Prediction Comparison of Flow Resistance in Channels with Rounded and Angular Coarse Rough Beds
Citation: Prediction Comparison of Flow Resistance in Channels with Rounded and Angular Coarse Rough Beds, American Research Journal of Civil and Structural Engineering, vol 1, no. 1, pp. 1-15.
Copyright This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Manning’s (n) is a coefficient representing quantity of friction which a channel applies against flow. In general, it explains how roughness is a channel. This experimental research tries to explore (n) by making 8 m length, 40 cm width and 40 cm height laboratory flume with adjustable slope. The flume was used to carry out a total of 72 experiments with 4 different slopes, 3 different flow rates and 2 types of sorting with angular and rounded aggregates. The results showed that the roughness coefficient of the beds covered with angular grains is on average 6.68% higher than that of the beds covered with rounded grains. Also, for a constant value, if the flow rate increases, Manning roughness coefficient will also decrease. It was also shown that parameters such as relative submergence, grain size and slope affect the roughness coefficient. Based on the results of this research, it can be concluded that in all of the experiments, the shear stress of the bed with the rounded particles declined 3.62% as compared to angular particles.
Keywords: Manning roughness coefficient, angular, rounded, rough bed
So far, many studies have been performed to estimate the roughness coefficient of flow resistance due to the size of the particles, but in these studies, the effect of particle shape is not clearly understood. In alluvial channels of Paul and Jarvis (1976), Bathurst and Ferguson (1986), Petit (1990), San Verida (1991), Robert et al (1992), Prandtl-Karman principle and vertical velocity distribution were used that velocity can be dependent on the logarithm of height. Shear velocity can be calculated according to velocity distribution equations.
MATERIALS AND METHODS
According to the research objectives, the experiments were conducted using a flume located at Hydraulic Laboratory of Shahrekord University. The flume was rectangular with adjustable slope (length, width and height of 8 m, 40 cm and 40 cm, respectively). To perform the tests, both particle shapes (angular and rounded) were provided in three average grain sizes (10, 20 and 30 mm). Then, for each particle shape, the flume bed was uniformly covered with the intended grading between its both ends with a height that was at least twice the height of D50. Then by creating a uniform flow through the gate located at the end of the flume, water depth readings according to the 4 tested slopes of 0.005, 0.01, 0.015 and 0.02, and the three (initial, intermediate, and final) flow rates of 10, 20 and 30 liters per second, three sections were considered along the flume at a spacing of 2 m. Also, the velocity at every section was measured using pitot tube at 0.2, 0.6 and 0.8 of the water depth at three points of the width of the flume. In order to roughen the river bed by using of sediments, three different gradations in 10, 20 and 30 millimeter sizes were used. Rounded sediments (collected from the river) and angular sediments (produced from the crusher) were employed after they were prepared and graded.
Figure1,2 show an example of angular and rounded particles with 2 gradations, respectively.
The factors affecting Manning roughness coefficient of rough beds are:
where n is Manning roughness coefficient, ρ is unit volume of water, v is average flow velocity, y is flow depth, μ is mechanical viscosity coefficient of water, g is gravity, and b is the width of the channel that was constant in this study (b= 0.4m). ks is the average size of the bed particles, s0 is the slope of channel floor, and SF is the shape factor of sedimentary aggregates.
Using Buckingham’s relation and by selecting the three variables of ρ, v and y as the repetitive variables, equation 4 can be transformed to equation 5 that includes 5 parameters:
where Re is the Reynolds number, Fr is the Froude number of flow, S0 is the channel bottom slope, is the parameter of relative submergence and SF is the shape factor of the aggregates.
RESULTS AND DISCUSSION
The effect of relative submergence on Manning roughness coefficient
In order to investigate the effect of the shape of sedimentary particles on Manning roughness coefficient, the (n) diagram was plotted versus k/ks in Fig. 5 for different flow rates for the bed sediments with the same grading.
THE EFFECT OF GRAINS SIZE ON MANNING ROUGHNESS COEFFICIENT
Along a rough bed in the flow direction, both the frictional drag force and the pressure drag of the fluid affect the bed. At the same hydraulic condition, the greater the roughness of the bed, the higher the drag force, since the grain surfaces facing the flow is increased. Therefore, at the same hydraulic conditions, if the particle size increases, Manning roughness coefficient increases. As a result, the drag force becomes smaller which results in reduced drag pressure. Therefore, increased flow rate and depth lead to decreased total drag force, and thereby, decreases the Manning roughness coefficient (Eslamian S. and et al. 2017 & Shayannejad M. and et al. 2015 & Ostad-Ali-Askari and et al. 2015).
As the diagrams in Fig. 6 shows, by increasing the particle size, the Manning roughness coefficient increases; and the increase in roughness coefficient of angular grains is much higher than that of the rounded grains.
The table 1 shows Using SPSS, and with regard to Manning roughness coefficient (n) as the dependent variable, R/Ks , S0 , and D as independent variables, linear regression analysis was carried out on both rounded and angular beds.
DIMENSIONLESS VELOCITY DISTRIBUTION; ANGULAR AND ROUNDED
The dimensionless images of velocity distribution in Fig. 9 and 10 suggest that in the rounded bed the slope of velocity variations is milder than the slope of changes in the angular bed. These conditions resemble those of old and young rivers: the angular bed resembles the young rivers whereas the rounded bed is similar to the old rivers.