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INTRODUCTION
In localized irrigation, the uniformity of water application along the lateral line is closely related to the variation of pressure in the emitters. This variation is caused by the loss of load along the pipe and the insertions of the emitters, the losses of position energy, the quality of the water in the pipe, the seals and the effects of water temperature on the exit regime and orifice of the emitter Gomes et al. (2013).
In the sizing of microirrigation systems, the variability between emitters due to the manufacturing process must be considered. Another important point is that the system may present disturbances of variation over time depending on the quality of the water and the management of the irrigation system used (Coelho, 2007).
Pizarro (1990) states that, for any type of emitter, between the emitted flow rate and the service pressure, there is the relationship called the emitter equation q = Kd (h) x which describes the hydraulic behavior of the emitters.
The self-compensating emitters have an elastic membrane with and without a hole that contracts or expands according to the pressure that acts, to allow a constant flow rate to pass through a range of inlet pressures and that is why they present the hysteresis phenomenon in their operation (Vélez et al., 2013). In addition, they state that the self-compensating emitters present the phenomenon of hysteresis in their operation, which is characteristic of any mechanism that uses elastic elements.
Physically, hysteresis is the tendency of a material to retain one of its properties with respect to the stimulus that has generated it (Pizarro, 1987 and Hernández, 1987). This concept applied to a self-compensating emitter with the presence of an elastomer, allows understanding that, under the variations of pressures that occur in these emitters in the microirrigation system in operating conditions, the flow - pressure curve will behave differently upwards and downward pressure, because the emitter responds differently when the pressure increases and when it drops.
On emitters, there are not enough reports of scientific papers that explain this type of phenomenon, although it is supposed that, physically it is a phenomenon that has a different behavior, though close, in both directions. Therefore, the objective of this work is to evaluate the phenomenon of hydraulic hysteresis in emitters and self-compensating irrigation tapes.
MATERIALS AND METHODS
The research was carried out at the University of Ciego de Ávila and in areas of “Ceballos” Agroindustrial Company. For the evaluation of the models of self-compensating emitters Vip Line and the Naan PC, the methodology of Pizarro (1996) was used and for the case of the compensating Aqua Traxx irrigation tape the methodology used was based mainly on the recommendations specified in the Mexican standard (IMTA. MX, 2003).
Determination of the hydraulic hysteresis and flow-pressure curves (q = f (h))
For the determination of the curve q = f (h), the aspects indicated in the Standard ISO.9260: 91 (1991) were taken into account. Irrigation equipment for Agriculture Drippers Specifications and test methods. Then, 4 flow measurements were taken for each dropper in this series (numbers 3, 12, 13, 23) randomly selected according to Pizarro (1990) and the variation of the emission rate was determined based on the inlet pressure. Each emitter was tested in stages and with pressures not exceeding 50 kPa from zero pressure to 1.2 times the maximum pressure (Pmax). Regulated emitters were tested at different pressures within the regulation range. The reading of the results was taken during 3 minutes after reaching the test pressure.
In the case of self-compensated emitters, in addition to taking the flow rates corresponding to rising pressure points, once the maximum pressure within its working range was reached, the test was carried out in a downward direction of pressures, in order to assess the phenomenon of hysteresis due to the elastomer.
In the case of the self-compensating Aqua Traxx irrigation tape, 25% of the emitters of the sample obtained were randomly taken, identifying each of them. As in the evaluation of dropper type emitters, those selected on the belt were tested at different pressures within a range from 0 to 1.2 times the maximum pressure (Pmax).The self-compensating emitters were operated within the amplitude of regulation, increasing or decreasing the inlet pressure and the curve was constructed (q = f (h)).
RESULTS AND DISCUSSION
Figure 1 shows the behavior of the hydraulic hysteresis (qh) and pressure flow (q) curves. As it can be seen, the behavior for both cases seems similar; however, it is very different, obtaining a second-degree polynomial with coefficients of ratio above 90% for both cases. In this case, the hysteresis or recoil curve is a characteristic process of the self-compensating emitters, due to an elastic membrane of silicone material that is inside this type of emitter called elastomer. Hysteresis is the tendency of a material to retain one of its properties with respect to the stimulus that has generated it (Hernández, 1987).
In addition, the pressure flow ratio of the Vip Line transmitter with self-compensating flow, nominal flow of 3.9 L/h and a compensation range between (68-413 kPa), which responds to two equations obtained in experimental conditions of polynomial type, an ascending and another descending one. The latter equation, as the emitter is self-compensating, is affected by the phenomenon of the hysteresis of the material, an aspect that can be observed in the difference of the flow-pressure curves, registered with ascending and descending pressures.
It is necessary to emphasize that the relationship between the flow rate and the pressure was typical of the condition of self-compensation of this type of emitters. The parallel tendency of the curve q = f (h) with respect to the axis of the pressures can be observed specifically in the interval between 75 kPa and 375 kPa, indicating that the self-compensation behavior of the flow with respect to the applied pressure manifested a relationship satisfactory with a coefficient of determination of 94% (R2 = 0.9482).
These results coincide with those obtained by Bliesner (1990, 2006), Boman (2002), Gil et al. (2002) and Armonis (2006) with other emitter models, where they evaluate compensating and non-compensating drippers and determine the flow rate for each model evaluated, only for the pressure flow curve. These authors did not evaluate the hysteresis phenomenon in these emitters.
FIGURE 1 Hydraulic hysteresis and flow ratio - pressure of the self-compensating Vip Line dropper nominal flow of 3.9 L/h.
Figure 2 shows the results obtained in the hydraulic hysteresis and pressure flow ratio (q = f (h)) of the Naan PC dripper, with a nominal flow of 4 L / h and a compensation range of 68-475 kPa.
In a self-compensating emitter, the presence of the elastomer allows understanding that under the variations of pressures that occur in a microirrigation system in operating conditions, the flow-pressure curve will have a different behavior in an upward and downward direction of the pressures, because the emitter responds differently by increasing the pressure with respect to when it drops. As it can be seen in the figure, the hydraulic hysteresis and pressure flow curves are different in the ascending and descending state of the flow. In addition, the correlation coefficients obtained were qh: 0.91% and q: 0.92%, which evidences a good adjustment in the equations of second grade and that coincides with that obtained by Talamini et al. (2018), but in other models of self-compensating emitters.
Due to the behavior of the curve q = f (q) obtained, it is inferred that the flow responds to the service pressures following a certain compensation trend according to the value obtained of 91% determination coefficient. R2 = 0.910.
However, it is evident that the flow increases in a very low proportion with respect to the increase in pressure. That demonstrates the high compensation of this dripper, which is evidenced by the fact that at 100 kPa the flow reached 4.2 L / h and at 275 kPa the flow rate was 4.0 L/h, with a high compensation capacity in this model.
As this emitter is self-compensating is also affected by the phenomenon of hysteresis of the material, an aspect that is observed in the difference of the curves q = f (h) registered with ascending and descending pressures and whose equations are of the polynomial type obtained under experimental conditions. These results coincide with those obtained by Ribeiro et al. (2014).
FIGURE 2 Hydraulic hysteresis and flow-pressure ratio of the Naan PC dropper model with a nominal flow rate of 4 L/h.
Figure 3 shows the hydraulic hysteresis and flow-pressure relationship of the self-compensating Aqua Traxx belt, which has a nominal flow of 1,021L / h and a compensation range of 68,966 - 172,416 kPa. In the figure, there is a strong relationship between flow and pressure, which is evidenced by the coefficient of determination obtained, which reached a value of 0.9969 for the case of (qh). It can be pointed out that the variations obtained in the flow rates when the pressure varies, vary from the parameters given by the manufacturer according to the nominal flow of this model. These results coincide with those obtained by Cunha et al. (2008), but in this case, the author obtained R2 lower than those described in this work for other types of self-compensating emitters. In addition, the behavior of the Aqua Traxx irrigation tape can be seen, in which the best fit of the second-degree polynomial equation was achieved, reaching a ratio coefficient of qh: 0.99%. This coincides with that obtained by Carmenates et al. (2019).
FIGURE 3 Hydraulic hysteresis ratio and flow-pressure of the belt or drip pipe Aqua Traxx Self-compensating, nominal flow of 1,021 L/h.
Coinciding with Casado & Sirgado (2015) the phenomenon of hydraulic hysteresis has been little studied, however, the manifestation of the phenomenon in the ascent and descent phases can be affirmed. Ascent phase: for the water with surface tension (σ) to start to flow out of the hole of an emitter of diameter (d) in contact with the atmosphere. It is necessary that the pressure (P) in the pipe is greater than (4 σ / d) in order to overcome the overpressure exerted by the surface tension (σ) due to the formation of a convex meniscus of diameter at the outlet of the hole as it is shown in Equation 1.
This expression indicates that in an emitter of diameter d, water begins to flow out of the hole when the pressure P is greater than four times the surface tension (σ) of the water divided by 4, because a convex meniscus is formed that exerts an overpressure on the emitter. With a pressure P, only emitters having a diameter larger than the minimum required diameter (dmin), that is calculated as shown in Equation 2, can be discharged.
After the value of this overpressure is exceeded, a film of water forms around the pipe that eliminates the meniscus and the emitters work normally.
Descent phase: the descent phase is different since it is not necessary to overcome the meniscus overpressure. This behavior is related to the reduction of the curvature of the drops when leaving the emitter, because the pipe is totally surrounded by a film of water that considerably diminishes the effects of the meniscus overpressure (Casado & Sirgado, 2015).
CONCLUSIONS
In the relationship of the hydraulic and flow hysteresis - pressure curves in the models of self-compensating emitters evaluated, correlation coefficients greater than 90% were obtained, obtaining polynomial equations under experimental conditions of the form y = ax2 + bx + c.
The curve that represents the discharge of the emitter in the ascent and descent phases is physically different in the three models of emitters evaluated, because the meniscus overpressure is different in both phases.
The elastomer in the self-compensating emitters influences the presence of the phenomenon of hydraulic hysteresis, obtaining the best equation adjustment of qh: 99% in the Aqua Traxx irrigation tape.
