C=l R 1/6 1/6 C=33. (ii) Annals of Arid Zone 24(5) (1985) .,,- MANNING'S COEFFICIENT OF ROUGHNESS FOR RIVERS OF

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1 Annals of Arid Zone 24(5) (1985) MANNING' COFFICINT OF ROUGHN FOR RIVR OF.,, WTRN RAJATHAN N.. Vangani and A. K. Raila Central Arid Zone Research Institute, Jodhpur342 3 The discharge measurements of a river are important for developing economically viable pjects such as irrigation, power pduction and flood contl. For the rivers which rise to flood heights and recede too quickly, it often becomes necessary to detcrmine the velocity by several alternative empirical formulae rather than making direct valocity observations with the help of a current meter. Among the most commonly used empirical formulae, Manning's is the more popular and perferred one for its simplicity (Hiranandani and Chitale, 1964). The computation of velocity by such empirical formula depends on a number of factors e.g, energy gradient, depth, and ughness coefficient. Out of these factors, the pblem faced in choosing the correct value of the coefficient of ughness 'n' has, however, limited the use of the Manning's formula. In this paper an attempt has been made to assess the correct value of the M:Jnning's ughness coefficient for rivers of the Luni basin in western Rajasthan. In western Rajasthan, only the Luni and its tributaries have a defined integrated drainage system, All the streams of this region including the river Luni are ephemeral and their flow is a reflex of the monsoon rains. In 1979, 24, stream gauging sites were established for estimating the stream flow, highest flood level and suspended sediment load. After each flow three samples of the river bed material were randomly collected fm the css section of the stream gauging, sites. The composite of the three samples weighing 1 g was used for the mechanical analysis by the sieve method. The samples consisted for pebbles to fine sand particles. The. mean diameter of sand particles. was measured by the methods of Wentworth (1926) and Krumbein (1936). At each gauging station, nonrecording staff gauges were installed and the gauge heights were. recorded hourly during the flow. Manning (189), derived the following relationship between the Chezy's (I775) constant and the coefficient of ughness as under: C=l R 1/6 n imilarly Karaushev et. al. (1983) derived the following pposition for the Chezy's constant which is based on the particle size of the river bed material and the average depth of flow: C=33 I\1) H \ 1/6 (i) (ii)

2 259: N.. VAt.'GAl';I AND AX KALL\ F the above two equations, the third equation was derived as under : n =R 1/6 33 thjd) 1/6 Where, C =Chezy's constant n =ghness cc efficient (iii) R =hydraulic mean depth H =average depth of flow d =average diameter of river bed material The equation(iii) is adequate for obtaining ughness coefficient "n'. The data required are hydraulic mean depth, avltage depih of flow and average diameter of the river bed material. The value of "n', at low as well as high stages (depth of fl)w), witl be valid if physical characteristics of the river remains unchanged at both the stages (llaranadani and Chitale, 1964). With the help of the equation(iii), the values of "n' for different rivers of the Luni basin have been worked out (table I). There was an exponential decrease!n the particle size d )wnstream till the intduction of sedmiments of different regions into"the main river The mean diameter of the bed material at Kori omeser and Jhumpelao was more than 1 mm. This could be attributed to the cky and graveliy piedmont plains above the gauging sites and the short length of the stream run. For the remaining gauging sites, the streams had to travel for a longer distaace. Further, some other streams eljoined into the main stream due to which the mean diameter of the bed material was found to vary fm.16 to.76 mm. This clearly indicates that the mean diameter of the bed material depends upon the geomorphic conditions of the basin and the length of the stream run. By putting values of the average depth of flow, the corresponding value of the hydraulic mean depth and the mean diameter in equation(iii), the value of 'n' was determined. The determined coefficieut of ughness 'n' was lowest (.19) at Gandev gauging station which is located at the far downstream of the basin where the flow reaches after a long run of about 35 km thugh the sandy terrain. imilarly, the highest value of 'n' (.321) was observed at omesar which is located below the foot hills. The value of 'n' at the reamining gauging stations varied fm.29. to.295. Horion (197) pposed.2 'n' va lue for the stream of noncolloidal bed materials in order to get an appximate estimate of the discharge. uch generalized values of 'n' give an arbitrary estimak of the discharge because every river section has its own geomorphological and geological conditions. The present investigation revealed that such err may vary fm 1.5 to 6.5 per cent for the study area. It is thus. important that for monitoring discharge fm any river section, the coefficient of ughness 'n' must be computed by a convenient method so as as to minimise the err. ACKNOWLDGMNT The authors are thankful to Dr. K.A. hankarnayan, Director and hri Bimal

3 COFFICINT OF ROUGHN : 26.., N c: (!) u ;(!) o..::! U "'C:l ;> \ t t M V) V) ":t ":t c::. (!) t N N ":t \ N V) N \ N ":t ":t N N N N N N N N N N N N._ c: '=? U c:.. c: (!) «l ;> ;: \ \ \ \ \ N t oo N N V) \ N \ t "'3" t t M "'3" N '' r: v: \ \ V). \ \ V) "'3" N M ::a' \ M V) M «l V) \ t \ \ (!)(!). l': t ":t. ;>.... loci '2 <...(1) "'C:l N,.J <l) to. "'C:l,"'C:l :Qo; V) t V) bc: \ V) t \ V) \ M N t V) \ \ \ "'3" \ t. _"'C:l M M "'3" M \ N N N t V) «l (!)(!)«l (!) 88. (!) "@ '. CQ CQ.F. ;>. :Q 'i:. ';:; ' «l '2 '2 '2 '2 '2..;::,..<:; en (!) v..:.:: '3 s:: s::..., <l) '3 c:...l...l...l...l...l. ti) ti) (/) ' s:: V) (I) 'u u...:s c;. U ;>. c:: ;>..;:: ;> d) 'u 8 c:. 'u c<j.. 'i: Q) c<j.. c<j c<j :) ' c; ' Q)' : s:: '2 ;>. c:: '2 c<j,.. :) b c<j c<j :) ''.c (I) c<j....l ti) ii:: ti) ti)..! Q) c: d d r tl)t;.. s:: ti.i <

4 261 : N.. VANGANI AND A.K. KALLA '1 N "<t N "<t N t o \ N V) V) '1 M r') t oo \ N N N N N N N N N N N C: c) c '1 "<t \ \ \ M C\ "<t C\ M N C'\ N N N \ \ M M eṉ.. M "<t M C"? '1 C M V) N & N t M V) N N "<t C"! ": t: M r: C'! \ N... u ṟo u. C '> V) t o V) "<t ;.a \D t oo V) t oo V) v: M M V) M M \D '1 \D :>..c <':l "c; '>.....c c;l 'C,. crl U... "c;..c.?:.. '>..c "' "' '2 =.....::.::?: 2 s ' ' n c;l tn C/J tn..., lzl lzl u "' C.J "' C <C ''..c l: a.:::> 'C ' '>..... <!) Vi?:.;:: c "'?:...::.:: a c : r tn lzl p., z < lzl A::: t<

5 COFFICINT OF ROUGHN : 262 Ghose, Head, Basic Resources tudies Division of CAZRI, Jodhpur, for pviding the necessary facilities and to hri P.C. Chatterji, Geologist for his valuable suggestions while formulating the Pject. RFRNC Chezy, Antione de Manuscript report on the canal de I'Yvette. Part containing formula translated into nglish by Clemens Herschel, one hundred fifteen experiments, on the carrying capacity of large riveted metal conduits, note D, , JohnWiley and ons, Hiranandani, M.G. and Chitale,.V tream gauging. Central Water and Power Research tation, Poona. 342 p. Horton,. R ' Weir experiments, coefficients and formulae. U.. Geological urvey and Water uppiy. 2 p. Karaushev, A.B. and Alekslev, L.P cientific basis for rational Utilization, Conservation and Management of water resourees, part II, Moscow University Press. 27 p. Karumbcin, W.e ize frequency distribution of sediment. ' J. ed Pet. 4: Manning, Robert, 189. Flow of water in open channels and pipes. Ins!. Civil ng. Ireland Trans. 2:138 p. Wentworth. C.K Methods of mcchanical analysis of sediments. Univ. IOlVa tudies in Natural History. Bull. 1I :552..