3. Laboratory measurements in rectangular smooth and rough ditch

The experimental tests were carried out in the Hydraulics Laboratory of Basilicata University, on two free surface rectangular flumes of 9 m length and with a cross section of 0.5 � 0.5 and 1 � 1 m, whose slope can vary from 0 up to 1%. Figure 1 shows pictures about the flume, one of the bed configuration and the flow-meters.

The bed roughness (d) has been modulated between smooth surfaces, with 0.0005 m roughness height, and a rough bottom, obtained with both a sand bed, with a characteristic diameter of 0.002m and standard deviation ffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>d</sup>84=d<sup>16</sup> <sup>p</sup> <sup>¼</sup> <sup>1</sup>:67, and a set of wood spheres of 0.035 m in diameter.

The measurement reaches were placed at the distance of 4 m from the beginning of the flumes, in order to damp large-scale disturbances and allow a quasi-uniform water depth. In the end section of the flume, a grid was installed to regulate the water depth for each assigned discharge or rather to obtain a small longitudinal variation of the flow depth. The experiments were performed in steady flow conditions for different values of discharge (0.015–0.100 m<sup>3</sup> /s) and slope (0.05–1%). The measurement cross section was located in the middle of the rough reach in order to observe a fully developed flow, avoiding edge effects. The flow depth was measured by two hydrometers placed at both the beginning and the end

Figure 1. The experimental apparatus for laboratory measures.

of the measurement reach, and the water depth, D, was assumed as the average value. The velocity was acquired through a micro current-meter with a measuring head diameter of 0.01 m, while the water discharge was measured with a concentric orifice plate installed in the feed pipe and on a laboratory weir placed at the end of the flumes, and compared to the value calculated according to the velocity-area method [23], with a maximum error of around 1–2%. In particular, the adopted velocity-area method must be applied dividing the cross section into a fixed number of verticals and thus, on each vertical, a fixed measurement points are selected. In each point along the vertical, the velocity is acquired in order to compute the mean velocity of the flow along each vertical. Furthermore, the number of measures on each vertical was chosen with respect to the criterion that the difference in velocity between two consecutive points was less than 20%, of the higher measured velocity value, and the points close to the channel bottom and the water surface was fixed according to the size of the micro-current meter.

In such a way, two roughness configurations were enabled:

studied by Greco [9] using a wide volume of data collected in the field on several cross sections along different rivers and in the laboratory [20–22], showing values of Φ(M) ranging in the

The experimental tests were carried out in the Hydraulics Laboratory of Basilicata University, on two free surface rectangular flumes of 9 m length and with a cross section of 0.5 � 0.5 and 1 � 1 m, whose slope can vary from 0 up to 1%. Figure 1 shows pictures about the flume, one of the bed

The bed roughness (d) has been modulated between smooth surfaces, with 0.0005 m roughness height, and a rough bottom, obtained with both a sand bed, with a characteristic diameter of 0.002m

The measurement reaches were placed at the distance of 4 m from the beginning of the flumes, in order to damp large-scale disturbances and allow a quasi-uniform water depth. In the end section of the flume, a grid was installed to regulate the water depth for each assigned discharge or rather to obtain a small longitudinal variation of the flow depth. The experiments were performed in steady flow conditions for different values of discharge

middle of the rough reach in order to observe a fully developed flow, avoiding edge effects. The flow depth was measured by two hydrometers placed at both the beginning and the end

<sup>p</sup> <sup>¼</sup> <sup>1</sup>:67, and a set of wood spheres of 0.035 m in diameter.

/s) and slope (0.05–1%). The measurement cross section was located in the

3. Laboratory measurements in rectangular smooth and rough ditch

[0.5–0.9] interval.

10 Irrigation in Agroecosystems

configuration and the flow-meters.

and standard deviation ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

(0.015–0.100 m<sup>3</sup>

d84=d<sup>16</sup>

Figure 1. The experimental apparatus for laboratory measures.


Table 1 synthetically reports the ranges of variation of the main parameters observed during the experiments for the RRF and SRF configuration, while Q is the water discharge, D is the water depth, D/d is the relative submergence, B/D is the aspect ratio, and Φ(M) is the ratio between the mean and maximum velocities.

For each configuration and for all the stages explored, a relevant bulk of velocity measurements was collected in order to provide a detailed reconstruction of the flow field allowing to obtain mean, Um, and maximum, Umax, cross section velocities.

Figure 2 shows the linear relationship existing between the pairs (Umax; Um) for the two configurations investigated, RRF and SRF.

From Figure 2, some useful issues arise. Even if the correlation among homogeneous data is very strong in both cases with R<sup>2</sup> greater than 0.95, it is immediately realized a slight different behavior between rough and smooth channels. That is, for the smooth rectangular flow, Φ(M) assumes the value 0.9, while for the rough condition, the value decreases to 0.67. That is, in other terms, it seems to be evident and sufficiently confirmed, the dependence of the velocity ratio on the roughness here represented by the relative submergence D/d as discussed in the previous section for Eq. (14).


Table 1. Range of variation for the main parameters of the laboratory experiments.

Figure 3 clearly outlines such an outcome, showing how the velocity ratio is austerely dependent on relative submergence in case of rough flows, while it is sufficiently uniform for values of D/d > 20. Furthermore, the same picture proposes several literature data collected by other authors during experimental laboratory campaigns carried on smooth and rough flumes [22, 24–27], plotted and compared to those arising from the here presented research activity. The same Figure 4 immediately deals with the robust correspondence between data sets related to the low rough/smooth flow conditions for which the hypothesis of the constant value of meanto-maximum velocities ratio might be assumed consistent, at least from an operative point of view for D/d > 20. At the same time, Eq. (14) still remains compelling for D/d < 20, but it needs to be recalibrated and the coefficients A<sup>Φ</sup> and B<sup>Φ</sup> can be assumed 0.136 and 0.468, respectively

Informational Entropy Approach for Rating Curve Assessment in Rough and Smooth Irrigation Ditch

http://dx.doi.org/10.5772/intechopen.78975

13

Such a result can be immediately implemented in the operative chain of water discharge assessment, in order to derive the rating curve in a ditch or artificial channel. Furthermore, such knowledge allows us to assess the level of integrity of the channel in terms of sensitive changes

Furthermore, in case of D/d > 20, typical of concrete channels, the setting of rating curve is quite direct collecting few measures of velocity, in a little volume of the flow field mainly located in the center of the upper part of the cross section where is generally located at the maximum

in the bottom roughness, may be due to the local deposition of sediment or vegetation.

Figure 4. Comparison between the computed (Qcalc) and observed (Qobs) discharges.

(R<sup>2</sup> = 0.95).

Figure 2. Average vs. maximum velocities observed for rough and smooth channel.

Figure 3. Velocity ratio vs. relative submergence.

Figure 3 clearly outlines such an outcome, showing how the velocity ratio is austerely dependent on relative submergence in case of rough flows, while it is sufficiently uniform for values of D/d > 20. Furthermore, the same picture proposes several literature data collected by other authors during experimental laboratory campaigns carried on smooth and rough flumes [22, 24–27], plotted and compared to those arising from the here presented research activity. The same Figure 4 immediately deals with the robust correspondence between data sets related to the low rough/smooth flow conditions for which the hypothesis of the constant value of meanto-maximum velocities ratio might be assumed consistent, at least from an operative point of view for D/d > 20. At the same time, Eq. (14) still remains compelling for D/d < 20, but it needs to be recalibrated and the coefficients A<sup>Φ</sup> and B<sup>Φ</sup> can be assumed 0.136 and 0.468, respectively (R<sup>2</sup> = 0.95).

Such a result can be immediately implemented in the operative chain of water discharge assessment, in order to derive the rating curve in a ditch or artificial channel. Furthermore, such knowledge allows us to assess the level of integrity of the channel in terms of sensitive changes in the bottom roughness, may be due to the local deposition of sediment or vegetation.

Furthermore, in case of D/d > 20, typical of concrete channels, the setting of rating curve is quite direct collecting few measures of velocity, in a little volume of the flow field mainly located in the center of the upper part of the cross section where is generally located at the maximum

Figure 4. Comparison between the computed (Qcalc) and observed (Qobs) discharges.

Figure 2. Average vs. maximum velocities observed for rough and smooth channel.

Figure 3. Velocity ratio vs. relative submergence.

12 Irrigation in Agroecosystems

velocity. Thus, assuming the value of Φ(M) equal to 0.9, the mean velocity can be computed and the water discharge as well. The benefit even deals with the reduction of measurement time and costs. On the other side, once performed velocity measurements in a cross section following the above mentioned procedure, the observed value of Φ(M) can suggest whether or not some changes in bed roughness occurred.

Finally, the use of the entropy velocity profile gives a robust feedback in terms of operative assessment of water discharge, due to the easy and immediate evaluation of the M parameter.
