INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH OLUME, ISSUE, OCTOBER ISSN - Usig Four Types Of Notches For Compariso Betwee Chezy s Costat(C) Ad Maig s Costat (N) Joyce Edwi Bategeleza, Deepak T. J., Eric L.W.K., Muir H. K. Abstract: I this techical paper, Chezy s ad Maig s costat were compared, usig four differet otches o the plai bed. The first phase of this paper ivolves desigig of the otches, usig Auto Cad software followed by fabricatio. The secod phase ivolves carryig out Experimets i ope chael Laboratory by usig hydraulic bech. The fial phase ivolves calculatios of Chezy s ad maig s costats. It was see that, Chezy s costat is directly proportioal to actual discharge While Maig s costat i iversely proportioal to actual discharge. Chezy s costat has higher value compared to Maig s costat value. Also Maig s Stadard deviatio is smaller compared to that of Chezy s. This idicates the accuracy of the resistace coefficiet due to the fact that the smaller the value of stadard deviatio the higher the level of accuracy. Therefore, the coefficiet of resistace is more adaptable, simple ad accurate i Maig s costat. Key words: Ope chael flow, Hydraulic bech, Coefficiets of Resistace, Actual discharge INTRODUCTION May Researchers have bee workig o Ope Chael over the years, to discover ad upgrade the theory o Hydraulic structures ad elemets. The results obtaied from previous experimet shows how Ope Chael have bee developed ad modified to a large extet ad it has become more useful i life tha before. For example Resistace Coefficiets (Maig s ad Chezy s Costat) was discovered after a series of so may experimets. The compariso of these Resistace Coefficiets (Maig s ad Chezy s Costat) has ofte bee doe i Ope chael laboratory, usig weirs istead of usig otches. The aim was to determie the accurate ad adaptable coefficiet of resistace. I order to come up with ew results of the compariso, otches were used istead of weirs. The otches are cosidered to be more accurate tha weirs (ASTM, ). Table: Summary of few typical values of maig s () Chael type Surface material ad form Maig s rage River earth, straight.-. earth, meaderig.-. gravel(-mm) straight.-. gravel(-mm) widig.-. Ulied caal earth, straight.-. rock, straight.-. lied caal Cocrete.-. Lab models Mortar.- Perspex. (CIE Fluid Mechaics, ) Joyce. E, School of Civil Egieerig, Uiversity of East Lodo, Lito Uiversity College, Malaysia Deepak T.J., Head of Disciplie, Civil Egieerig- FOSTEM, INTI Iteratioal Uiversity, Malaysia, PH-. E-mail: deepak_tj@gmail.com CHEZY S EQUATION Chezy s equatio is the discharge equatio which was improved by a Frech egieer aroud the year. Its applicatio is to compute the depth-discharge relatioship. It is derived as show below; Force producig motio = frictio force restig motio pgals o KPL Cacellig L i both sides ad rearragig, it gives, pg A S K P = Groupig all the costats, it gives Chezy s roughess coefficiet, C= pg K ad P A = R Hece, substitute C ad R ito equatio (ii) = This is the stadard Chezy s formula (the first formula for uiform ope chael flow) Where by is the mea velocity of water flow, C is chezy s costat, R is hydraulic mea depth ad Sois the bed slope. Chezy s costat(c) depeds o the ature of Chael walls ad with H. (Hamill.L, ) MANNING S EQUATION Maig s Equatio was itroduced i, after a series of studies of evaluatio of C (Chezy s costat), so as to help egieers i producig results which are more adaptable compare to Chezy s formula. It is due to the fact that, Chezy s formula was t able to provide results which could satisfy the egieers (especially Irrigatio Egieers). Stadard Maig s formula ( = R / S / /), is very simple to use ad it gives good results, compared to Chezy s formula. Maig s formula is oe of the Empirical equatios which ca replace the variatios of C (i Chezy s formula) with m.below is the formula which shows how the replacemet is doe. By cosiderig Chezy s equatio, = C Replacig C with becomes = Mm C Mm or MR therefore the equatio s IJSTR
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH OLUME, ISSUE, OCTOBER ISSN - k M Ca also be replaced by k z be, = m s or = R S z or. Hece the equatio will Where: is elocity, k or z is coversio costat, is Maig s roughess Coefficiet, m or R is hydraulic radius ad S is slope of the eergy grade lie. It is used i determiig the Chael Uiform flow capacity. (J.B Calvert, ) MATERIALS AND METHODS MATERIALS Acrylic plastic The Notches are made of Acrylic plastic (i form of a sheet) istead of usig metal. Grider machie was used i the cuttig work of the plastic accordig to the give specificatios as show below. -otch: opeig (depth:mm ad agle: ), size of mm(h) x mm(w) -otch: opeig (depth:mm ad agle: ), size of mm(h) x mm(w) Rectagular otch: opeig (depth:mm ad width: mm), size of mm(h) x mm(w) Trapezoidal otch: opeig (depth:mm ad width:mm), size of mm(h) x mm(w) METHODS There were three types of quatitative variables used durig the experimet, amely; Idepedet variable (water flow or discharge), cotrolled variable (width) ad depedet variable (Height). The machie used i the experimet was hydraulic bech because the otches ca be easily istalled. Its legth ad width are mm ad mm respectively. APPARATUS USED: Hydraulic bech, Stop watch, Wig Nut screw Flow meter, Pump,Rectagular otch, Trapezoidal otch, o ad o - otch. The required apparatus were cleaed before proceedig with the experimet. Flow meter, stop watch ad other required equipmet were well checked ad calibrated before startig the experimet. The rectagular Notch was clamped to the hydraulic bech by usig the wig ut Screw. The discharge valve was adjusted ito.l/s ad the the hydraulic bech was switched o ad water was allowed to discharge. The water was left to flow withi miutes so as to get a steady water flow. The Several readigs of flow rate (Q), time, water level upstream/water head above the otch(h) ad Chael width(b) were the take while icreasig the flow rate each time at a iterval of miutes. The rectagular otch was replaced by -otch ad the the above procedures were repeated. The -otch was replaced by -otch ad the above procedures were repeated. Fially the -otch was replaced by Trapezoidal otch ad the above procedures were repeated. EMPERICAL STUDY The Actual Discharge was obtaied directly from the IJSTR experimet. Hece the Actual Discharge was used to fid Chezy s ad Maig s Costat usig the formulas show below. Q A Chezy s Costat equatio C A Where by R, A= wetted area i a chael while P= P wetted perimeter i a chael. Maig s Costat equatio / / R S Whereby, Q = Actual Discharge, A = Flow cross sectio area, = Mea velocity, R = Hydraulic mea radius, S = Bed slope, c = Chezy s costat ad = Maig s costat Stadard deviatio equatio xi x S. D N Whereby; S is Stadard deviatio, Xi is each value i the sample, X is mea of the values ad N is umber of samples RESULTS AND DISCUSSION Ru Q(m /s) B(m) H(m) (m/s) C............................................................ Average,C&... This part idicates sample of calculatio of Maig s costat, Chezy s Costat ad tables of results for each otch ad discussio. Rectagular otch Sample of calculatio to fid C ad Bed slope (S) = sice is a plai bed C Q..m / s A.
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH OLUME, ISSUE, OCTOBER ISSN - R A.. m P.. C.. R S / /... Table : shows the results of Rectagular otch Ru Q(m /s) B(m) H(m) (m/s) C.................... Average,C&.......................... o -otch Table : shows the results of o -otch o -otch................. Average,C& Trapezoidal otch.. Table : shows the results of Trapezoidal otch Ru Q(m /s) B(m) H(m) C............................................................. Average,C&... Table to idicates the results of elocity, chezy s ad maig s costat obtaied after the completio of the calculatios. Chezy s icreases i all the tables while maig s decreases. Resistace Coefficiets Statistical Aalysis Table : shows Average c ad ad variaces for the type of otches Ru Table : shows the results of -otch Q(m /s) B(m) H(m) (m/s) C.................................................. IJSTR Type of Notches c (Xi-X) (Xi-X). Rectagular otch..... v-otch..... v-otch..... Trapezoidal otch.... Average of C &.. Sum.. The above table sigifies variaces of Maig s ad Chezy s costat. Maig s has smaller value of variace compare to that of chezy s. Likewise the stadard deviatio of Maig s costat () is. while that of Chezy s costat (c) is..
Chezy's(c) INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH OLUME, ISSUE, OCTOBER ISSN - Below are the graphs showig the relatioship betwee Chezy s, Maig s ad Flow rate. Chezy's(c) s Flow rate(q) y =.x - E- R² =... Discharge Q(Cumecs) Figure : Chezy s ad Maig s s. Actual Discharge of o -otch Figure: Chezy s ad Maig s s Actual Discharge of rectagular otch IJSTR Figure : Chezy s ad Maig s s. Actual Discharge of Trapezoidal otch The above graphs of Chezy s agaist Flow rate ad Maig s agaist Flow rate shows how Chezy s ad Maig s relates with the flow rate. Chezy s costat icreases whe actual discharge icreases (asceds). While Maig s costat decreases whe actual discharge icreases (desceds). This idicates that the higher the discharge value, the higher the Chezy s costat ad vice versa. Ulike Maig s costat,
Maig's variace Chezy's ariace INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH OLUME, ISSUE, OCTOBER ISSN - the higher the discharge value, the lower the Maig s value. This implies that Chezy s costat is iversely proportioal to Maig s costat. Relatioship betwee Chezy s& the type of otches ad Maig s & types of otches Chezy's variace s Type of otches Types of otches Maig's variace s Type of otches... discharge icreases while Maig s costat decreases as the actual discharge icreases. It was observed from the graphs ad the data that Chezy s costat ad Maig s costat varies idirectly. This meas that whe chezy s costat icrease maig s costat decrease. Also Chezy s has big value of stadard deviatio compare to maig s. The smaller the value of stadard deviatio the higher the level of accuracy, therefore Maig s has high level of accuracy tha chezy s costat. I additio to that, it was discovered that the Coefficiet of Resistace is more adaptable, simple ad accurate i Maig s costat. This is due to the fact that it gives small value which satisfy majority of the researchers. The evidece is see from the record of the geerally recogized tables ad figures ad from the stadard deviatio. These records help i givig a clear prove about Maig s costat. REFERENCE [] ASTM () America Society for Testig ad Materials. ASTM D. Stadard method for opechael flow measuremet of water with thi-plate weirs. [Olie] Available at: http://global.ihs.com (Accessed o th Jauary ) [] B.C. Ye, (). Ope Chael Flow Resistace. Joural of Hydraulic Egieerig [] Calvert, J.B. () Ope-Chael Flow [Olie] Available at: http //mysite.du.edu/etuttle/tech/opech.htm (Accessed o Jauary, ) [] Chow,.T. () Ope-Chael Hydraulics. Sigapore: McGraw-Hill [] CIE Fluid Mechaics () Ope Chael ydraulics.[olie] availableat: www.efm.leeds.ac.uk/cie/cie/opechael Hydraulics.pdf (Accessed o th March, ) Types of otches [] Hamill L. () Uderstadig Hydraulics Palgrave Macmilla New York Figure : Average Chezy s ad Maig s variace s Type of otches By referrig to the obtaied stadard deviatio results of Chezy s ad Maig s, the highest stadard deviatio is see o Chezy s while the lowest stadard deviatio is see o Maig s. This also helps to verify the level of accuracy betwee the two coefficiets of resistace. Therefore, Maig s has high level of accuracy tha chezy s because it has smaller value of stadard deviatio. I additio to that, the highest variace of chezy s average is obtaied o v-otch ad the lowest variace is obtaied o rectagular otch. While highest variace of Maig s average is obtaied o trapezoidal otch ad the lowest variace is foud o v- otch. This idicates how Chezy s ad Maig s are idirectly related. CONCLUSION The fudametal objectives of this paper were accomplished. The results verified that Chezy s costat icreases as actual IJSTR