Development of a digital open channel flow measuring device for surface irrigation Open Access

The irrigation sector, being the largest user of water in India, requires 40% more water by 2050 to meet the food demand of the ever-increasing population. Hence, it becomes imperative to implement judicious water management technology to save water and enhance agricultural water productivity. Keeping this in view, the present study developed a portable, low-cost digital openchannel flow measuring device (a modified flume) to measure the discharge rate and volume of irrigation water. The modified flume was designed, fabricated, and tested at the hydraulic flume testing facility of the Water Technology Centre, ICAR-IARI, New Delhi. The device features two configurations: (1) a straight contraction with a curved diverging section and (2) a curved contraction with a straight diverging section. Both configurations were tested with three contraction ratios: 53.33%, 61%, and 70%. It was observed that the device with a 70% contraction ratio straight converging section (30° angles) and a curved diverging section was the best among all experimented designs. Subsequently, a digital sensing system with a waterproof ultrasonic sensor, microcontroller, data logger, and temperature sensor was mounted. The validated rating curve was embedded in the microcontroller through programed code to display the flow depth, discharge rate, and supply volume in a period of time. Nonetheless, the developed device can be tested under different channel shapes and sizes to ascertain its measurement accuracy and wider applicability.

A good agricultural practice must include the knowledge of water usage by crop and techniques that permit efficient irrigation management. Therefore, the information on the quantity of water supplied to the field would assist in making decisions on when to stop and start irrigation events for different crops (Kumar & Sarangi 2022). When water is over-applied, the excess water percolates below the root zone of the crop without additional benefit to the crop (Abioye et al. 2022). On the other hand, a deficit amount of water, especially during critical growth periods of the crop, can result in the reduction of yield. The measurement of the quantity of water delivered and received by users will ensure that each user gets a fair share, establish a more equitable distribution of available water in the command area, and promote conservation of this precious resource. Monitoring how much water is being delivered in real-time with measuring devices can help farmers or canal authorities deliver the required amount of water to the fields according to crop growth stages and improve water productivity (Kumar & Sen 2020; Kumar et al. 2023). Moreover, for the development of an efficient on-farm water management plan, it is necessary to quantify how much water is being delivered to fields. Accurate water measurement provides the on-farm irrigation decision-maker with the information needed to achieve the best use of the irrigation water applied while minimizing negative environmental impacts. The amount of water applied to a field is a function of time, flow rate, and area. The area to be irrigated and the time of supply of irrigation water can be easily recorded, whereas the flow rate in an open channel requires appropriate instruments or methods for its measurement. Accurate flow measurement of an open channel can prove to be challenging because the flow is not under pressure, and pipe measuring devices such as venturi, electromagnetic, or strap-on transit-time flow meters are not viable.

Measuring water in an open channel is an important step toward water conservation (Samani et al. 1991; Kumar & Sarangi 2022; Kumar & Sen 2023). With the increasing demand for improved water management techniques around the world, there is an urgent need for low-cost and accurate flow measuring devices. Open channel flow measurement devices do not measure the flow directly. Instead, some devices measure the velocity of the flow, and others measure changes in head (flow depth) or pressure. Among the major types of measurement devices used in surface irrigation (open channels) are weirs, flumes, current meters, orifices, propeller meters, venturi meters, electromagnetic meters, turbine meters, ultrasonic meters, and pitot tubes (Santhosh & Roy 2012). Open channel flow measuring devices employ the principles of either the weir or the orifice, and each device is adapted to be used in specific locations (Kumar 2020; Kumar & Sarangi 2022). Moreover, the ideal measuring device would be inexpensive to construct, simple to operate and free from working parts, require little maintenance, provide accuracy in its measurement, not be affected by sand, silt, or floating trash and require minimal loss of head in the channel. Several design and development efforts for standardizing different dimensions of measuring devices in open channels have been made, viz. venturi flume (Cone 1917), Parshall flume (Parshall 1928), trapezoidal flume (Hyatt 1965), cut-throat flume (Skogerboe 1969), circular flume (Hager 1988), simple flume (Samani & Magallnez 2000). Ever since the development of the Parshall flume (Parshall 1928), attempts have been made to simplify its construction, improve the accuracy, and reduce the cost of open channel flow measuring devices. Parshall flume, cut-throat flume, trapezoidal flume are the most commonly used devices particularly in flat topography and with small channel gradients. The discharge becomes a function of only a single flow depth which is measured at some location upstream from where the critical depth/flow occurs. Critical flow in an open channel can be created through three general methods: raising the bottom of the channel (Replogle 1975; Bos et al. 1984), contracting the cross-sectional area of the flow (Skogerboe et al. 1967a, 1972; Hager 1988; Samani et al. 1991; Samani & Magallnez 1993, 2000), and reducing the bottom elevation to create a critical flow. Contracting the cross-section of the flow is one of the simplest methods of creating a critical flow for measuring the flow in an open channel (Samani et al. 1991; Hager 1988; Samani & Magallnez 2000). These attempts resulted in the development of the cut-throat flume (Robinson & Chamberlain 1960; Skogerboe et al. 1967b) and the Replogle, Bos, and Clemmens flume (Bos et al. 1984). Measuring flow by contracting the flow cross-section is often the simplest and cheapest method, as it does not require complex inflow and outflow transition (Samani 2017). The ideal condition for the measurement of discharge is that the throat section should be sufficiently constricted to produce critical depth. Therefore, most of the measurement structures utilize the principle of passing the flow through critical depth, leading to free flow conditions in which the discharge depends only on the upstream flow depth. However, when the downstream depth of flow increases to the point that the upstream depth of flow is affected, then free flow conditions cease, and the flow is said to be submerged. When submerged flow conditions exist, the stage and discharge relationship developed for free flow conditions is no longer valid (Hyatt 1965). The term free flow is often used when critical depth occurs in a flume. Flumes designed to operate under free flow conditions will be submerged sometimes, due to either unusual operating conditions downstream or the accumulation of mass and/or vegetation in the channel. Details of existing hydraulic measurement methods, such as weirs, orifices, calibrated flumes, and other indigenous flow measuring devices, along with their drawbacks, limitations, and future scope, are provided in Kumar & Sarangi (2022).

The open channel flow measuring device serves as the backbone of water measurement networks for open channel irrigation to enhance surface irrigation efficiency (Goel et al. 2015). Different kinds of flumes, viz. Parshall flume, cutthroat, and long-throated flume, are being used in India and abroad for the measurement of flow in open channels. But these flumes are associated with many known and unknown errors. The major lacunae in the use of the Parshall flume are the difficulty in the configuration of the throat section, its sloping floor, and field installation. Furthermore, a major cause for error with Parshall flumes is the submergence due to the backwater effect. Besides this, the structural settlement of the Parshall flume causes errors in flow measurement (Skogerboe & Hyatt 1967; Abt & Staker 1990; Prasad 1991; Kruse 1992; Genovez et al. 1993; Abt et al. 1989, 1994; 1995; 1998). Furthermore, the incorrect entrance geometry and gauge location cause an error in flow measurement using the Parshall flume. Moreover, efforts have been made by researchers around the globe to modify the design of existing flumes and to develop a flume that would overcome the limitations of the Parshall flume.

A meticulous review of literature pertaining to flow-measuring devices and the digital sensing system for open field channels revealed the non-availability of a portable and digital flow-measuring device for surface irrigation. Keeping in view the above, an effort was made in this study to develop a low-cost digital flow-measuring device for open channels to obviate the majority of the limitations pertaining to the use of weirs, orifices, calibrated flumes, or other indigenous flow-measuring devices.

The experiment was undertaken at the hydraulic flume testing facility of Water Technology Centre, ICAR-IARI, New Delhi, using the developed flow measuring device to determine its best hydraulic dimensions. The detailed descriptions of the principle of discharge measurement in open channel flow, different components of the flow measuring device, and the digital sensing system, besides the calibration and testing of the developed device, are presented in the following sections.

The discharge rate in the open channel can be measured by multiplying the flow velocity with the wetted area of the flowing water in the channel. To accomplish this, the flow velocity at a given flow depth and the corresponding wetted area in the channel need to be measured as and when there is a change in the flow depth. Moreover, such an approach in an open channel becomes cumbersome and necessitates the periodic measurement of velocity and the corresponding wetted area of the channel. Besides this, the friction of the channel surface, surface tension, and aerodynamic pressure cause instability of the water surface and pose hindrances in quantifying the wetted area accurately on real-time basis. Therefore, the measurement of discharge at a particular section of an open channel is undertaken using a calibrated depth vs. discharge relationship through the development of a rating curve, which would give accurate discharge estimation until the shape of the channel remains intact and the free flow condition prevails (Parsaie et al. 2017; Kumar & Sen 2024). The field channels may be made up of brick- cement or earth. Limitations with these channels are that the masonry channel constructed in the field is of a constant shape without any section along the flow length to ensure a static (stable) depth of flow, which restricts its calibration, whereas the shape of earthen channels varies, which also requires frequent generation of the rating curve for accurate flow measurement. These limitations can be obviated by the installation of a calibrated permanent or portable structure with the rating curve to measure the discharge in the open channel. The basic principle in the design of the primary device (portable structure) was to create a critical flow condition by either contracting some part of the channel section,changing the bottom slope, raising the channel bottom or a combination of all these three approaches in the measuring devices (Skogerboe et al. 1967a, 1972; Replogle 1975; Bos et al. 1984; Hager 1988; Samani et al. 1991; Samani & Magallnez 1993, 2000). Hence, the occurrence of critical flow permits the application of hydraulic principles to determine the unique relationship between the head (depth of flow) and discharge rate with high precision and accuracy. In this invention, the primary flow measuring device was based on the contraction of the central part of the device, the level of the bottom floor, and was designed without a throat section to create the critical flow. Furthermore, a digital flow depth measuring ultrasonic sensor was integrated with the device, and the head vs. discharge equation (rating curve) was embedded in the microcontroller to measure the discharge rate instantaneously and the total volume of water passing through the device over a period.

The design of open channel flow measuring devices is primarily intended for use in field channels for surface irrigation. ‘Field channel’ is the open channel used for supplying water to farmers' fields in a command area and is fed by the water courses under the canal command network. Field channels in canal commands are designed to carry about 1 cusec (28.3 L s⁻¹) of water, which is fed from water courses through adjustable proportionate modules. In India, a field channel is generally either an earthen or masonry (brick-cement) structure. Keeping this in view, the measuring device was designed to fit into the existing field channel in any canal command in India. However, the device can also be used in any open channel with minor modification of the channel shape or preparation of an approach section to fit the structure with minimal effort. The bottom width of the flow measuring device was determined based on the principle of the most economical rectangular channel to carry the maximum discharge rate in the field channel (28.3 L s⁻¹). Based on this, the bottom width was designed to be 0.30 m (30 cm). The length of the device (85 cm) was decided from the experiment to ensure that the smooth transition of flow from the channel to the measuring the device and from the device to the downstream channel occurs.

The experiment was conducted with a flow rate varying from 1.5–20 L s⁻¹, which was in line with the field channel in a canal command area. To experiment with the above-mentioned flow range, the discharge rates at various depths of flow were measured volumetrically. The depth of flow in the approach section was regulated by the gate valve to bypass the excess flow rates to the storage tank. At a given flow rate, a fixed volume of water was collected in the sample collecting tank, and the time taken for such collection of a fixed volume was recorded. Subsequently, the discharge rate (L s⁻¹) through the flume was calculated by dividing the fixed volume (L) collected in the sample tank by the collection time (s). The same procedure was repeated three times for the measurement of each flow depth to avoid errors in measurement, and the average discharge was calculated for each flow depth passing through the measuring device. The occurrence of critical depth was measured after averaging the discharge for a particular depth of flow in the diverging section, and the location of critical depth was measured and noted.

A theoretical criterion for critical flow is the state of flow in which the specific energy (H) is the minimum for a given discharge (Q).

The most appropriate values of a and b were determined by the nonlinear least square grid search (NLIN) procedure using the Statistical Analysis System (SAS, version-9.4) software Copyright (c) 2002–2012 by SAS Institute Inc., Cary, NC, USA. The PROC NLIN procedure performs univariate nonlinear regression using the least squares methods. Fitting nonlinear models can be a difficult task. There is no closed-form solution for the parameter estimates, and hence the process is iterative. This procedure solves the nonlinear regression problem by one of the following five algorithms: (i) the steepest-descent or gradient method, (ii) the Newton method, (iii) the modified Gauss–Newton method, (iv) the modified Gauss–Newton method, and (v) the Marquardt method. From the above methods, the Marquardt method used by the NLIN procedure is considered for the present investigation to estimate the coefficient and exponent having the smallest sum of squared errors (SSE). The initial values of ‘α’ and ‘β’ for the NLIN procedure were determined from the power function developed using the observed data of different flow depths passing through the device and corresponding discharge rates. Then, to validate the developed empirical models, performance indicators like mean absolute deviation (MAD), mean square error (MSE), root mean square error (RMSE), and mean absolute percentage error (MAPE) are used with actual discharge rate and estimated discharge rate.

Fabricated flow measuring devices with different dimensions of the contraction and diverging section besides contraction ratios (Table 1) were tested to select the best-designed flow measuring device. It was observed during the experiment that at the contraction section, a hydraulic drop in the water surface occurred due to side contractions causing appreciable curvature of the flow profile accompanied by an abrupt acceleration of flow. The flow profile in the contraction section of the device depends upon the discharge and side contractions. In general, the basic principle in the design of an open channel flow measuring device is to ensure the occurrence of critical flow in the downstream section, thereby creating a tranquil flow with minimal celerity and stable depth of flow in the upstream section for the more accurate measurement of depth and subsequent discharge passing through the device. Keeping this in view, the occurrence of critical depth for different designed dimensions was investigated. In general, the critical depth occured at different locations corresponding to different side contractions and different shapes of converging and diverging sections of designed dimensions. Also, the flow in the contraction and downstream sections of the device was more abrupt with an increase in the contraction ratio. The designed devices have curved converging and straight diverging sections with 30° and 45° angles, as shown in Figure 1(a) and vice versa with a straight converging section (i.e. with 30° and 45° angles), as in Figure 1(b) was experimented with under different contraction ratios and varying discharge rates. The occurrence and location of critical depth from the transition point of converging and diverging sections for both devices are presented in Table 2. It was observed from Table 2 that the contraction ratio played a major role in the occurrence of critical flow, and with lower contraction ratios, i.e. 53.33 and 60%, the critical flow occurred at a higher discharge rate of 4.5 and 2.5 L s⁻¹ and above, respectively. Whereas with a contraction ratio of 70%, the critical flow occurred early at 1.5 L s⁻¹. Besides this, the occurrence of critical depth was not affected much due to the different shapes of converging and diverging sections. However, with the curved converging section and straight diverging section, the location of the critical depth varied from 7.3 cm to 12.5 cm, corresponding to 70 and 53.33% contraction ratios, respectively. Moreover, for the straight converging section and curved diverging section, the location of critical depth was still lower, ranging from 6.3 to 10.2 cm apropos to 70 and 53.33% contraction ratios, respectively. The distance of critical flow from the transition point was still lower with a straight converging section of 45° angle (i.e. 6.3 cm) than that of 30° angle (i.e. 6.5 cm). It can be concluded that critical flow occurred for lower flow depths with a higher contraction ratio (70%) than lower contraction ratios (53.33 and 61%). Such flow behavior in the open channel may be the lower contraction ratio does not create sufficient head in the converging section to create a critical flow in the downstream section.

Overall, based on the occurrence of critical flow and its location in the downstream section pertaining to different designed dimensions of the flow measuring device, it was indicated that the device with a 70% contraction ratio having a straight converging section with either a 30° or 45° angles and a curved diverging section was better than other experimented designs. The criterion of such selection was that the device could create a stable depth (sub-critical depth) in the upstream section under a wide discharge range besides the lowest discharge rate. Moreover, the critical flow occurred in the downstream section, and the length of such occurrence was minimal, which would lead to the fabrication of a smaller device, leading to savings in material, cost, and ease of portability. Further, the flow depth and discharge rate relationship of different designs without throat sections was developed to ascertain the best device that can measure the discharge more accurately.

Overall, it was observed from the flow depth vs. discharge relationship of 12 sets of designed devices with three contraction ratios that 11 sets performed well as per the prediction error statistics. However, in the device with a contraction ratio of 53.33% and having curved converging and straight diverging sections with 45° angle, the coefficient ‘α’ exceeded the limiting skewness value of 0.25 and hence cannot be considered the best representative model simulating the real field situations. Further, the developed rating curves of all designed devices were validated under variable flow depth situations to arrive at the best-designed dimension of the flow measuring device.

Accurate measurement of flow depth in an open channel on a real-time basis is the prime factor leading to more accurate quantification of discharge by the flow measuring device. Moreover, the depth of flow in an open channel is a highly variable phenomenon, and properly calibrated sensors would capture an accurate flow depth in the channel. The developed flow measuring device, mounted with a digital sensing system, was validated under varying flow depths in the open channel. The flow depth was measured with MAD; 0.21 ± 0.01 cm, by the JSN-SR04T ultrasonic sensor (Kumar et al. 2023), and the discharge rate was displayed in the digital system as per the rating curve equations embedded in the microcontroller. However, the actual discharge was measured in the sample collection tank. The average discharge rate of five successive readings was taken as recorded in the flow sensing system. Prediction error statistics of validation results of all experimented devices were compared to select the best design of the flow measuring device.

Flow depth vs. discharge Equations (7a)–(7d) developed for different shapes of the converging and diverging sections, as detailed in section 3.1.1, were embedded in the digital sensing system pertaining to specific devices. These devices were experimented with in the hydraulic flume testing facility. The prediction error statistical parameters MAD, MSE, RMSE, and MAPE of all designed and tested devices with a contraction ratio of 53.33% are presented in Table 4. It is observed from Table 4 that the MAD, MSE, RMSE, and MAPE were lowest for curved-d converging sections with straight diverging sections with 45° angle and maximum for straight converging sections with 30° angle with curved diverging sections. However, the MAPE of all models was greater than 5, which indicated that the developed device with the rating equation will not perform at its best to simulate real field situations.

Flow depth vs. discharge equations (i.e. Equations (8a)–(8d)) developed in section 3.1.2 were embedded in the microcontroller of the digital sensing system and used in the experimental setup for subsequent validation. The same procedure was followed, as mentioned in section 3.2.1. Referring to Table 4, the MAPE pertaining to the validation results of all four devices was greater than 5.0, which also raised an issue on its accuracy on subsequent use for flow measurement.

Similarly, the equations in section 3.1.3, i.e. Equations (9a)–(9d), under a 70% contraction ratio and different shapes of converging and diverging sections, were embedded in the microcontroller of the digital sensing device. The designed flow-measuring devices mounted with the sensing system were operated under varying flow depths, and the corresponding discharges were estimated and observed. It is observed from Table 4 that the MAD, MSE, RMSE, and MAPE values for the 70% contraction ratio were lower than the contraction ratios of 53.33 and 61%. Moreover, the MAPE value for the straight converging section with a 30° angle and curved- diverging section was the lowest (4.32) and was finally selected as the best-designed section for the measurement of open channel flow.

The output of the sensing system displays data and stores data in the data logger pertaining to discharge rate besides the total flow volume in a given time span, which is useful for irrigating specific farmland with a desired depth of water. A developed device with a straight converging section (30° angle) and a curved diverging section having a 70% contraction ratio estimated the discharge rate in close agreement with the observed discharge rate, which was corroborated with the lowest MAPE (4.3) among all tested devices. The finalized design of the new flow measuring device was 85 cm in length and 30 cm in width. The transition point in the contraction section was 54.5 cm from the upstream edge of the device (l_a + l_b). The digital sensing system was mounted over it with a sensor depth of 45 cm from the channel bottom.

The development of a low-cost, portable, and digital open-channel flow measuring device marks a significant advancement in irrigation water management and a critical step toward improving water use efficiency in irrigation systems. However, multi-location trials of the device may be necessary to enhance its practical relevance and broader impact. Field validation under diverse channel shapes, sediment loads, and environmental factors is essential to ensure the versatility of the device for operation under real-world situations. Prioritizing user-friendliness and ease of maintenance is crucial for adoption by farmers with limited technical expertise. Additionally, assessing cost-effectiveness, production costs, scalability, and commercialization for mass deployment will establish its economic viability. Employing advanced data analysis techniques can enhance the interpretation and utility of collected data while ensuring compatibility with smart irrigation systems that can facilitate real-time monitoring and decision-making. Addressing environmental impacts, social and economic implications, and ethical concerns such as data privacy will further promote sustainable and responsible adoption. Therefore, refining these aspects will strengthen the device's contribution to achieving efficient and sustainable water management in agriculture.

Accurate measurement of irrigation water plays a significant role in not only saving water but also enhancing water productivity in agriculture. Indiscriminate use of water coupled with inaccurate scheduling of irrigation in agriculture poses hindrances to the attainment of sustainability in irrigated agriculture. To enhance the water productivity of canal commands and other regions under surface irrigation, there is a need for low-cost flow measuring devices in the field channels of canal commands to supply a measured quantity of water as per crop water requirements to farmers' fields. Keeping this in view, an attempt was made in this study to develop a portable, low-cost, and digital sensing device to measure the discharge rate and the volume of water passing through the irrigation channel in a given period of time. The flow measuring device was a modified flume without a throat section and a contraction (70%) of the central part to create the critical flow. Furthermore, a digital flow depth sensing system using an ultrasonic sensor was integrated with the device, and the head vs. discharge equation was embedded in the microcontroller to measure the discharge rate instantaneously and the total volume of water passing through the device over a given period of time. Nonetheless, the device will be useful for the canal commands of the country not only to enhance the agricultural water productivity but also to bridge the gap between the potential lag, i.e. irrigation potential created and utilized.

The authors acknowledge the financial assistance to undertake research under the sub-project of ‘Hub and Spoke model (DIC: 24-596)’ funded by MHRD, GoI, in collaboration with IIT, Kanpur, and operational at the Division of Agricultural Engineering, ICAR-Indian Agricultural Research Institute, New Delhi.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.