Magnetism Laboratory PARALLEL-PLATE CAPACITATOR 1. Goal. The goal of this practice is the stuy of the electric fiel an electric potential insie a parallelplate capacitor.
More informationFluid Pressure and Fluid Force
SECTION 7.7 Flui Pressure an Flui Force 07 Section 7.7 Flui Pressure an Flui Force Fin flui pressure an flui force. Flui Pressure an Flui Force Swimmers know that the eeper an object is submerge in a flui,
More informationDevelopment of the Vortex Mass Flowmeter with Wall Pressure Measurement
10.478/msr-01-000 MEASUREMENT SCIENCE REVIEW, Volume 1, No. 1, 01 Development of the Vortex Mass Flowmeter with Wall Pressure Measurement Zhiyong Li 1,, Zhiqiang Sun 1, 1 School of Energy Science an Engineering,
More informationinflow outflow Part I. Regular tasks for MAE598/494 Task 1
MAE 494/598, Fall 2016 Project #1 (Regular tasks = 20 points) Har copy of report is ue at the start of class on the ue ate. The rules on collaboration will be release separately. Please always follow the
More informationTable of Common Derivatives By David Abraham
Prouct an Quotient Rules: Table of Common Derivatives By Davi Abraham [ f ( g( ] = [ f ( ] g( + f ( [ g( ] f ( = g( [ f ( ] g( g( f ( [ g( ] Trigonometric Functions: sin( = cos( cos( = sin( tan( = sec
More information3-D FEM Modeling of fiber/matrix interface debonding in UD composites including surface effects
IOP Conference Series: Materials Science an Engineering 3-D FEM Moeling of fiber/matrix interface eboning in UD composites incluing surface effects To cite this article: A Pupurs an J Varna 2012 IOP Conf.
More informationThermal conductivity of graded composites: Numerical simulations and an effective medium approximation
JOURNAL OF MATERIALS SCIENCE 34 (999)5497 5503 Thermal conuctivity of grae composites: Numerical simulations an an effective meium approximation P. M. HUI Department of Physics, The Chinese University
More informationAustralian Journal of Basic and Applied Sciences
Australian Journal of Basic an Applie Sciences, 9(1) January 015, Pages: 38-45 AENSI Journals Australian Journal of Basic an Applie Sciences ISSN:1991-8178 Journal home page: www.ajbasweb.com Velocity
More informationLecture 1b. Differential operators and orthogonal coordinates. Partial derivatives. Divergence and divergence theorem. Gradient. A y. + A y y dy. 1b.
b. Partial erivatives Lecture b Differential operators an orthogonal coorinates Recall from our calculus courses that the erivative of a function can be efine as f ()=lim 0 or using the central ifference
More informationThis section outlines the methodology used to calculate the wave load and wave wind load values.
COMPUTERS AND STRUCTURES, INC., JUNE 2014 AUTOMATIC WAVE LOADS TECHNICAL NOTE CALCULATION O WAVE LOAD VALUES This section outlines the methoology use to calculate the wave loa an wave win loa values. Overview
More informationEvaporating droplets tracking by holographic high speed video in turbulent flow
Evaporating roplets tracking by holographic high spee vieo in turbulent flow Loïc Méès 1*, Thibaut Tronchin 1, Nathalie Grosjean 1, Jean-Louis Marié 1 an Corinne Fournier 1: Laboratoire e Mécanique es
More informationPrep 1. Oregon State University PH 213 Spring Term Suggested finish date: Monday, April 9
Oregon State University PH 213 Spring Term 2018 Prep 1 Suggeste finish ate: Monay, April 9 The formats (type, length, scope) of these Prep problems have been purposely create to closely parallel those
More informationSPE Copyright 1999, Society of Petroleum Engineers Inc.
SPE 664 Effect of Flow Through a Choke Valve on Emulsion Stability M.J. van er Zane, SPE, K.R. van Heuven, J.H. Muntinga, SPE, an W.M.G.T. van en Broek, SPE, Delft University of Technology Copyright 1999,
More informationELECTRON DIFFRACTION
ELECTRON DIFFRACTION Electrons : wave or quanta? Measurement of wavelength an momentum of electrons. Introuction Electrons isplay both wave an particle properties. What is the relationship between the
More informationInvestigation Of Compressor Heat Dispersion Model
Purue University Purue e-pubs International Compressor Engineering Conference School of Mechanical Engineering 2014 Investigation Of Compressor Heat Dispersion Moel Da Shi Shanghai Hitachi Electronic Appliances,
More informationDusty Plasma Void Dynamics in Unmoving and Moving Flows
7 TH EUROPEAN CONFERENCE FOR AERONAUTICS AND SPACE SCIENCES (EUCASS) Dusty Plasma Voi Dynamics in Unmoving an Moving Flows O.V. Kravchenko*, O.A. Azarova**, an T.A. Lapushkina*** *Scientific an Technological
More informationBasic Differentiation Rules and Rates of Change. The Constant Rule
460_00.q //04 4:04 PM Page 07 SECTION. Basic Differentiation Rules an Rates of Change 07 Section. The slope of a horizontal line is 0. Basic Differentiation Rules an Rates of Change Fin the erivative of
More informationAntiderivatives and Indefinite Integration
60_00.q //0 : PM Page 8 8 CHAPTER Integration Section. EXPLORATION Fining Antierivatives For each erivative, escribe the original function F. a. F b. F c. F. F e. F f. F cos What strateg i ou use to fin
More informationGeneral Physics ph 213 Midterm Exam II (Ch 24 27) November 14, False, they don t have to be flat but they must be perpendicular to E-field.
General Phsics ph 13 Miterm am II Ch 7 November 1, 005 Name: Tpe am is close boo an close notes. Use onl our note car. Write all wor an answers in the papers provie. Show all our wor an eplain our reasoning
More informationPHY 114 Summer 2009 Final Exam Solutions
PHY 4 Summer 009 Final Exam Solutions Conceptual Question : A spherical rubber balloon has a charge uniformly istribute over its surface As the balloon is inflate, how oes the electric fiel E vary (a)
More informationDual Vortex Structure Shedding from Low Aspect Ratio, Surface-mounted Pyramids
Dual Vortex Structure Shedding from Low Aspect Ratio, Surface-mounted Pyramids Robert J. Martinuzzi Department of Mechanical and Manufacturing Engineering Schulich School of Engineering University of Calgary
More informationChapter 9 Method of Weighted Residuals
Chapter 9 Metho of Weighte Resiuals 9- Introuction Metho of Weighte Resiuals (MWR) is an approimate technique for solving bounary value problems. It utilizes a trial functions satisfying the prescribe
More informationA hyperbolic equation for turbulent diffusion
Nonlinearity 13 (2) 1855 1866. Printe in the UK PII: S951-7715()1271-X A hyperbolic equation for turbulent iffusion Sanip Ghosal an Joseph B Keller Center for Turbulence Research, Stanfor University, Stanfor,
More informationApplication of the homotopy perturbation method to a magneto-elastico-viscous fluid along a semi-infinite plate
Freun Publishing House Lt., International Journal of Nonlinear Sciences & Numerical Simulation, (9), -, 9 Application of the homotopy perturbation metho to a magneto-elastico-viscous flui along a semi-infinite
More informationV q.. REASONING The potential V created by a point charge q at a spot that is located at a
8. REASONING The electric potential at a istance r from a point charge q is given by Equation 9.6 as kq / r. The total electric potential at location P ue to the four point charges is the algebraic sum
More informationLaboratory Study on Comparison of the Scour Depth and Scour Length of Groundsill with the Opening and Groundsill without the Opening
Journal of the Civil Engineering Forum Vol. 2 No. 1 (January 2016) Laboratory Stuy on Comparison of the Scour Depth an Scour Length of Grounsill with the Opening an Grounsill without the Opening Ani Hairani
More informationLQG FLUTTER CONTROL OF WIND TUNNEL MODEL USING PIEZO-CERAMIC ACTUATOR
5 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES LQG FLUTTER CONTROL OF WIND TUNNEL MODEL USING PIEZO-CERAMIC ACTUATOR Tatsunori Kaneko* an Yasuto Asano* * Department of Mechanical Engineering,
More information2-7. Fitting a Model to Data I. A Model of Direct Variation. Lesson. Mental Math
Lesson 2-7 Fitting a Moel to Data I BIG IDEA If you etermine from a particular set of ata that y varies irectly or inversely as, you can graph the ata to see what relationship is reasonable. Using that
More informationThe effect of nonvertical shear on turbulence in a stably stratified medium
The effect of nonvertical shear on turbulence in a stably stratifie meium Frank G. Jacobitz an Sutanu Sarkar Citation: Physics of Fluis (1994-present) 10, 1158 (1998); oi: 10.1063/1.869640 View online:
More informationPerformance Optimization of Jet Actuator Arrays for Active Flow Control
Performance Optimization of Jet Actuator Arras for Active Flow Control P. Scholz, J. Ortmanns, C.J. Kähler and R. Radespiel Technische Universität Braunschweig, Institut für Strömungsmechanik, Bienroder
More information1. An electron moves from point i to point f, in the direction of a uniform electric field. During this displacement:
Chapter 24: ELECTRIC POTENTIAL 1 An electron moves from point i to point f, in the irection of a uniform electric fiel During this isplacement: i f E A the work one by the fiel is positive an the potential
More informationLecture 2 Lagrangian formulation of classical mechanics Mechanics
Lecture Lagrangian formulation of classical mechanics 70.00 Mechanics Principle of stationary action MATH-GA To specify a motion uniquely in classical mechanics, it suffices to give, at some time t 0,
More informationComputed Tomography Notes, Part 1. The equation that governs the image intensity in projection imaging is:
Noll 3 CT Notes : Page Compute Tomograph Notes Part Challenges with Projection X-ra Sstems The equation that governs the image intensit in projection imaging is: z I I ep µ z Projection -ra sstems are
More informationCENTURION UNIVERSITY OF TECHNOLOGY & MANAGEMENT,ODISHA CUEE-2015
CENTURION UNIVERSITY OF TECHNOLOGY & MANAGEMENT,ODISHA CUEE-015 PHYSICS 1. The imensional formula of angular momentum is a) ML T - b) MLT - c) MLT -1 ) ML T -1. If A B = B A, then the angle between A an
More informationAEROACOUSTIC INVESTIGATION OF THE EFFECT OF A DETACHED FLAT PLATE ON THE NOISE FROM A SQUARE CYLINDER
Abstract AEROACOUSTIC INVESTIGATION OF THE EFFECT OF A DETACHED FLAT PLATE ON THE NOISE FROM A SQUARE CYLINDER Aniket D. Jagtap 1, Ric Porteous 1, Akhilesh Mimani 1 and Con Doolan 2 1 School of Mechanical
More informationSelf-focusing and soliton formation in media with anisotropic nonlocal material response
EUROPHYSICS LETTERS 20 November 1996 Europhys. Lett., 36 (6), pp. 419-424 (1996) Self-focusing an soliton formation in meia with anisotropic nonlocal material response A. A. Zoulya 1, D. Z. Anerson 1,
More informationV = Flow velocity, ft/sec
1 Drag Coefficient Preiction Chapter 1 The ieal force acting on a surface positione perpenicular to the airflow is equal to a ynamic pressure, enote by q, times the area of that surface. Dynamic pressure
More informationA Pair of Large-incidence-angle Cylinders in Cross-flow with the Upstream One Subjected to a Transverse Harmonic Oscillation
Proceedings of the 2010 International Conference on Industrial Engineering and Operations Management Dhaka, Bangladesh, January 9 10, 2010 A Pair of Large-incidence-angle Cylinders in Cross-flow with the
More informationProblem 1 (20 points)
ME 309 Fall 01 Exam 1 Name: C Problem 1 0 points Short answer questions. Each question is worth 5 points. Don t spen too long writing lengthy answers to these questions. Don t use more space than is given.
More informationDiagonalization of Matrices Dr. E. Jacobs
Diagonalization of Matrices Dr. E. Jacobs One of the very interesting lessons in this course is how certain algebraic techniques can be use to solve ifferential equations. The purpose of these notes is
More informationEffects of wavelength and amplitude of a wavy cylinder in cross-flow at low Reynolds numbers
J. Fluid Mech. (2009), vol. 620, pp. 195 220. c 2009 Cambridge Universit Press doi:10.1017/s0022112008004217 Printed in the United Kingdom 195 Effects of wavelength and amplitude of a wav clinder in cross-flow
More informationPolynomial Inclusion Functions
Polynomial Inclusion Functions E. e Weert, E. van Kampen, Q. P. Chu, an J. A. Muler Delft University of Technology, Faculty of Aerospace Engineering, Control an Simulation Division E.eWeert@TUDelft.nl
More informationCalculus I. Lecture Notes for MATH 114. Richard Taylor. Department of Mathematics and Statistics. c R. Taylor 2007
Calculus I Lecture Notes for MATH 4 Richar Talor Department of Mathematics an Statistics c R. Talor 2007 last revision April 5, 2007 MATH 4 Calculus I Page 2 of 26 Contents Preinaries 6 2 Functions 6 2.
More informationChapter-2. Steady Stokes flow around deformed sphere. class of oblate axi-symmetric bodies
hapter- Steay Stoes flow aroun eforme sphere. class of oblate axi-symmetric boies. General In physical an biological sciences, an in engineering, there is a wie range of problems of interest lie seimentation
More informationAPPROXIMATE SOLUTION FOR TRANSIENT HEAT TRANSFER IN STATIC TURBULENT HE II. B. Baudouy. CEA/Saclay, DSM/DAPNIA/STCM Gif-sur-Yvette Cedex, France
APPROXIMAE SOLUION FOR RANSIEN HEA RANSFER IN SAIC URBULEN HE II B. Bauouy CEA/Saclay, DSM/DAPNIA/SCM 91191 Gif-sur-Yvette Ceex, France ABSRAC Analytical solution in one imension of the heat iffusion equation
More informationPhysics 2212 GJ Quiz #4 Solutions Fall 2015
Physics 2212 GJ Quiz #4 Solutions Fall 215 I. (17 points) The magnetic fiel at point P ue to a current through the wire is 5. µt into the page. The curve portion of the wire is a semicircle of raius 2.
More informationADIT DEBRIS PROJECTION DUE TO AN EXPLOSION IN AN UNDERGROUND AMMUNITION STORAGE MAGAZINE
ADIT DEBRIS PROJECTION DUE TO AN EXPLOSION IN AN UNDERGROUND AMMUNITION STORAGE MAGAZINE Froe Opsvik, Knut Bråtveit Holm an Svein Rollvik Forsvarets forskningsinstitutt, FFI Norwegian Defence Research
More informationExperimental evidence of the connection between flow fluctuations and dynamics of vorticity structures in the wake of a triangular prism.
Experimental evidence of the connection between flow fluctuations and dynamics of vorticity structures in the wake of a triangular prism. Guido Buresti, Giacomo Valerio Iungo Department of Aerospace Engineering,
More informationHomework 7 Due 18 November at 6:00 pm
Homework 7 Due 18 November at 6:00 pm 1. Maxwell s Equations Quasi-statics o a An air core, N turn, cylinrical solenoi of length an raius a, carries a current I Io cos t. a. Using Ampere s Law, etermine
More informationImproving the Lorentz Force Amplitude of an EMAT Using Stacked Coil Configuration
Sensors & Transucers, Vol. 155, Issue 8, August 213, pp. 262-27 Sensors & Transucers 213 by IFSA http://www.sensorsportal.com Improving the Lorentz Force Amplitue of an MAT Using Stacke Coil Configuration
More informationINFLUENCE OF SURFACE ROUGHNESS THROUGH A SERIES OF FLOW FACTORS ON THE PERFORMANCE OF A LONGITUDINALLY ROUGH FINITE SLIDER BEARING
ANNALS of Faculty Engineering Huneoara International Journal of Engineering Tome XIV [2016] Fascicule 2 [May] ISSN: 1584-2665 [print; online] ISSN: 1584-2673 [CD-Rom; online] a free-accessmultiisciplinarypublication
More informationLecture Introduction. 2 Examples of Measure Concentration. 3 The Johnson-Lindenstrauss Lemma. CS-621 Theory Gems November 28, 2012
CS-6 Theory Gems November 8, 0 Lecture Lecturer: Alesaner Mąry Scribes: Alhussein Fawzi, Dorina Thanou Introuction Toay, we will briefly iscuss an important technique in probability theory measure concentration
More informationTwo- and Three-Dimensional Validation of Icing Model
APCOM & ISCM 11-14 th December, 13, Singapore To- an Three-Dimensional Valiation of Icing Moel *Ryosuke Hayashi¹ an Makoto Yamamoto 1 Grauate School of Mechanical Engineering, Tokyo University of Science
More informationPhys102 Second Major-122 Zero Version Coordinator: Sunaidi Sunday, April 21, 2013 Page: 1
Coorinator: Sunaii Sunay, April 1, 013 Page: 1 Q1. Two ientical conucting spheres A an B carry eual charge Q, an are separate by a istance much larger than their iameters. Initially the electrostatic force
More informationSensors & Transducers 2015 by IFSA Publishing, S. L.
Sensors & Transucers, Vol. 184, Issue 1, January 15, pp. 53-59 Sensors & Transucers 15 by IFSA Publishing, S. L. http://www.sensorsportal.com Non-invasive an Locally Resolve Measurement of Soun Velocity
More informationA Comparison of Two and Four Microphone Standing Wave Tube Procedures for Estimating the Normal Incidence Absorption Coefficient
A Comparison of Two an Four Microphone Staning Wave Tube roceures for Estimating the Normal Incience Absorption Coefficient Jason Kunio a Brüel & Kjær Soun an ibration N.A. 37 Bowes R Ste Elgin, IL 623,
More informationVertical Sluice Gate Discharge Coefficient
, Scienceline Pulication Journal of ivil Engineering an Uranism Volume, Issue : 8-4 () ISSN-5-4 Vertical Sluice Gate Discharge oefficient Navi Nasehi Oskui * an Farzin Salmasi M Sc Stuent of hraulic structures,
More informationMATH 205 Practice Final Exam Name:
MATH 205 Practice Final Eam Name:. (2 points) Consier the function g() = e. (a) (5 points) Ientify the zeroes, vertical asymptotes, an long-term behavior on both sies of this function. Clearly label which
More informationComputed Tomography Notes, Part 1. The equation that governs the image intensity in projection imaging is:
Noll 6 CT Notes : Page Compute Tomograph Notes Part Challenges with Projection X-ra Sstems The equation that governs the image intensit in projection imaging is: z I I ep μ z Projection -ra sstems are
More informationThis is a repository copy of PIV studies of coherent structures generated at the end of a stack of parallel plates in a standing wave acoustic field.
This is a repository copy of PIV stuies of coherent structures generate at the en of a stack of parallel plates in a staning wave acoustic fiel. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/79741/
More informationNumber of wireless sensors needed to detect a wildfire
Number of wireless sensors neee to etect a wilfire Pablo I. Fierens Instituto Tecnológico e Buenos Aires (ITBA) Physics an Mathematics Department Av. Maero 399, Buenos Aires, (C1106ACD) Argentina pfierens@itba.eu.ar
More informationEvaluation of Column Breakpoint and Trajectory for a Plain Liquid Jet Injected into a Crossflow
ILASS Americas, 1 st Annual Conference on Liqui Atomization an Spray Systems, Orlano, Floria, May 008 Evaluation of Column Breakpoint an Trajectory for a Plain Liqui Jet Injecte into a Crossflow S.M. Thawley,
More informationEXPERIMENTAL STUDY OF THE AIR-WATER SHEAR FLOW IN A HYDRAULIC JUMP
EXPERIMENTAL STUDY OF THE AIR-WATER SHEAR FLOW IN A HYDRAULIC JUMP b H. CHANSON an T. BRATTBERG Department of Civil Engineering, The Universit of Queenslan, Brisbane QLD 4072, Australia Abstract : Although
More informationFluid Flow Around and Heat Transfer from Elliptical Cylinders: Analytical Approach
JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER Vol. 19, No., April June 5 Flui Flow Aroun an Heat Transfer from Elliptical Cyliners: Analytical Approach W. A. Khan, J. R. Culham, an M. M. Yovanovich University
More informationMonitoring of Mechanical Properties of Gypsum Using the Impulse Excitation Method
Monitoring of Mechanical Properties of Gypsum Using the Impulse Excitation Metho RICHARD ŤOUPEK, TOMÁŠ PLACHÝ, MICHAL POLÁK, PAVEL TESÁREK Department of Mechanics, Faculty of Civil Engineering Czech Technical
More informationA new identification method of the supply hole discharge coefficient of gas bearings
Tribology an Design 95 A new ientification metho of the supply hole ischarge coefficient of gas bearings G. Belforte, F. Colombo, T. Raparelli, A. Trivella & V. Viktorov Department of Mechanics, Politecnico
More informationA Quantitative Analysis of Coupling for a WPT System Including Dielectric/Magnetic Materials
Progress In Electromagnetics Research Letters, Vol. 72, 127 134, 2018 A Quantitative Analysis of Coupling for a WPT System Incluing Dielectric/Magnetic Materials Yangjun Zhang *, Tatsuya Yoshiawa, an Taahiro
More informationSystem Modeling of MEMS Gyroscopes
Proceeings of the 5th Meiterranean Conference on Control & Automation, Jul 7-9, 7, Athens - Greece T-7 Sstem Moeling of MEMS Groscopes Ramar Rashe an H. Momeni* * Tarbiat Moares Universit, Facult of Engineering,
More informationAN EXPERIMENTAL STUDY ON LAMINAR-TURBULENT TRANSITION AT HIGH FREE-STREAM TURBULENCE IN BOUNDARY LAYERS WITH PRESSURE GRADIENTS
EPJ Web of Conferences, 00 (0) DOI: 0.05/epjconf/0500 Owned b the authors, published b EDP Sciences, 0 AN EXPERIMENTAL STUDY ON LAMINAR-TURBULENT TRANSITION AT HIGH FREE-STREAM TURBULENCE IN BOUNDARY LAYERS
More informationA Design Method for USBL Systems with Skew Three-element Arrays
A Design Metho for USBL Sstems with Skew Three-element Arras MIKHAIL ARKHIPOV Department of Postgrauate Stuies Technological Universit of the Mixteca Carretera a Acatlima Km. 2.5, Huajuapan e Leon, Oaxaca,
More informationAssignment 1. g i (x 1,..., x n ) dx i = 0. i=1
Assignment 1 Golstein 1.4 The equations of motion for the rolling isk are special cases of general linear ifferential equations of constraint of the form g i (x 1,..., x n x i = 0. i=1 A constraint conition
More informationINFLUENCE OF IMPERFECT BONDING ON INTERFACE OF MAGNETO- ELECTRO-ELASTIC HETEROSTRUCTURES: SH WAVES DISPERSION RELATIONS
NFLUENCE OF MPERFECT BONDNG ON NTERFACE OF MAGNETO- ELECTRO-ELASTC HETEROSTRUCTURES: SH WAVES DSPERSON RELATONS J. A. Otero, jaotero@icmf.inf.cu, H. Calas, hcalass@gmail.com nstituto e Cibernética, Matemática
More informationShort Intro to Coordinate Transformation
Short Intro to Coorinate Transformation 1 A Vector A vector can basically be seen as an arrow in space pointing in a specific irection with a specific length. The following problem arises: How o we represent
More informationInternational Conference on Methods of Aerophysical Research, ICMAR 2008
International Conference on Methods of Aerophysical Research, ICMAR 8 EXPERIMENTAL STUDY OF UNSTEADY EFFECTS IN SHOCK WAVE / TURBULENT BOUNDARY LAYER INTERACTION P.A. Polivanov, А.А. Sidorenko, A.A. Maslov
More informationThe influence of the equivalent hydraulic diameter on the pressure drop prediction of annular test section
IOP Conference Series: Materials Science an Engineering PAPER OPEN ACCESS The influence of the equivalent hyraulic iameter on the pressure rop preiction of annular test section To cite this article: A
More informationChapter 6: Energy-Momentum Tensors
49 Chapter 6: Energy-Momentum Tensors This chapter outlines the general theory of energy an momentum conservation in terms of energy-momentum tensors, then applies these ieas to the case of Bohm's moel.
More informationIERCU. Institute of Economic Research, Chuo University 50th Anniversary Special Issues. Discussion Paper No.210
IERCU Institute of Economic Research, Chuo University 50th Anniversary Special Issues Discussion Paper No.210 Discrete an Continuous Dynamics in Nonlinear Monopolies Akio Matsumoto Chuo University Ferenc
More informationApplications of First Order Equations
Applications of First Orer Equations Viscous Friction Consier a small mass that has been roppe into a thin vertical tube of viscous flui lie oil. The mass falls, ue to the force of gravity, but falls more
More informationIntroduction Basic principles Finite element formulation Nonlinear algorithms Validation & examples Oofelie::MEMS, driven by SAMCEF Field Perspectives
Non linear behavior of electrostatically actuate micro-structures Dr. Ir. Stéphane Paquay, Open Engineering SA Dr. Ir. Véronique Rochus, ULg (LTAS-VIS) Dr. Ir. Stefanie Gutschmit, ULg (LTAS-VIS) Outline
More informationEXPERIMENTAL INVESTIGATION ON PNEUMATIC COMPONENTS
Conference on Moelling Flui Flow (CMFF 03) The 12 th International Conference on Flui Flow Technologies Buapest, Hungary, September 3-6, 2003 EXPERIMENTAL INVESTIGATION ON PNEUMATIC COMPONENTS Zoltán MÓZER,
More information5-4 Electrostatic Boundary Value Problems
11/8/4 Section 54 Electrostatic Bounary Value Problems blank 1/ 5-4 Electrostatic Bounary Value Problems Reaing Assignment: pp. 149-157 Q: A: We must solve ifferential equations, an apply bounary conitions
More informationPerturbation Analysis and Optimization of Stochastic Flow Networks
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. XX, NO. Y, MMM 2004 1 Perturbation Analysis an Optimization of Stochastic Flow Networks Gang Sun, Christos G. Cassanras, Yorai Wari, Christos G. Panayiotou,
More informationMAE 210A FINAL EXAM SOLUTIONS
1 MAE 21A FINAL EXAM OLUTION PROBLEM 1: Dimensional analysis of the foling of paper (2 points) (a) We wish to simplify the relation between the fol length l f an the other variables: The imensional matrix
More informationof a molecule possessing a vibrational energy hν is
Question 1 (a) A pulse N:YAG laser is to be employe in a Rayleigh scattering experiment to etermine gas temperature. The laser can be use at 532 nm (secon harmonic), 355 nm (thir harmonic), or 266 nm (fourth
More information