Flow discharge coefficient of crest weirs with covered vegetation

The flow data of mountainous rivers is very important in hydrological forecasting. Crest weirs with smooth surface have been widely used and studied, while there is little information on the weir covered with vegetation. In this experiment, the flow coefficient reduction are systematically investigated by different density flexible artificial vegetation, in addition to the changes of discharge, crest length and height. The equivalent roughness height of vegetation on the weir was calculated. It was found that the flow coefficient with vegetation is smaller than smooth crest. According to the ratio of upstream water head to the length of vegetation weir crest, the experimental flow can be divided into broad-crested weir flow rate of H/L < 0.4 and narrow-crested weir flow rate of H/L > 0.4. The flow coefficient reduction rate of both types of weir flow rates varies to a certain extent. Experimental data showed that the crest weir height H/P played a different law for the broad-crested weir and narrow-crested weir. Taking into account the influence of vegetation, crest length and height, empirical formula for flow coefficient was proposed for flow estimation correction.


Introduction
As a common hydraulic control facility in hydraulic engineering, the flat top weir is commonly used to provide data support for estimating river flow, simply by reading the upstream water level of the weir: Where Q = flow rate, CD = flow coefficient, B = the width of the weir, g = gravitational acceleration, and H = total head on weir.However, in natural river channels, vegetation often exists at the top of the weir, and covering the weir with vegetation often reduces its drainage capacity. Figure 1 shows an example of a weir covered with vegetation.Numerous experiments have been conducted on the flow coefficients of various geometric shapes and water heads of engineering weirs [1][2][3][4][5][6].And the development pattern of flow coefficient has been analysed [5][6][7][8][9][10][11][12][13][14][15][16][17].But little consideration is given to whether there is vegetation roughness on the top of the weir.So it is necessary to properly calibrate the weir discharge coefficient for the additional flow resistance caused by the increase in vegetation roughness, in order to ensure accurate flow estimation.
Several new experiments were conducted on a rectangular finite crest length weir to discuss the issue of water overflow in vegetation covered weirs.This study used five different densities of artificial vegetation to cover the top of the weir, and used a total of nine weir shapes with three different weir lengths and three different weir heights to study the discharge coefficient.

Experimental device
The experimental device is a horizontal rectangular glass channel, and its width is 0.4m, length is 7m, height is 0.5m.The water flows from the underground reservoir into the water tank and then into the channel.The length of the water tank is 4m, the width is 1.8m, and the height is 1.2m.The flat top weir model is fixed at a distance of 3.5m from the entrance of the rectangular glass channel.The three types of weirs in this study have heights of 0.05m, 0.1m, and 0.2m, and lengths of 0.2m, 0.5m, and 1m, respectively.
Six different roughness levels of weir flow were tested, including smooth PVC boards and five different densities of artificial vegetation.Artificial vegetation consists of flexible stems 7 cm long and leaves 1 cm long.For specific information on artificial vegetation, please refer to previous articles by where y is the vertical direction, ym is the virtual friction of the flow where the ideal velocity becomes zero, ks is the equivalent roughness, κ is the von karman constant, the friction velocity u* = gS(h -ym), S is the friction slop, h is the flow depth.

Discharge coefficient for roughness configurations
For all tests, the free surface were recorded for 0.07 < h/L < 1.3.Figure 2 shows flow pattern photos of different weir heights, lengths, and vegetated roughness configurations.The experiment recorded the free surface profiles on the weir.For all tests, the flow depth rapidly decreases at the upstream of the weir.Figures 3a-3c show that for weirs of different heights, as the height of the weir decreases, the depth of the water flow decreases.Figures 3d-3e show that for smooth crest weir of h/L < 0.3, the flow depth is relatively constant downstream of the weir.For h/L > 0.3, the free surface profile gradually decreases long the wrest weir.Figures 3f-3j present the free surface profiles on the crest weir with vegetation configurations.The presence of vegetation roughness causes the free surface profile on the weir to no longer be horizontal.All experiments obtained the corresponding discharge coefficients from equation ( 1), and the experimental data showed that the discharge coefficients varied with changes in h/L, h/ks, and h/(h+P).Figure 4 shows the calculated discharge coefficients for different heights of weirs with a length of 0.2m.The discharge coefficients increase with the increase of h/L, h/ks, and h/(h+P).3) and ( 4) with all data obtained from this experiment, using f1 = tanh[2.6(h/ks)0.4(h/L)0.5(P/L)0.1]and f2 = [(h/ ks)0.9(h/L)1.2(P/ks)-0.5]0.08.Most data points are within the range of ± 10% for the equations.

Conclusions
This study conducted a series of experiments on a finite length weir with vegetation roughness.For five different densities of artificial vegetation roughness, the discharge coefficients of nine types of weirs with three different weir heights and three different weir lengths were studied.The experimental results show that for weirs with vegetation roughness, compared with smooth weirs, the free surface levels were not parallel, and the discharge coefficient significantly decreases.On the basis of extensive analysis of experimental results, two empirical correlation equation was established for the flow coefficients of weirs with vegetation roughness.

Figure 1 .
Figure 1.Weirs with vegetation roughness Bai et al. (2022).The bottom of the vegetation is the zero point position in the normal direction, and the densities of the five artificial vegetation types are determined by their adjacent longitudinal distances Δx and adjacent lateral distances Δz.Six types of bed roughness were determined by fitting the general wall law of stable uniform flows (Kaimal and Finnigan 1994, Bai et al. 2023):

Figure 3 .
Figure 3. Water surface profiles under different flow rates, vegetation roughness configurations, weir heights and lengths: (a, b, c, d, e) Smooth weir; (f, g, h, i, j) Weir with high-density vegetation.

Figure 4 .Figure 5
Figure 4.The change of dimensionless flow coefficient Cd as a funciton of h/L , h/ks and h/(h+P) for a weir length of 0.2m

Figure 5 .
Figure 5. Prediction of dimensionless flow coefficient for weirs covered with vegetationcomparison of measured data to equations (3) and (4)