Determination of constants in uniform flow formula for small discharges in open channels

Abstract

An attempt was made to find out the constants in the general uniform flow formula for small discharges less than 10 1/s in cement lined and earthen channels. These constants were compared with the constants in the well known and widely used uniform flow formulae such as Manning’s and Chezy’s equation and checked their validity for small channels. Experiments were conducted for different discharges varying from 1 to 9 1/s and for different slopes of 1/2000, 1/3000, 1/4000 and 1/5000 in cement lined and earthen channels. With the help of a computer, analysis was made to establish a relationship between velocity v, hydraulic radius R and slope S. The expirical equation obtained are

In cement lined channel V = 9.199 R0.7591 S0.1103 i.e. V = 1/0.1087 R0.7591 S0.1103 In earthen channel V = 47.2286 R0.844 S0.307 i.e. V = 1/0.0212 R0.844 S0.307 From the comparison of actual velocity with velocity obtained by using Manning’s equation, it was found that Manning’s equation was not applicable to small channels having discharges less than 10 1/s. In both the channels, actual velocity was roughly two times greater than the Manning’s velocity. The average ratio of actual and computed velocity using the best fit equations and the coefficient of determinations in the two cases were near unity. Hence the best fit equations obtained in the study are recommended for the design of small channels. Manning fixed the value of exponent of S as 0.5 based on some theoretical assumptions. So it was decided to find the value of n and the exponent of R in both the channels by fixing the value of exponent of S as 0.5. The equations obtained are In cement lined channel V = 1/0.00428 R0.7827 S0.5 In earthen channel V = 1/0.00408 R0.8696 S0.5 These equations were good but their reliability were less than that of the previous equations.Since Manning’s equation is an university accepted form, comparison was made between the recommended n values and the n values obtained in the study by fixing the value of exponent of R and S as 0.67 and 0.5 respectively. The equations obtained are In cement lined channel V = 1/0.00609 R0.67 S0.5 In earthen channel V = 1/0.00778 R0.67 S0.5 Though the reliability of these equations were comparatively less than the earlier cases, it gave reasonably good results. So these equations are also recommended for the design of small channels with different n values for cement lined and earthen channels. Chezy’s constant C was determined from the best fit equations by fixing the value of exponent of R and S as 0.5. The equations obtained in two channels are In cement lined channel V = 94.91√RS In earthen channel V = 74.771√RS These C values obtained are recommended for the design of small channels in Chezy’s equation than the C values obtained from Manning’s and Kutter’s equations using Manning’s recommended n values. Soil in which earthen channel was constructed was classified based on texture. Since the soil was sandy loam, the best fit equation obtained in earthen channel is applicable only for sandy loam soil.