# Experimental Study on Wetland Hydraulic Characteristics of Vegetated Drainage Ditches

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## Abstract

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## 1. Introduction

_{d}with respect to the water flow. By summarizing previous research achievements, Wu et al. [6] carried out flume experiments with horsehair, which indicated that the average water velocity increased and the roughness coefficient declined to a gentle level as water depth increased in a non-submerged condition. Huai et al. [7,8] put forward the arithmetic solutions of velocity distribution and hydraulic elements at a steady flow of the vegetated open channel by implementing mechanical analysis and precise observation of water flow. Researchers investigated the velocity distribution characteristics and turbulence structure of water flows with vegetation [9,10,11].

## 2. Materials and Methods

#### 2.1. Study Site

^{2}. It has been determined that lateral leakage from the rice field to the drainage ditch through the ridge is about 2 mm/d; drainage discharge of subsurface water by the ditch is, on average, 0.20 L/s. In the event of storms once in five years, one-day maximum direct surface runoff and drainage capacity are 110.00 mm and 3.56 L/s, if it is discharged in three days.

#### 2.2. Experiment Design and Measurements

#### 2.2.1. Experiment Design

#### 2.2.2. Measurements

#### Section Measurement: Cross- and Longitudinal-Section Measurement

#### Measurement of Flow and Velocity of the Ditch

#### Measurement of Plant Density and Plant Morphological Parameters

#### 2.3. Data Analysis

_{D}of plants obstructed the water flow and affected the roughness coefficient. Factors, including plant type, whether the plants were submerged, stem thickness, deflection angle of stem leaves, and plant density, affected the plants’ resistance to water flow. The dragging effect of plants to water flow was reflected in the drag coefficient, denoted as C

_{d}. The correlation between plant drag coefficient C

_{d}’, which eliminated the impact of plant density and the Reynolds number of plant stem Re

_{s}, was expressed by k [6], i.e., the eigenvalue of the plants.

^{1/3}; $Q$ is the flow rate, m

^{3}/s; i is the ditch’s gradient, which is dimensionless. According to measurements, gradient values in all three ditch sections were 1:504; E

_{s}is the specific energy that contains kinetic hydraulic energy and hydraulic potential, m; A is the discharge section area, m

^{2}; R is the hydraulic radius of the discharge section, m; u and d are the numbers of sections upstream and downstream.

_{b}without vegetation by hypothesizing that the velocity was as small as possible, with a function deduced as follows:

_{b}is the roughness coefficient of the bottom boundary, s/m

^{1/3}, which was 0.025 in the test according to local conditions; C

_{d}is the drag coefficient, which is dimensionless; A

_{c}is the cross-sectional area of the ditch section, m

^{2}; A

_{i}is the frontal area of a single plant, m

^{2}; L is the selected insulation length, which was 10 m in the test.

_{d}that was used to quantitatively describe the resistance of a certain object to fluid in water hydraulics was determined by Equation (2). This value was not a constant; instead, it varied with velocity, flow direction, object position, and size. With other conditions remaining the same, a smaller drag coefficient corresponded to a smaller drag force of the object acting on the water flow.

_{D}, which could be calculated by the following equation as the average water velocity at the surface of plants and the plants’ drag coefficient:

_{D}is the plant’s resistance to water flow, N; ρ is the density of water, kg/m

^{3}; A is the plant’s frontal area; λ is the total water area with submerged plants in the upstream direction in the unit volume of the ditch section, m

^{2}/m

^{3}, with the equation given as follows:

_{d}’ is the plant drag coefficient, 1/m. This is different from the drag coefficient C

_{d}since the C

_{d}represents the drag coefficient of all plants within the ditch section to the water flow, while C

_{d}’ is a more rational value with plants’ growth distribution density λ taken into consideration.

_{d}’ and plant stem’s Reynolds number Re

_{s}showed the following relation with non-submerged flow:

_{s}is the plant stem Reynolds number, which is also dimensionless; k are the plant characteristics, a dimensionless constant. Plant stem Reynolds number was determined by the following equation:

_{s}is the water velocity at the surface of plant stems, m/s; μ is the dynamic viscosity of water, kg/m·s.

_{a}, and q

_{hs}. Tracer tests using Rhodamine WT and YSI sensors, nine discharges of all situations were conducted. Wetland residence time distribution (RTD) was measured by tracer concentration and time, and the RTD function was described as [28]:

^{3}; Q is the water flow rate, m

^{3}/day. E is the RTD function, 1/day; and t is the time, given in days.

_{a}) was the average time that the tracer particle spends in the wetland, is measured by:

_{a}is the residence time, given in days.

_{n}and surface loading could be determined by q

_{hs}[29]:

_{n}is the nominal time, given in days; V is the wetland water volume, m

^{3}; q

_{hs}is the hydraulic surface loading, m

^{3}/(m

^{2}·d); A

_{w}is the surface area of the constructed wetland, m

^{2}. Since it is the indices, such as cross-section, that matter in a small drainage ditch, dimensions would be inconsistent if Equations (7) to (10) were applied. In order to keep hydraulic performance indices of the constructed wetland in the band wetland and dimensions consistent, it was assumed that the standard lengths of all drainage ditches were 1000 m.

## 3. Results

#### 3.1. Variation of the Roughness Coefficient of Drainage Ditch with Vegetation

#### 3.2. Variation of Plant Resistance to Water Flow

_{D}, was 1.49–25.17 N, which increased with water flow, and that the comparison between different plants suggested that ${\mathrm{F}}_{{D}_{Juncus}}>{\mathrm{F}}_{{D}_{Zizanialatifolia}}{\mathrm{F}}_{{D}_{Acoruscalamus}}$ (Figure 5).

_{D}and roughness coefficients n indicated that the difference was caused by plants’ frontal area. According to plant investigations, the total area of submerged Juncus, Zizania latifolia, and Acorus calamus in the frontal area was 28.8 m

^{2}, 26.4 m

^{2}, and 9.7 m

^{2}, respectively.

#### 3.3. Relationship between Plant Drag Coefficient and Stem Reynolds Number

_{d}’ and Reynolds number of plant stem Re

_{s}at different water flow rates. The correlation of these two values were analyzed by Equation (5). Results suggested drag coefficients of different plants all declined as Reynolds number dropped (Figure 6). Fitting result could be fitted using the power function suggested by Equation (5). Value k of Juncus, Zizania latifolia, and Acorus calamus was 1.79, 1.65, and 1.49, respectively. Existing studies [3,6] indicated that this value was 1.0~2.0 in a non-submerged condition, in Wu et al’s paper, different value of k of vegetation was discussed both of his results and others’ results, k values are due to the differences in vegetation characteristics and may depend on the stiffness, density and configuration of the plants.

#### 3.4. Wetland Hydraulic Characteristics of a Drainage Ditch with Vegetation

_{a}> 2 days, and hydraulic surface loading q

_{hs}< 0.1 m

^{3}/(m

^{2}·day). As indicated by Figure 7, the three kinds of plants met the requirements when the average surface flow velocity was less than 16.3 mm/s, during which the ditch showed excellent wetland characteristics.

## 4. Discussion

_{d}of different plants took on varied orders with plant resistance to water flow, revealing that the drag coefficient subject to the impact of plants on water flow showed different characteristics. In the test, the drag coefficient of Juncus varied in a minimum range as water flow changed, and this value was the smallest when the water flow rate was the same, suggesting that Juncus could cause a minimum drag force to water flow as other conditions remained the same. The traditional leaf area index (LAI) in this research was in the context of immersed surfaces and drag. The LAI below water and its vertical distribution are of interest, and a direct relation between them would be expected [33].

_{d}’, with respect to the impact of plant density and stem Reynolds number Re

_{s}of plant stems, indicated different plants varied with each other regarding the correlation coefficient k that could be used to describe the characteristics of the drag effect of plants to water flow at different flow rates. As for the k number, in this research differs from 1.49 to 1.79. The trend that the drag coefficient decreases with the Reynolds number was confirmed by previous studies [35,36,37], while different studies have different k numbers—in Lee et al.’s study the k number was 0.70 [38], and in Wilson et al.’s study the k number varies from 1.50 to 1.85 [39]—and the value of k was thought to be related to the properties of vegetation.

## 5. Conclusions

- (1)
- The roughness coefficient of the drainage ditch with vegetation declines as the water flow rate increases, with its value lying between that of the small natural river and that of the free surface flow-constructed wetland. When it comes to different plants, ${\mathrm{n}}_{Juncus}>{\mathrm{n}}_{Zizanialatifolia}{\mathrm{n}}_{Acoruscalamus}$, the drainage ditch with vegetation is capable of floodwater discharge when the flow rate is large.
- (2)
- Plant resistance to water flow increases as the flow rate rises; for different plants the flow rate remains the same, ${\mathrm{F}}_{{D}_{Juncus}}>{\mathrm{F}}_{{D}_{Zizanialatifolia}}{\mathrm{F}}_{{D}_{Acoruscalamus}}$, which is because the total stem area of Juncus in the upstream direction is the largest.
- (3)
- The plant drag coefficient C
_{d}declines as the flow rate increases; the eigenvalue k of correlation coefficient of plant drag coefficient C_{d}’ without the impact of plant density and Reynolds number Re_{s}varies in different plants. When it comes to Juncus, Zizania latifolia, and Acorus calamus, this value k is 1.79, 1.65, and 1.49, respectively. - (4)
- As the water flow rate rises, the residence time of the drainage ditch with vegetation, as a kind of band wetland, declines while the hydraulic surface loading becomes larger. Drainage ditches with vegetation show excellent wetland hydraulic performance when the flow rate is small.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 2.**Drainage ditch sections with different plants: (

**a**) Juncus; (

**b**) Acorus Calamus; and (

**c**) Zizania Latifolia.

**Figure 3.**Roughness coefficient of drainage ditches with different plants at varied discharge flow rates.

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**MDPI and ACS Style**

Zhao, S.; Cui, Y.; Luo, Y.; Li, P.
Experimental Study on Wetland Hydraulic Characteristics of Vegetated Drainage Ditches. *Water* **2017**, *9*, 311.
https://doi.org/10.3390/w9050311

**AMA Style**

Zhao S, Cui Y, Luo Y, Li P.
Experimental Study on Wetland Hydraulic Characteristics of Vegetated Drainage Ditches. *Water*. 2017; 9(5):311.
https://doi.org/10.3390/w9050311

**Chicago/Turabian Style**

Zhao, Shujun, Yuanlai Cui, Yufeng Luo, and Peifeng Li.
2017. "Experimental Study on Wetland Hydraulic Characteristics of Vegetated Drainage Ditches" *Water* 9, no. 5: 311.
https://doi.org/10.3390/w9050311