Sprinkle and Trickle Irrigation System Design Using Tapered Pipes for Pressure Loss Adjusting

Accurate computing of amount of pressure loss is very important in sprinkle and trickle irrigation system design. Not correctly adjusted of pressure loss are causes lack of appropriate performance or failure of sprinkle and trickle irrigation system. By tapered pipes, pressure loss adjusted using increasing or decreasing of pressure head. In this study using HydroCalc software, ability of single and tapered pipes in pressure loss adjusting has been compared. Single and tapered laterals were able to adjusting of pressure loss but single manifolds were not able to achieving to the desired pressure head. In single lateral-tapered manifold system due to the lower pressure loss in laterals, can be use from several types of pipe diameters for manifolds but in tapered lateral-tapered manifold system due to the more pressure loss in laterals, the choice is limited. The best diameters for tapered manifolds with single lateral were 69.2-36.8 mm, 69.2-58.2-36.8 mm, and 58.2-46.0-36.8 mm whereas the best diameters for tapered manifold with tapered lateral were 69.2-46.0-36.8 mm.


Introduction
Many tries have been done to appropriate design of sprinkle and trickle irrigation system, which some of them will be described in the following.Molina-Martínez and Ruiz-Canales (2009) evaluated drip irrigation lateral diameters with on-line emitters using a Pocket PC software.As results, it showed with a figure with light emitting diodes (LED), the commercial diameters that could be used.Other results implemented in this tool were the maximum and minimum pressures for each diameter and a table that showed, on a comparative basis, whether the pressure tolerance of every diameter was exceeded or not.Bresler (1977) presented principles and application of trickle-drip irrigation o soil-water management.Lesikar, Weynand and Persyn (2004) evaluated the application uniformity of subsurface drip distribution systems in difference pressures.He showed that low operating pressures might be attributed to design and/or installation problems.Rareş (2009) designed a drip irrigation system using HydroCalc irrigation planning.He found that the use of HydroCalc allows the designer, dealer or end-user to evaluate the performance of micro irrigation in-field components, such as: Drip laterals and micro sprinklers, Sub mains and manifolds, Main lines (PVC, PE, etc.), Valves Energy calculation.Reynolds, Yitayew and Petersenc (1995) designed low-head bubbler irrigation systems.They showed that these systems could operate at pressures as low as 1 m (3.3 ft).Zapata, Playánb and Martínez-Cobb (2007), presented a contribution to the design of collective pressurized irrigation networks in solid-set sprinkler-irrigated windy areas successfully.Jackson and Kay (1987) used of pulse irrigation for reducing clogging problems in trickle emitters.A laboratory study on a sandy loam soil has demonstrated that pulsed flows up to three times the equivalent continuous flow can be used with little change to the soil wetting pattern.Yazar, Sezen and Sesveren (2002) studied LEPA and trickle irrigation of cotton in the Southeast Anatolia Project (GAP) area in Turkey.The research results revealed that both the trickle and LEPA irrigation systems could be used successfully for irrigating cotton crop under the arid climatic conditions of the GAP area in Turkey.Colombo and Oron (2006) designed and managed a tool for trickle irrigation using plant water accessibility function (PWA).Simulated values and field observed values were in good agreement, demonstrating the potential usefulness of the proposed PWA function as a design and management tool for trickle irrigation systems.Oron (1982) presented technical and economic considerations in the design of closed conduit irrigation systems.Valiantzas (2003Valiantzas ( & 2005)), designed microirrigation submain units using tapered manifold and laterals.The design variables were the lengths of two given pipe sizes for the laterals as well as the appropriate lengths of the available pipe sizes for the manifold.Tapered laterals and manifold were selected in such a way that the sum of the costs of the laterals and the manifold is minimized, while the hydraulic design criterion was ensured.The case of a single-diameter lateral with tapered manifold pipeline was also examined.The design procedure could be also applied in sprinkle irrigation tapered laterals.Valiantzas and Dercas (2005) analyzed multidiameter center-pivot sprinkler laterals.A comparison test with a numerical stepwise method indicated that the proposed analytical approach was sufficiently accurate for practical applications.Provenzano, Pumo and Di Dio (2005) evaluated head loss in drip irrigation laterals.Relative errors on the pressure head estimation for the examined cases were always ±2.4%, and therefore the proposed methodology could serve for a quick, approximate evaluation of the total head loss along the laterals.Valiantzas (2008) in other research presented a power formula for the Carcy-Weisbach pipe flow equation.The usefulness of the formula was demonstrated in an application concerning the optimal design of a delivery pipeline with pumping.The power form of the friction formula facilitates the formulation of the problem leading to the derivation of a simple equation from which the economic diameter was explicitly calculated.Kale, Singh and Mahar (2008) designed pressurized irrigation subunit as optimal.The verification of operating inlet pressure head obtained by the proposed model with accurate numerical step-by-step method suggested that it was mostly accurate.Martí, Provenzano, Royuela and Palau-Salvador (2010) predicted integrated emitter local loss using artificial neural networks successfully.Anwar (1999) presented an adjusted factor for pipelines with multiple outlets and outflow.He claimed that this factor might find application in the design of tapered sprinkle and trickle irrigation pipelines.Sepúlveda, Zazueta, Vergot and Bucklin (2005) used handheld computers for hydraulic calculations of microirrigation subunits.They presented an intermediate correction factor was developed that allows computation of head loss between any two points of a multiple outlet line.Sammis, Williams and Wu (1990) developed a trickle irrigation scheduling model successfully.
Appropriate design of sprinkle and trickle irrigation system studied in many previous researches but in none of them pressure loss has not been adjusted using the best selection of diameters and lengths for single and tapered pipes.In this paper, using HydroCalc software pressure loss adjusted for sprinkle and trickle irrigation system and the best diameters and lengths have been determined for both single and tapered pipes.

Materials and Methods
In this study used from HydroCalc software for sprinkle and trickle irrigation system design.Tables 1 and 2 shows input data for lateral and manifold design, respectively.In HydroCalc software flow rate variation and emission uniformity are calculated as follows (Gilary, 2008): Where FV is flow rate variation (%), Q max is the maximum discharge of emitters (L/h), Q min is the minimum discharge of emitters (L/h), EU is emission uniformity (%), CV is coefficient of variation of discharge rates, and n is number of emitter for each plant.
Usually, single laterals are used, because they are convenient to install and maintain, but tapered laterals may be less expensive (Keller & Bliesner, 1990).Tapered laterals are sometimes used on steep slopes where the increase in pressure from the slope would result in too much pressure at the end (SCS, 1991).
For tapered laterals, pipe friction head loss (h f ) in lateral must be computed in a three-step process (Keller & Bliesner, 1990): Step I-Computing h f by follow equation for the full length of the lateral that has the larger diameter pipe.
Where h f is pipe friction head loss (m), F is reduction coefficient to compensate for the discharge along the pipe, L is length of the lateral (m), and J' is equivalent head loss gradient of the lateral with emitters (m/100m) as follows: J'=J(S e +f e )/S e (4) Where S e is spacing between emitter connections along the lateral (m), f e is emitter connection loss as an equivalent length of lateral (m), and J is head loss gradient (m/100m) as follows: Where K is constant, 7.89×10 7 for metric units for water at 20℃, Q is flow rate (L/s), and D is inside diameter of pipe (mm).
Step II-Computing h f values for both the large-and the small-diameter pipes for a lateral length equal to the length of small-diameter pipe and determine the difference between these values.
Step III-The h f for the tapered lateral will equal the h f found in step I plus the difference in the two h f values found in step II.

Results and Discussion
Table 3 shows obtained results for lateral design.For on line emitter there are four choices to select inside diameter (28.8. 22.2, 17.4, and 13.6 mm).According to the table 3 if there is not a budget problem, an inside diameter equal to 28.8 mm due to the minimum of pressure loss (7 cm) is the best state for single lateral design.Otherwise, for reducing the costs a tapered lateral that make from inside diameters equal to 17.4 and 13.6 mm and lengths equal to 60 and 40 m for each diameter, respectively, is the best choice.In this state amount of pressure loss is 1.00 meter.Figures 1 and 2 shows pressure head in length of single and tapered lateral, respectively.In figure 2 amount of pressure head decreases with greater intensity in second pipe (small diameter).Tables 4 and  5 shows obtained results for manifold design in single lateral-single manifold system and tapered lateral-single manifold system, respectively.
For manifold design, there are 11 choices to select inside diameter (101.6, 83.0, 69.2, 58.2, 46.0, 36.8, 27.2, 21.2, 17.0, 13.2, and 9.8 mm).According to the tables 4 and 5 amount of end pressure in none of inside diameters has not reached the desired value (10.07 and 11.0 m).In addition, if using smaller diameters, amount of pressure head is lower than 10.07 and m in manifold and are not suitable for manifold design.The velocity should be limited to about 2 m/s in manifolds (SCS, 1991) and in HydroCalc software should be limited to 2.5 m/s (Gilary, 2008).Table 6 shown obtained results for manifold design in single lateral-tapered manifold system.In tapered manifold for adequate flushing, the diameter of the smallest pipe should be no less than one-half that of the largest pipe (SCS, 1991).Thus according to the diameter of lateral is 28.8 mm the smallest pipe is 36.8mm and two diameters 101.6 and 83.0 are not suitable.After combining remained four diameters, table 6 shows that three combinations are suitable due to the closest amount of end pressure (10.08 m) to required pressure head of single lateral (10.07 m).Figures 3, 4, and 5 shows pressure head in these three combinations.In figure 3 amount of pressure head decreases with greater intensity in second pipe (457 m) and in figures 4 and 5 amount of pressure head decreases with greater intensity in third pipe (440 and 404 m).Table 7 shown obtained results for manifold design in tapered lateral-tapered manifold system.In this system due to the higher pressure loss in tapered lateral there is only one appropriate choice (69.2-46.0-36.8mm). Figure 6 shows pressure head for this choice.In Figure 6 amount of pressure head decreases with greater intensity in third pipe (373 m).
Table 7. Obtained results for manifold design in tapered lateral-tapered manifold system

Conclusions
In this study using HydroCalc software, ability of single and tapered pipes in pressure loss adjusting has been compared.Single and tapered laterals were able to adjusting of pressure loss but single manifolds were not able to achieving to the desired pressure head.In single lateral-tapered manifold system due to the lower pressure loss in laterals, can be use from several types of pipe diameters for manifolds but in tapered lateral-tapered manifold system due to the more pressure loss in laterals, the choice is limited.Abbreviations FV = Flow rate variation (%) Maximum discharge of emitters (L/h) Q min = Minimum discharge of emitters (L/h) EU = Emission uniformity (%) CV = Coefficient of variation of discharge rates n = Number of emitter for each plant h f = Pipe friction head loss (m) F = Reduction coefficient to compensate for the discharge along the pipe L = Length of the lateral (m) J' = Equivalent head loss gradient of the lateral with emitters (m/100m) S e = Spacing between emitter connections along the lateral (m) f e = Emitter connection loss as an equivalent length of lateral (m).J = Head loss gradient (m/100m) K = Constant, 7.89×10 7 for metric units for water at 20℃ Q = Flow rate (L/s) D = Inside diameter of pipe (mm) N l =Number of laterals KD = Coefficient related to the emitter type Exponent = Coefficient related to the emitter type

Table 1 .
Input data for lateral design

Table 3 .
Obtained results for lateral design

Table 4 .
Obtained results for manifold design in single lateral-single manifold system Figure 1.Pressure head in length of single lateral Figure 2. Pressure head in length of tapered lateral

Table 5 .
Obtained results for manifold design in tapered lateral-single manifold system

Table 6 .
Obtained results for manifold design in single lateral-tapered manifold system Pressure head for a tapered manifold (69.2-46.0-36.8mm) in tapered lateral-tapered manifold system Figures 3. Pressure head for a tapered manifold (69.2-36.8mm) in single lateral-tapered manifold system Figures 4. Pressure head for a tapered manifold (69.2-58.2-36.8mm) in single lateral-tapered manifold system Figures 5. Pressure head for a tapered manifold (58.2-46.0-36.8mm) in single lateral-tapered manifold system Figures 6.