ANALYSIS AND MODELING OF COMBINED DISCHARGE THROUGH BOX CULVERTS AND OVER CONTRACTED BROAD-CRESTED WEIRS

Transcription

1 Seventh International Water Tehnology Conferene Egypt 1-3 April 003 ANALYSIS AND MODELING OF COMBINED DISCHARGE THROUGH BOX CULVERTS AND OVER CONTRACTED BROAD-CRESTED WEIRS Adel-Azim M. Negm Assoiate Professor, Dept. of Water & Water Strutures Eng., Faulty of Engineering, Zagazig University, Zagazig, Egypt ABSTRACT An experimental investigation is onduted on simultaneous flo through ulvert and over road-rested eir. The flo at the ulvert outlet is onsidered as sumerged flo. Both the ulvert and the road-rested eir (BCW) idths are smaller than the hannel idth. The harateristis of the simultaneous flo through oth strutures and the effets of flo and geometrial parameters of the struture ere presented in the first part of this paper. In this part, disharge predition models are developed using (a) multiple linear regression, () asi disharge equations of BCW and ulvert and () artifiial neural netorks. The predition and performane of eah of the three models are ompared using four riteria, namely, (i) mean relative asolute error, MRAE, (ii) root mean square error RMSE, (iii) oeffiient of orrelation, R, and standard error of estimate, SEE. Analysis of results indiated that the ANNs are poerful predition tool ompared to other models folloed y the model ased on the asi disharge equations of BCW and ulvert. Sensitivity analysis is also onduted to reflet the relative importane of the involved variales. Keyords: Broad-rested eirs, Culvert, Predition models, Simultaneous flo, Hydrauli strutures, Artifiial neural netorks 1. INTRODUCTION Both ulverts and road-rested eirs are used for flo rate measurements in open hannels as a separate struture. When existing ulvert eomes inadequate to arry the required disharge due one reason or another, one of to alternatives are ommon, a replaement y a ne ulvert of larger apaity or apaity improvement y installing another one adjaent to the old. A third alternative may e proposed y employing a road-rested eir over the ulvert dek y onstruting the eir alls aove the ulvert ody and elevating the roaday aove the eir through a ridge. Figure 1 shos a definition sketh for this alternative to illustrate the involved variales in the present paper. The third Alternative as investigated y Mohamed [1] and Negm [] from the hydraulis point of vie. A short revie of the related studies to eah struture separately as introdued y Mohamed [1] and Negm [].

2 Seventh International Water Tehnology Conferene Egypt 1-3 April 003 h Q eir H Q ulvert P L D H d h t Q S o B Figure 1. Definition sketh for simultaneous flo through ox ulvert and over ontrated road rested eir. Flo through ulverts is ontrolled y many variales inluding the inlet geometry, roughness, size, slope, approah and tailater onditions. Exat determination of type of flo through ulvert needs laoratory or field investigations. Generally speaking, ulverts may e floing full or partly full. They floing full hen oth the inlet and the outlet are sumerged or hen the inlet is sumerged and the outlet is not ut the ulvert is long enough to e onsidered as hydraulially long, Cho [3]. Variety of flo types ould take plae through ulverts. The riteria ontrolling eah type of flo and the orresponding disharge equation ould e found in e.g. Hershy [4] and Frenh [5]. For more detailed information on different types of flo though ulverts, Manning roughness oeffiients and disharge oeffiients for ulvert, interested reader an onsult Bodhaine [6]. On the other hand, road-rested eir (BCW) is a simple measurement devie ith the advantage of easy onstrution, easy installation and struture staility. The speifiation of road-rested eirs and installation proedures for aurate measurements an e found in e.g. Bos [7]. A revie of the studies onerning free and sumerged flo harateristis over suppressed BCW as presented in Negm and Alshaikh [8] Reently, an experimental investigation as onduted y Mohamed [1] to study the harateristis of simultaneous flo over ontrated BCWs and through ox ulverts. The effets of sumergene S, relative idth of eir /D, and relative idth of ulvert /D, on the omined dimensionless disharge Q / D gd (ith D eing the height of the ulvert vent, is the idth of ulvert vent, Q is the omined disharge and g is the gravitational aeleration). The folloing regression model (R = and SEE = 0.177) as provided to estimate the disharge through the omined struture having a ottom slope equals

3 Seventh International Water Tehnology Conferene Egypt 1-3 April 003 Q / D gd H = S (1) D Whih is valid ithin the folloing limitations: 3 S 4, 1.4 /D 3, 1.67 /D 3, 0.53 / 1.86 and S o = Mohamed s ork as extended y Negm [] to investigate the effets of slope and oth flo and geometrial parameters of the simultaneous flo. All the olleted data due to oth studies of Mohamed [1] and Negm [] as used to develop a general predition model instead of Eq.(1) to inlude the effet of ottom slope along ith the other parameters as follos (R = and SEE=0.174): H Q / D gd S = S o () D D D Whih is valid ithin the folloing limitations: 3 S 4, 1.4 /D 3, 1.67 /D 3, 0.53 / 1.86 and S o In this paper, disharge predition models are developed using to different approahes. The first is y utilizing the asi equations of ulvert and BCW and the seond y applying the artifiial neural netorks. Results of oth models are ompared to those of equations 1 and. D D. THEORETICAL ANALYSIS The simultaneous disharge shon y Figure 1 ould e otained y summing up the disharge over the road-rested eir and that passing through the ulvert. The disharge over the road-rested eir an e omputed from the folloing equation, Bos [7] and Negm and Alshaikh [8] 3 / Q = CdC v gh (3) 3 3 In hih Q is the disharge over the eir, C d is the oeffiient of the disharge of the eir, C v is the oeffiient of veloity, C v =(H o /h ) 1.5, H o is the total energy head over the eir, H o =h +V a/g, V a is the veloity of approah, V a = Q/(BH), Q is the total inoming disharge, B is the idth of the approahing hannel, H is the depth of flo in the approahing hannel, is the idth of eir, g is the gravitational aeleration and h is the head of ater over the eir. On the other hand, the disharge passes through the ulvert h t /D>1.0 and H/D>1.0 is given y the folloing equation, Frenh [5] ( H h ) g t Q = CDA o 3 1 ( 9C 4 / (4) + Dn L / R o ) In hih Q is the disharge through the ulvert, A o is the ross setional area of the ulvert, R o is the hydrauli radius of the ulvert, C D is the disharge oeffiient of the 1/

4 Seventh International Water Tehnology Conferene Egypt 1-3 April 003 ulvert, n is the Manning roughness oeffiient of the ulvert materials, L is the length of the ulvert, h t is the tailater depth donstream the ulvert. The simultaneous disharge over the eir and through the ulvert ould e otained y adding equation 4 to equation 3: 1/ ( ) ( ) 3 / g H h t Q = F CdC v gh + C DA o 4 / 3 (5) C Dn L / R o In hih F is a fator to aount for the interation eteen the flo over the eir and that through the ulvert. The interation fator F is to e determined experimentally or from field data henever availale. 3. EXPERIMENTAL ARRANGEMENT The experimental ork of the present paper as onduted y Mohamed [1] and Negm [] in a horizontal retangular flume 30.5 m ide, 31 m high and 9.5 m long.. The flume is equipped ith a tail gate to ontrol the tailater depth. A entrifugal pump lifts ater from underground sump to the flume inlet. Water runs through the flume then returns ak to the sump tank via a measuring tank. The olleted experimental data are used in this paper to alirate equation 5 and to train the developed artifiial neural netork model. A typial tested model onsisted of a ontrated road-rested eir omined ith one vent ox ulvert ith the same total length from entrane to exit of 40 m. Also, the height of the ulvert arrel as kept onstant to 6 m. Nine data sets (143 runs) as olleted y Mohamed [1] hile only four sets (77 runs) ere arried out y Negm [] as indiated y Tale 1. During the ourse of the experimental programs, the flo at oth inlet and outlet of the ulvert ere sumerged and the ulvert is floing full. Also, the approahing disharge to the struture as more than the apaity of the ulvert and thus a flo over the eir as expeted. The reorded measurements inlude the flo depth at 40 m upstream from the ulvert inlet and just donstream of the ulvert to ensure that the flo over the eir is free. The tailater depth as reorded several times for eah disharge to aount for the effet of sumergene. The disharge as measured y a pre-alirated V-noth installed in a measuring tank loated elo the flume outlet at its donstream end and is onneted diretly to underground sump tank. Water depths ere measured using a preise point gauge (up to ± 0.1 mm auray) mounted on instrument arriage.

5 Seventh International Water Tehnology Conferene Egypt 1-3 April 003 Tale 1 Experimental onditions of the olleted data Series S /D /D / S o Soure A Ref. [1] B Ref. [1] C Ref. [1] D Ref. [1] E Ref. [1] F Ref. [1] G Ref. [1] H Ref. [1] I Ref. [1] TA Ref. [] TB Ref. [] TC Ref. [] TD Ref. [] 4. CALIBRATION OF THE PROPOSED MODEL The disharge through the omined struture ould e omputed using equation (5). If the folloing fators are ell defined: 4.1. MANNING ROUGHNESS COEFFICIENT OF THE CULVERT MATERIALS N. Sine all the tested models in this paper are made from smooth and lean prespex, the Manning roughness oeffiient is assumed to e THE DISCHARGE COEFFICIENT OF THE CULVERT, C D For this partiular type of flo through ulvert, the disharge oeffiient of the ox ulvert ith ing alls and the square top entrane is not eveled is taken as 0.75, Frenh [5] THE COEFFICIENT OF VELOCITY OF THE WEIR C V Sine eah of the eir idth and the ulvert idth is less than the hannel idth, the approahing hannel is ide enough suh that the approah veloity is very small and hene the oeffiient of veloity ould e negleted. Hoever, the total energy is omputed and the average oeffiient of veloity for the eir is found to e This means that onsidering the energy head ill inrease the flo due to the eir y an amount of aout %. Therefore, the oeffiient of veloity is assumed unity in this ork.

6 Seventh International Water Tehnology Conferene Egypt 1-3 April THE DISCHARGE COEFFICIENT OF THE WEIR C d The values of h /L is almost less than 0.4 hile h /(h +P) is almost less than In this ase a orretion fator of 1.05 is applied to the asi disharge oeffiient of the road-rested eir hih is equal to C d = Hoever, the use of the asi disharge oeffiient of is aurate enough eause the use of the orretion fator does not improve the performane of the equation signifiantly. When using the asi oeffiient of disharge, the values of R and RMSE are and 0.43 respetively hile they are and hen a orretion fator is applied. Therefore, C d is assumed to e THE INTERACTION FACTOR F The simultaneous disharge is omputed using equation 5. Under the assumption F=1. The value of F is then omputed y dividing the atual measured disharge y the omputed disharge. Several approahes ere employed in order to selet a proper value of F. The est approah as to orrelate the interation fator F to the fators of equation hih govern the simultaneous disharge as it improves the performane of the predition model (equation 5). The otained regression equation for F is as follos (R =0.954 and SEE=0.087) H F = S S o (6) D D D 5. VERIFICATION OF THE MODEL (EQUATION 5) Equation 5 ith F as defined y equation 6 is used to ompute the simultaneous disharge over the eir and through the ulvert. Also, equations 1 and are used to do the same. The omputed values are ompared to the measured simultaneous disharge. The omparisons are displayed in terms of the mean relative asolute error MRAE, the root mean square error RMSE, the orrelation oeffiient R, and the standard error of estimate SEE. The results are shon in tale. Tale Comparison eteen measurements and preditions of equations 1, and 5 Criterion Eq. 1. Eq.. Eq. 5, F= Eq. 6. ANN MRAE% RMSE R SEE Residuals, R Max. +ve error Max. ve error % Os. ith error <5% (<.5%)

7 Seventh International Water Tehnology Conferene Egypt 1-3 April 003 Also, Figure presents the omparison eteen the measurements and the predition of equation (5) ith F defined y equation 6. Clearly, from Tale 1 and Figure, equation (5) performs satisfatory ell ompared to other developed regression models eause equation (5) has the loest vales of MRAE, RMSE and SEE and the highest value of R ompared to equations (1) and (). 6. BUILDING THE ARTIFICIAL NEURAL NETWORKS MODEL Artifiial neural netorks or simply neural netorks are a ne ay of analyzing data. They have a unique aility to learn omplex patterns and trends in the data emulating the human aility to solve ompliated prolems. Therefore, neural omputing are ased on the ay that iologial system, suh as human rain, ork. The human rain is made up of many neurons. Eah of the rain ells is onneted to many others in a netork that adopts and hanges as the rain learns. In neural omputing, proessing elements (PE) replae the neurons and these PEs are linked together to form neural netorks. Eah PE performs a simple task. It is the onnetions eteen the PEs that give neural netorks the aility to learn patterns and interrelationship in data through the ertain eights assoiated to the onnetions PEs. Early orks on using ANN in the field of hydraulis ere pulished during the last deade, e.g. Gruert [9], Diike and Aott [10] and Diike et al. [11]. 5.0 Predited disharge Q L/s Eq. 5. (Exp. data of Moh. 00) Eq. 5. (Exp. data of Negm 00) Line of Equality Measured disharge Q L/s Figure. Predition of equation (5) ith F as given y equation 6 versus measured data due to Mohamed [1] and Negm []

8 Seventh International Water Tehnology Conferene Egypt 1-3 April 003 The most important tool of ANN applied in this study is the multi-layer pereptrons (MLP) hih is a neural netork modeling tool that is optimized for predition and foreasting appliations, Neural Connetion [1]. The MLP an e used to lassify patterns or to predit values from data. The MLP learns from examples y providing the data to the neural netork through an input tool or input layer hih onsists of a numer of PEs equals the numer of input variales or fields suh that eah PE represents one variale or one filed. These data are proessed in a seond layer alled hidden layer eause of all the proessing and omputations through this ore layer are hidden from the users. More than one hidden layer ould e used depending of the omplexity of the appliation (if no hidden layer is used, it is a simple pereptron).the proessed data are sent to the output layer that onsists of a numer of PEs equals to the numer of targets (or numer of desired outputs) in the appliation. All the PEs or neurons of eah layer are onneted the PEs of the preeding and folloing layers y links or onnetions ithout feedak (therefore they are MLP foreord netorks) ut not to other neurons ithin the layer. A typial netork of this type for the present appliation onsisted of three layers as shon in Figure 3. Input layer of 6 neurons (or 6 PEs) to represent the dimensionless variales S, H/D, /D, /D, / and S o. An output layer to represent the single output variale (the disharge). The hidden layer eteen the input and the output layer to reeive the input, to perform the omputations and to the send the outputs to the output layer. The hidden layer uses a transfer or ativation funtion to modify the input to the neuron. The transfer funtion may e linear, sigmoid or tansh. Sigmoid or tansh are smooth nonlinear funtions and one of them is normally hosen eause the learning algorithm requires a response funtion ith a ontinuous, single-valued first derivative. Building the MLP netork is knon as training. The folloing steps summary the netork training proesses ased on akpropagation learning algorithm, Neural Connetion [1] and Negm [13]. i- The values of the eights are set to initial random values. The normalized input pattern X p (S, H/D, /D, /D, / and S o ) and the normalized target pattern T p (Q) are shon to the netork. ii- The output (O) from eah node in a layer is alulated. The output from a node j in the seond layer is given y: n O = φ = x + (7) iii- j ( ) i 1 ij i j in hih φ is the ativation or transfer funtion of the node. The ativation funtion in the present appliation is the hyperoli tangent funtion (tansh) and j is the ias eight of the node j. The eights () eteen nodes are adjusted, starting from the output layer and orking akards. The ne eight is given y: ij(s + 1) = ij(s) + ηδpjopj (8) in hih ij (s) is the eight eteen nodes i and j at step s efore adjustment hile ij (s+1) is the same eight after adjustment, O pj is the output value at node j, δ pj is the error of pattern p at node j and η is the learning rate. The error δ pj is given y δ = O pj ( 1- O pj )(T pj -O pj ) (9) pj

9 Seventh International Water Tehnology Conferene Egypt 1-3 April 003 iv- The steps from ii to iv are repeated until the error eteen the desired and the neural netork output reahes a gloal minimum. S Input layer 1 Hidden layer Output layer H/D 1. /D /d /D Q / 5 5 S o 6 ais 1 ais Figure 3 Topology of the developed ANN for the present appliation 6.1. TRAINING, VALIDATING AND TESTING THE ANN MODEL The Neural Connetion [1] is used to train the netork of the present appliation. Several runs are performed using different values of the initial eights until optimal initial eights are otained. In this appliation, the initial random eights are found to e ithin ± 0. 0 generated using a seed of 7. The est ativation funtion is found y trial and error to e the tansh. The appliation is run again ith different numer of neurons in the hidden layer. Many omputer experiments are arried out using 1, 3, 6, 9, 1, 15, 0, 30, 50 and 100 neurons at the hidden layer. It is found that the est results are otained at 6 neurons and no further improvement is otained in the orrelation oeffiient eteen oserved and predited disharges. Similarly, the maximum numer of iteration is found to e 500 (over a range of 10 to iterations). Further inrease in the iterations shos no improvement till aout 500. Further inrease more than 500 inreases the validation system error and dereases the training system error. An over-training ours in this ase and the netork is alled over-trained netork hih in turn lose the apaility to generalize. 6.. STABILITY OF THE NETWORK One the struture of the netork is determined, its staility is studied. Several omputer experiments are onduted using the pre-determined struture of the netork ut in eah ase the data sets are hosen randomly in different ays. The results of six experiments using different seeds of 5, 1, 3, 7, & 10 are shon in Tale 3. Experiment no. four sho the est results, hoever, its results are not varying largely ompared to other experiments.

10 Seventh International Water Tehnology Conferene Egypt 1-3 April 003 Tale 3 Results of netork staility Data set Exp.1 Exp. Exp. 3 Exp. 4 Exp. 5 Exp. 6 Training, R Validation, R Test, R Figure 4 shos the predition of the ANN model versus the measured disharges. Clearly, exellent agreement as otained. 6 Estimated Q L/se Training data Test data Line of Equality Measured Q L/se Figure 4. Predition of ANN model versus the measured data for oth training and test data sets 6.3. SENSITIVITY ANALYSIS Sensitivity analysis is important in order to find the relative importane of the different dimensionless variales involved in the predition model. Building the predition model several times ith one different dimensionless variale removed per time. Results of sensitivity analysis indiated that the importane of the variales is dereased in the folloing order, H/D, S, /D, S o, / and /D. Tale 4 presents the results of the sensitivity analysis. The perentage redution in the orrelation oeffiient eteen the measured and the predited values hen a partiular dimensionless variale is removed from the model is alulated. Clearly, the model is greatly affeted hen H/D is removed eause the redution in the orrelation oeffiient is the largest (1.0%), folloed y the sumergene ratio here a perentage redution in R is 4.86%. Removing of other variales indiated less

11 Seventh International Water Tehnology Conferene Egypt 1-3 April 003 redution in R. This highlight the fat that the variales H/D and S should e determined very preisely to ensure reliale preditions. Tale 4 Results of sensitivity analysis Data set /D / So /D S H/D R % redution Importane ANN MODEL VERSUS OTHER MODELS Figures 5a and 5 sho the omparison among the predition of the different models and the measured disharges. These figures indiate that the preditions due to ANN models are very lose the line of equality, folloed y the predition to equation (5), then equation () and equation (1). This order is also lear from Tale. Predited disharge Q L/s (a) Eq. 1. Eq.. Eq. 5. ANN Line of Eq. Predited disharge Q L/s () Measured disharge Q L/s Measured disharge Q L/s Figure 5. Comparison among preditions of different models using data from (a) Ref. [] and () Ref. [1] Figures 6a, 6 and 6 present the omparison among different models and the measured data for different sumergene ratio S, different eir idth ratio /D and different ulvert idth ratio /D respetively. These three sets ere seleted to represent the asi dimensionless ratios S, /D and /D affeting the flo through the strutures. The data in the first to figures are due to Negm [] and that in third figure are due to Mohamed [1]. Clearly, the aove stated order is lear in these figures. These figures indiate that the results of the predition models agreed generally ell ith the trend of the experimental data, here Q nd ( Q nd = Q / D gd ) inreases ith the inrease of H/D, ith the inrease of S (Figure 6a), ith the inrease of /D (Figure 6) and ith the inrease of /D (Figure 6).

12 Seventh International Water Tehnology Conferene Egypt 1-3 April 003 Qnd (a) S = 3.00, /d=3.0. So= H/D S Eq. 1. Eq.. Eq. 5. ANN Qnd () S = 3.33, /D=3.0, So= H/D /D Eq. 1. Eq.. Eq. 5. ANN Qnd () S = 3.0, /D=1.4, So= H/D /D Eq. 1 Eq. Eq. 5 ANN Figure 6. Typial omparisons among different predition models and measured data for (a) different values of S, Ref. [], () different values of /D, Ref. [], and () different values of /D, Ref.[1].

13 Seventh International Water Tehnology Conferene Egypt 1-3 April CONCLUSIONS The folloing main onlusions ould e stated: 1- The proposed predited model (equation 5) for omputing the simultaneous disharge over BCW and through ulvert (flo type 4) is muh etter than regression model (equations 1 and ) and ould e used for ide range of parameters provided equation 6 is re-uilt for the same range. - The preditions of the developed ANN model are muh etter than all other models inluding equation 5. In fat, most of the predited values (aout 98%) have errors less than.5%. 3- Sensitivity analysis indiated that the most important dimensionless variale is the relative upstream ater depth H/D, folloed y the sumergene S, then /D, S o, / and finally /D. NOMENCLATURE A o ross setional area of the ulvert; idth of the ulvert vent; j the ias eight of the node j; idth of the eir; B idth of the hannel; C oeffiient of disharge for eir; C D oeffiient of disharge for ulvert; C V oeffiient of veloity; D depth of ulvert vent; F simultaneous flo interation fator; G gravitational aeleration; ht tailater depth; h head over the eir; H depth of ater upstream the struture; Hd depth of ater just donstream the struture; H o total energy head; L length of the ulvert; n Manning roughness oeffiient; Q omined disharge; Q disharge through the ulvert; Q nd non-dimension disharge ( Q nd = Q / D gd ); Q disharge over the eir; R determination oeffiient; R orrelation oeffiient; R o hydrauli radius; P height of the eir; T target; O pj output value at node j; V a veloity of approah;

14 Seventh International Water Tehnology Conferene Egypt 1-3 April 003 S sumergene; S o ottom slope; ij (s) eight eteen nodes i and j at step s efore adjustment; ij (s+1) eight after adjustment; δ error of pattern p at node j; η φ pj learning rate; and ativation or transfer funtion of the node. ABBREVIATIONS ANN = Artifiial Neural Netork BCW = Broad-Crested Weir Eq. = equation Exp. = Experiment MLP = Multi-Layer Pereptron MRAE = Mean Relative Asolute Error Ref. = Referene RMSE = Root Mean Square Error Tansh = Hyperoli tangent funtion PE = Proessing Element SEE = Standard Error of Estimate REFERENCES [1] Mohamed, M.S, Charateristis and Predition of Simultaneous Flo Over Broad-Crested Weirs and Through Culverts, Egyptian Journal for Engineering Siene and Tehnology (EJEST), Faulty of Engineering, Zagazig University, Egypt. Vol. 6, No. 1, 00, pp [] Negm, A.M., Experimental Investigation on Simultaneous Flo through Comined Box Culverts and Over Contrated Broad-Crested Weirs, Pro. nd Int. Conf. for Advaned Trends in Engineering (MICATE 00), April 7-9, Faulty of Engineering. Al-Minai University, Egypt, 00. [3] Cho, V.T., Open Channel Hydraulis, MGra-Hill Int. Book Co., Tokyo. Japan, [4] Hershy, R.W, (Editor), Hydrometery, John Wile & Sons, Ne York, [5] Frenh R.H., Open Channel Hydraulis, MGra Hill Book Company, Ne York, [6] Bodhaine, G.L., Measurement of Peak Disharge at Culverts y Indiret Methods. U.S. Geologial Survey, Tehniques of Water Resoures Investigations, Book 3, Chap. A3. Washington, 1976, First reprinted in [7] Bos, M.G. (Editor), Disharge Measurement Strutures, Oxford & IBH Pulishing Co., Ne Delhi, [8] Negm, A.M., Alsheikh, A., Charateristis of Flo Over Contrated Broad- Crested Weirs, Engineering Bulletin (Civil Engineering), Faulty of Engineering, Ain Shams University, Cairo. Egypt, Vol.3, No. 3, 1997, pp

15 Seventh International Water Tehnology Conferene Egypt 1-3 April 003 [9] Gruert, J.P, Appliation of Neural Netorks in Stratified Flo: Staility Analysis, Journal Hydrauli Engineering, Vol. 11, No. 7, 1995, pp and Disussion, Vol. 13, No. 3, 1997, pp [10] Diike, Y.B. and Aott, M.B., Appliation of Artifiial Neural Netorks to the Simulation of a To Dimensional Flo, Journal of Hydrauli Researh, Vol. 37, No. 4, 1999, pp [11] Diike, Y.B., Minns, A.W. and Aott, M.B., Appliations of Artifiial Neural Netorks to the Generation of Wave Equations From Hydrauli Data, Journal of Hydrauli Researh, Vol. 37, No. 1, 1999, pp and Disussion in Vol. 38, No. 4, 000, pp [1] Neural Connetions, ANNs Softare and User Manuals, SPSS In./Reognition Systems In, [13] Negm, A.M., Predition of Hydrauli Design Parameters of Expanding Stilling Basins Using Artifiial Neural Netorks, Egyptian Journal of Engineering Siene and Tehnology (EJEST), Vol. 6, No. 1, 00a, pp. 1-4.