Introduction
The problem of designing an irrigation system, i.e. the hydraulic sizing of irrigation systems, must be aimed at obtaining a satisfactory uniformity of supply (EU>90%) of the different dispensing devices and therefore obtain uniformity of irrigation distribution to all plants, as non-uniform distributions can determine both poorly irrigated areas and therefore non-optimal productions, and excessively irrigated areas in which excess water can cause problems of root asphyxia or the washing away of fertilizers present in the soil This can be made possible by keeping the variations in the flow rate delivered by the drippers within predetermined and in any case modest limits.
For the design of a company irrigation system, on the one hand, it is necessary to know the water volumes to be supplied during each watering and, on the other hand, to have an adequate basic cartography that highlights in detail the altimetry of the surfaces to be irrigated. The evaluation of the volumes of the individual waterings, as well as of the irrigation shifts, can be carried out through the application of water balance models of the water on the ground that allow to estimate the effective evapotranspiration consumption of the crops that must be applied with irrigation. Note that it is the volumes to be supplied in the case of each watering, having chosen the type of system (sprinkling, micro-irrigation) and the model of dispensing devices to be used, it is necessary to proceed with the tracing and subsequent hydraulic dimensioning of the network, which cannot be separated from knowledge of the plano-altimetric course of the land.
Collective irrigation systems
Collective irrigation systems are a complex of artifacts and equipment (intake work, adductor, distributors, dividers, dispensers, delivery hydrants, etc.) that allow the irrigation company that manages them (public or private body) to deliver the water to individual users. The complex of land served by the same distribution network is called an irrigation area (Fig. 1).
Collective irrigation is implemented through an irrigation system that can be implemented according to a canalized network or a piped network. The canalized network consists of a series of canals (in earth, concrete, etc.) which, through an intake structure, take water from a water supply source and deliver it to companies through a T-shaped piece called di stopping and shunting. The free-surface derivation is closely linked to the morphology of the land and, therefore, is often difficult to implement, since the choice of an optimal route of the canal appears complicated, both in relation to geological constraints and to the objectives of a hydraulic nature.
Figure 1 – Scheme of a collective irrigation network
In the past, it was preferred to build ducted networks due to the difficulties associated with laying the pipes. The excavation of the laying sections of the piped pipes, in fact, constituted a considerable economic burden in the construction of the network. The design of a canalized network involves the choice of the route, which depends on the morphology of the terrain to be crossed, the choice of the shape of the cross section as well as the knowledge of the flow to be conveyed.
The piped network, on the other hand, is made up of pressurized pipelines made of materials (PVC, steel, cast iron, etc.) that connect the water supply source with the delivery element, represented by a hydrant (trunk of pipe that comes out of the ground in the which delivery item is installed). If the distribution at company level takes place with irrigation methods with superficial expansion (by submersion, by infiltration from furrows) it is not necessary that the water be distributed with considerable pressure since, in company irrigation, the movement of water is dictated by the natural course of the land (from the slope of the field). If, on the other hand, the irrigation method by sprinkling is practiced at company level, it is necessary that the water be distributed with a pressure between 2 and 5 atm, while for micro-irrigation networks pressures of 1-2 atm are required in relation to the type of equipment dispensers used. Where irrigation machines are used, it is necessary to have even higher operating pressures (7-8 atm) that allow the machines to function.
Piped networks do not have limits relating to the slope of the slopes and have the advantage that they can be buried; therefore the limitations of the canalized networks concerning, for example, the crossing of roads that in the canalized networks is carried out with the use of siphons or channels placed at a certain height with respect to the road surface are no longer valid. In the design of pressurized collective irrigation systems, it is necessary to guarantee the hydrants the delivery of an assigned flow rate (module) at a given pressure. Note that both the altimetric position of the water supply source, established the flow rates that pass through the network and the diameter of the pipes, the calculation of the actual pressures at the delivery hydrants cannot ignore the knowledge of the altimetry of the ground, which allows to evaluate, in correspondence of each hydrant, the altimetric position of the same.
Dripline design
In a dispensing wing, the flow rates that flow into the various pipe sections can be determined if the distribution of the pressures in the duct is known and therefore if it is possible, for each dripper, to know the actual flow rate delivered, note that the curve is delivery feature.
To be able to accurately solve the design problem, it is therefore necessary on the one hand to know the functional relationship q (h) of the dripper used and its variability and on the other hand to have accurate procedures for estimating the pressure drops in the pipeline.
Therefore, once the operating pressure at the last dispenser has been set, the flow rate delivered by the last appliance placed along the wing can be deduced from the characteristic curve, which obviously coincides with that which flows into the pipe section between the last and previous dispenser. Once this flow rate value is known, it is possible to calculate the overall head losses that are determined in the section of the pipeline considered and therefore the pressure in correspondence with the immediately preceding dispenser; proceeding from downstream to upstream it is therefore possible to trace the distribution of pressures along the entire supply wing.
The head losses in the delivery wings
Along a dispensing wing both occurperdite di carico continue in the pipeline sections included between successive drippers, whichperdite di carico localizzate at the couplings of the drippers. Two important aspects must therefore be considered: the type of resistance law to be adopted for the evaluation of continuous losses and the influence of localized pressure drops caused by the presence of the nozzles along the wing.
The aforementioned losses, although singularly modest, in relation to the high number of regulators arranged along the wing, can on the whole assume a significant weight compared to the continuous losses [Bertolacci et Al, 1982], [Howell, Barinas, 1980], [Howell , Hiler, 1974], [Karmeli, Keller, 1975] and must therefore be taken into account in a correct hydraulic calculation.
Pressures and flows delivered in a dripline
The determination of the distribution of the pressures along the delivery wing and therefore of the flow rates delivered by the drippers arranged along the wing can be carried out through a calculation procedure that allows to evaluate, for the delivery wing, the extent of the pressure drops at the vary both in the dimensions of the dripper with respect to those of the duct, and in the distance between them. This procedure is based on the following input data:
- geometric quantities relating to the dispensing wing (internal diameter, length, interdistance between the drippers)
- geometry of the dispenser (internal diameter and length of the dripper)
- temperature of the water circulating in the duct
- curva caratteristica di erogazione of the drippers
- piezometric load at the last dispenser
- land morphology.
These data allow to evaluate the quantities involved for the correct design of a delivery wing.
The determination of the pressure distribution along a delivery wing can be achieved through an automatic calculation procedure which, by applying the equations of motion and continuity for predetermined boundary conditions, allows to evaluate, in correspondence with each regulator, the relative piezometric load and consequently the actual delivered flow rate. In particular, once the diameter of the pipe to be used has been fixed, it is possible to determine the actual piezometric trend, by imposing the piezometric load in correspondence with the last dispenser of the most hydraulically disadvantaged and secondary wing (or head ducts) and the main ducts. The choice of the piezometric load to be adopted must generally be made taking into account that the pressure at any dispenser in each irrigation sector does not differ by ± 10% from the nominal load (hn). In fact, taking into account that the exponent x of the dispensing law of many dispensers on the market is close to 0.5, a load variation of ± 10% determines flow rate variations of ± 5%. In cases where the exponent of the delivery law is closer to the value 1, it is advisable to reduce the range of pressure variations. Therefore, considering a delivery wing, the overall head losses must not exceed the value Y = 20% hn ± Δ, in which Δ represents the geometric difference in height between the two ends of the wing, considered positive if the ground slopes (in the direction current) and negative in the case of powering the wing in counter slope (arrangement generally to be avoided).
Having then established a load downstream of the wing equal to the desired one, proceeding from downstream to upstream, the calculation procedure allows to determine, in correspondence with each dripper, the piezometric height and consequently the actual flow rate delivered by it. The delivered flow is calculated on the basis of the flow-pressure relationship; note that it is possible to determine the continuous head losses and the localized head losses in correspondence with the n-1st dripper, it is thus possible to evaluate the total head losses in the section of the pipeline between the last dispenser (n-th) and the previous one (n-1st).
The piezometric load on the n-th dripper in a horizontal pipe is therefore equal to the sum of the piezometric load on the n-th dripper and the total head losses (continuous and localized) relating to the pipe section between the n-th and l ‘n-1st dripper, which in turn allows the calculation of the flow rate on the n-1st dripper.
The application of the equation of motion therefore makes it possible to evaluate, in the hypothesis that the variations in kinetic load in the pipeline (piezometric parallel to the line of total loads) are negligible, the piezometric height in correspondence with the section immediately upstream of the penultimate dispenser and, consequently, the flow rate delivered by it. Proceeding backwards, from downstream to upstream, it is possible to identify the piezometric trend and evaluate, for each dripper present on the dispensing wing, the actual flow rate delivered.
Sometimes, when dimensioning the dispensing wings within an irrigation sector, the piezometric height in correspondence with the derivation of the dispensing wing from the head pipe may be known. In the latter case, since the overall flow rate delivered by the drippers arranged along the wing is not known a priori, a first attempt flow rate is assumed for the pipe section between the upstream section of the wing and the first nozzle which makes it possible to evaluate the continuous head losses in the section of the pipeline considered and the localized losses in correspondence with the first distributor.
Once the morphology of the ground is known, the piezometric height relative to the valley end of the trunk under consideration can therefore be calculated. Proceeding from upstream to downstream it is possible to obtain, with reference to the first iteration, the piezometric trend and the distribution of the delivered flows. The sum of the flow rates delivered by the dispensers arranged along the wing constitutes the starting value of the flow rate to be assumed for the second iteration. The calculation must be repeated until the value of the overall flow delivered along the wing is equal to that assumed as the starting value.
In both cases, after having calculated the distribution of the delivered flows, it is possible to express, with reference to a supply wing or an irrigation sector, a quality judgment based on the determination of thecoefficiente di uniformità (Christiansen, 1942, Karmeli, Keller, 1975), which can be evaluated in relation to design data. If the calculated design uniformity coefficient value does not fall within the quality standards, it is necessary to change the piezometric load at the downstream end or the diameter of the pipes used or the length of the pipeline.
Verification of irrigation systems
In the verification of an irrigation system, as well as for the project, the network of pressurized pipelines without adjustment devices (reduction valves, one-way valves, etc.) can be schematized through a series of sides each consisting of a simple pipeline section , that is, with a single diameter and uniform roughness along the route; whose number is indicated with L. Each of the ends of the sides are defined nodes. The nodes are divided into external and internal nodes, the first, in number of S, are those in which the piezometric height is fixed through the presence of tanks, piezometric towers or other devices; the second ones, in number of N, are instead of unknown piezometric height.
Equation of motion on the sides of the network
The equation of motion in a pipe section of length L with endpoints j and j + 1 can be written as follows:
Hj-Hj + 1 = Y + Δ
where Hj and Hj + 1 are the extreme side loads and Y and Λ are respectively leperdite di carico continue occurring in the pipeline section and theperdite di carico localizzate which occur in correspondence with the drippers.
Continuity equations
The continuity equations express, in the hypothesis of an incompressible fluid, the balance of the incoming and outgoing flows in each node of the network. The continuity equations, written for all the internal nodes of the network, constitute a system of N independent linear equations.
Characteristic equation of the emitters
Therecurva caratteristica o characteristic equation of the dispenser represents the functional link between the flow rate delivered by the dispensing device and the piezometric height corresponding to the operating pressure h.
The geometric dimensions
The geometric height of the nodes is the vertical distance of each node of the network from a (reference) plane that can be placed on sea level, in this case we speak of absolute altitude, i.e. placed at a known reference altitude different from the level of the sea.
Analysis of a company water network
The verification calculation of a network of pipelines under pressure is faced by solving a system of equations consisting of:
- N continuity equations, written in all internal nodes of the network (linear equations) in the flow rates q unknowns circulating at the sides
- N characteristic equations of the dispensers (non-linear equations) which describe the hydraulic operation of the dispensers and which are written in all the internal nodes of the network (dispensing nodes) in the unknown flows Q delivered by the dispensers
- L equations of motion for all sides of the network (non-linear equations) in unknown piezometric heights.
Therefore, starting from the characteristics of the network (topology, diameters, lengths and roughness of the pipelines), the piezometric heights of the external nodes (those in which there are head or end tanks, or piezometric towers or similar devices) are fixed, by the resolution of the system in the 2N + L equations in the same number of unknowns determine the flow rates on the L sides, the piezometric heights of the N nodes and the N flows delivered by the distributors.
