The effect of density and height of vegetation in open channel on the Manning’s coefficient

One of an important parameter to study water flow in channel is Manning’s coefficient (n). This coefficient is produced not only from material forming the channel, but also due to presence of vegetation in channel. The aim of research is to study the effect of vegetation density and height on Coefficient of Manning in open channel. The study was conducted in open channel with 15.5 m long, 0.5 m wide and 1.0 m high. At the center of 3 m long of channel is planted with Sweet flag (Acorus calamus). The impact of various densities and heights of sweet flag were examined using fixed discharge to measure velocity and slope energy. Coefficient of Manning was obtained using Manning’s equation. Statistical analysis of variance with significance level of 0.05 was adopted to evaluate the effect of variables. The result showed that increasing density and height of Sweet flag make decreasing velocity and increasing Coefficient of Manning to be 0,043-0,064, or 1.40-2.10 times compared to un-vegetated channel (no=0.031). Based on statistical analysis, it is found that Fcalc=15.646 and 16.928 for vegetation density and height respectively, which is larger than FStat=2,603. It can be concluded that density and height of vegetation significantly influence on Coefficient of Manning.


Introduction
One of an important parameter to study water flow in channel is Coefficient of Manning (n). This coefficient is produced not only from material forming the channel, but also any obstacle including vegetation grown in channel.
In one hand, the vegetation which grows in the channel can protect the channel stable from scouring, but on the other hand, the presence of vegetations in the channel can increase the flow resistance making increase the loss of energy in the channel. Many prior researchers like [2][3][4][5]10], have studied concerning with flow resistance due to vegetation with different characteristics of vegetation in the channel. All studies agreed that the presence of vegetation in the channel can increase the values of Coefficient of Manning as effect of increasing flow resistance. But the study of flow resistance due to the vegetation is very complicated since there are many different kinds and type of plants changing in relation to time of growing, and may be definitely different from one place to another place. These inhomogeneous character of the vegetation in the field make difficulty to figure out the accurate prediction of the channel's roughness in a model of the equation. Because of its importance, so it is necessary to do further research by including for different treatments and type of vegetation growing in the channel to obtain the more reliable approach in general application of model.
The objectives of this research is to study and to test statistically the effects of density and height of Sweet flag (Acorus Calamus) on Coefficient of Manning The study was laboratory experimental research by using Jeringau or Sweet flag (Acorus Calamus) planted in the channel, as prior research done by [7][8], but different treatment.
[7] studied the influence of height variation of vegetation on flow resistance, where the results showed that there was an increase in flow resistance in the channel which was indicated by an increase in the Manning coefficient (nv) ranging from 0.01-0.031 due to an increase in plant height. Meanwhile, [8] studied the influence of density variation of vegetation on flow resistance in the channel, and gave the results of an increase in the Manning coefficient (nv) as an increase in vegetation density between 0.013-0.031. This shows that both studies provide significant manning coefficient values due to the influence of vegetation height and density even in separate conditions Because of these effects, then the main object of this research is to describe the Coefficient of Manning by combining both effect of density and height of vegetation.

Manning's Equation
The Manning's equation is one of well-known equation which is often used in hydraulics of open channel. This formula is a function of the dimension of channel, channel slope and roughness of channel [1]. The equation of Manning Equation, which is commonly used to calculate mean velocities in open-channel is formulated as below.
where; n is the channel roughness symbolled by Coefficient of Manning, V is mean velocity in m/s, R is hydraulic radius in m, and S is slope of water surface. The mean velocity is dependent on the amount of friction between the water and the channel so called channel's roughness which is correlated with the Coefficient of Manning (n). This coefficient contributes to turbulence, which dissipates energy, increase flow resistance and reduces flow velocity. The Coefficient of Manning (n) as in the Equations 1 is mainly produced from the roughness of materials which form channels. But, naturally the flow resistance is caused by many factors, therefore actually Coefficient of Manning should be determined using Equation 2. n = (n0 + n1 + n2 + n3 + n4)m5 (2) where; n0 is the base roughness of material forming the channel, n1 is the irregularity of channel surface, n2 is irregularity of channel section, n3 is the structure hindrance, n4 is the vegetation hindrance and m5 is correction factor for meandering channel alignment. The coefficients of n1, n2, n3 are assumed not significant and can be neglected, so Equation 2 in some cases is merely influenced by the roughness of material which form channel and due to vegetation [1], so can be written as in Equation 3.
In addition, [3] has completely published the values of Coefficient of Manning for thickets and woody vegetation. For these types and characteristics of vegetation [3] gave specific formula to estimate the Coefficient of Manning as in Equation 4.
where; Ai is individual vegetated area in sq. m, A is channel area in sq. m, CD is drag coefficient of vegetation, g is gravity in m/s 2 , Kn is conversion unit, L is length of channel in meter, n0 is roughness of material which form the channel and P is wetted perimeter in meter.

Experimental designs and methods
The procedure of research method which is applied in this research is the same as and follows the previous research done by [6][7][8][9]. The difference is only on placing vegetation treatments and method of data analysis. Steps of methodology in this research is described below.

Preparation and measurements
The preparation stage of research is to provide the channel, vegetation and equipment. In this research, the channel used is a wall glass flume with dimension of 15.50-meter-long, 0.50-meter-wide and 1.00-meter high. Thompson water gate is constructed at upstream of channel to control the discharge and water depth remain 45 cm. At 3-meter-long center part of channel is planted with Sweet flag (Acorus calamus). Type of sweet flag used in the research is shown in Figure 1. The equipment used in the research are Micro currentmeter (KENEK VO-301and Model VOT2-100-05) to measure the velocity and Point gauge (Armfield serial No. 6449-14) to measure the water profile.    Table 1.

Mean velocity
Mean velocity is obtained using Equation 5 below. This velocity is analysed using 10 points method based on the velocity at the point of water surface, 0.2h, 0.6h, 0.8h and bottom of channel.
where; h is depth of water in meter, Vm is mean velocity in m/s, Vp is velocity at the surface in m/s, V0.2h is velocity at water depth 0.2h in m/s, V0.6h is velocity at 0.6h in m/s, V0.8h is velocity at a 0.8h in m/s and Vd is velocity at the bottom in m/s.

Head losses and Slope of energy
Head losses of energy (hf) is obtained using the energy equation so called Bernoulli equation as explained in [1]. This value is calculated on the basis of water depth in upstream (Hu) and downstream (Hd), and velocity in upstream (Vu) and downstream (Vd). The total head losses of energy then can be formulated as in Equation 6 below. L h S f f =

Statistical analysis
The effect of vegetation height and density on Coefficient of Manning is test using two ways Analysis of variance (Anova) method with the confidence level (α) = 5% and degree of freedom (df) = (c-1,n-1) and (r-1,n-1) to obtain F statistic (Fstat.) for vegetation height and density respectively.

Mean velocity and its distribution
The velocity was collected from 3 locations measurement, namely at the upstream, the vegetated zone and downstream, then mean velocity was calculated based on average of 3 locations. The experiments were then repeated with six different densities and heights of vegetation; with fixed water depth in order to maintain fix flow. Based on the measurements of 36 series treatment, the mean velocity distribution is plotted as depicted in Figure 5. As can be seen in the figure that the velocity decrease as increase the density and height of vegetation, or it can be stated that the mean velocity tends to decrease as increase density and height of vegetation. This condition is caused by flow which is blocked by vegetation in the channel, so it cause backwater flow with different direction which make flow resistance is increasing and resulting on decreasing velocity. If compared to un-vegetated channel, the velocity is reducing by 28.68-43.82%. This will effect on flow system in the channel.

The Coefficient of Manning due to density and height of vegetation
Using Equations 8, after mean velocity (Vm) and slope of energy (Sf) are analysed, the total Coefficient of Manning (n) can be obtained, as tabulated in Table 3. As you can see in Table 3 that the values of n are in between 0.043-0.064, which is increasing as increasing density and height of vegetation. Maximum Coefficient of Manning is 0.064 and minimum is 0.043.   Table 4. In overall there are additional Coefficient of Manning due to combination of density and height of vegetation in the channel by 40-110% or 1.4 to 2.1 times if compared to un-vegetated channel. These values are rather similar to previous research of [7] in which there was an additional Coefficient of Manning due to vegetation height by 0.01-0.031, but the results are only applicable for vegetation density of 45 veg/m 2 . The similar results are also published by [8] in which Coefficient of Manning of vegetation with various density is found in between 0.011-0.031, but only applicable for 45 cm height of vegetation.

The influence of density and height of vegetation on coefficient of Manning
As mentioned above show that density and height of vegetation influence on coefficient of Manning. At a glance from Figure 6 and Figure 7 can be seen that there is an influence of density and height of vegetation on Coefficient of Manning. Figure 6 explain the relationship between coefficient of Manning and density of vegetation for different height of vegetation. The figure gives us the information that the trend of graph line tends to be raised when vegetation density and height are increased. The same trend also occurs when we change the relationship between Coefficient of Manning and height of vegetation for different density of vegetation, as in Figure 7. Both figure give us an idea on the effect of vegetation density and height on Coefficient of Manning, but we do not know how much the effect of those variables, therefore it is needed to analyse those effects using statistical analysis test.

Statistical test analysis
Statistical method of two ways analysis of variance (Anova) is applied to analyse and test the influence of density and height of vegetation on Coefficient of Manning. Based on the procedure described in 3.2.4 above, and using Equation 11-14, it is obtained the result of analysis and test as follows; Firstly, data collected from the measurements consist of 6 populations of vegetation density (r = 6) and 6 populations of vegetation height (c = 6) and each of them have 6 samples, so total samples (n) = 36. Using F distribution with confident level () = 0.05 and degree of freedom (v1 = (c-1); v2 = (n-1)) = (5 ; 35), the value of Fstat is obtained 2.603 for both density and height of vegetation, since they have the same number of population Secondly, data presented in Table 3 or Table 4 is analysed using Equation 11-14 and should be adjusted in respect to the procedure of Anova in Table 2. Then, a summary of the results obtained by the univariate Anova, which reflect the influence of density and height of vegetation on Coefficient of Manning is presented in Table 5.  Table 5 gives the value of Fcalc. = 15.646 for the effect of vegetation density, and Fcalc. = 16.928 for the effect of vegetation height. Since the FStat.is lower than Fcalc., the null hypothesis was rejected. Therefore, it can be clearly stated that density and height of vegetation are parameters significantly influencing on coefficient of Manning.
we clearly stated that Sweet flag (Acorus Calamus) or Jeringau as local name with various density and height give an effect on the Coefficient of Manning. This information must be entered hydraulically as applicable in the system of network channel, irrigation project or drainage. This should be our concern for operation and management of water resources projects, because the impact of increased resistance to flow due to the presence of vegetation can influence the water balance of water system.

Conclusion
We can conclude that the presence of Sweet flag (Acorus calamus) with different height and density in the channel can influence the mean velocity. The denser and higher vegetation, the more decreasing of mean velocity in the channel. When compared with un-vegetated channel, and mean velocity become decreasing of 28.68-43.82%. However, on the contrary, the total coefficient of Manning (n) tend to increasing in the range of 0.043 to 0.064 or increase of 1.40 to 2.10 times when compared to the unvegetated channel (where n0 is 0.031). This shows that there is an additional roughness of channel due to the effect of density and height of vegetation (nv) in between 0,012 to 0,034. In addition, based on analysis of variance, it can be clearly concluded that density and height of vegetation are parameters which strongly influence on the coefficient of Manning.
It would be fruitful to pursue further research by including other characteristics of Sweet flag, such as; diameter of trunk and width of leaf to see the flexibility and rigidity of vegetation so that the roughness of channel due to vegetation can be formulated more accurate.