Energy and momentum coefficients for wide compound channels

Abstract

Experiments were conducted in a straight smooth compound trapezoidal main channel flanked by two symmetrical floodplains having width ratio value ≈12. The point velocities were measured throughout the compound cross section and isovel patterns were analyzed to determine the values of kinetic energy coefficient (α) and momentum coefficient (β) under varying flow conditions of Froude no. between 0.277 to 0.444 and relative depth of between 0.11 and 0.43. The values obtained for α and β are 2.09 and 1.39 respectively, which are significantly higher than their respective values reported by previous researchers for compound cross sections of different size and shape. New relations are suggested to determine approximate values of α and β with R2 values more than 0.97. It is hoped that the present findings will provide new guidelines for design and research in trapezoidal compound channels

Experimental Analysis on the Use of Counterflow Jets as a System for the Stabilization of the Spatial Hydraulic Jump

“…Additionally, since in this last phase of the experiments the velocity measurements were available for four whole cross-sections on a regular grid, it was also possible to evaluate the error induced by assuming α b = α or neglecting it in the computation of the dissipated energy, observing that the use of α b instead of α causes an average error of 0.15%, with a maximum value of 1.16%, while neglecting it (i.e., α = 1) leads to an average error of 0.38%, thus confirming the suitability of approximating α with α b . Moreover, in these experiments, the values of α and β were found to be linearly dependent, according to the equation α = 3.01β − 2.01 (R 2 = 0.9975), in line with the observations of Mohanty et al [31]. Finally, Figure 8 shows the calculated dimensionless bed pressure coefficients, measuring the standard deviation, mean, and maximum positive and negative deviations from the mean (Equations ( 5)-( 7)) of the pressure fluctuations along the centerline of the flume, under Fr = 7.4 and different tailwater levels, as a function of y/P, y being the distance of Finally, Figure 8 shows the calculated dimensionless bed pressure coefficients, measuring the standard deviation, mean, and maximum positive and negative deviations from the mean (Equations ( 5)-( 7)) of the pressure fluctuations along the centerline of the flume, under Fr = 7.4 and different tailwater levels, as a function of y/P, y being the distance of each pressure transducer from the position of the counterflow jets (y/P = 1 indicates the position of the device, while y/P = 0 the expansion section).…”

Compound Channel’s Cross-section Shape Effects on the Kinetic Energy and Momentum Correction Coefficients

“…1), and β is the sum of momentum in each subsection divided by that of the entire section (Eq. 2) (Mohanty et al 2012). Thus,…”

“…In a river, if the main channel-floodplain velocity difference is high, the value of α can increase to more than 2 (Henderson 1966); in some related studies its value has been between 1 and 2 (Chow 1959). In their study on a symmetric smooth straight compound channel with broad floodplains, Mohanty et al (2012) have reported values of 2.09 and 1.39 for α and β, respectively, but Kolupaila (1956) have recommended average values of 1.75 and 1.25 for α and β, respectively, for over-flooded river valleys or channels fringed by floodplains. While Li and Hager (1990) suggest α = 1.15 and β = 1.06 in practical applications, Seckin et al (2009a) propose α = 1.156 and β = 1.056 for symmetric and asymmetric rectangular compound channels, and Parsaie (2016) recommends α = 2.2 and β = 1.4 for symmetric compound channels with smooth boundaries.…”

Kinetic Energy and Momentum Coefficients for Egyptian Irrigation Canals

“…Where: : ratio correlating cross section maximum and mean velocities; and : maximum cross sectional velocity. Mohanty et al (2013) suggested the following relationships on the basis of experimental data assuming logarithmic velocity distribution for smooth trapezoidal main channel flanked with two smooth wide symmetrical flood plains:…”

“…Mohanty et al (2013) derived the following relationship based on experimental data for straight trapezoidal channels with flood plains:…”