HYDRAULICS_3 Design of Irrigation Systems by László Ormos

Lateral pipes The hydraulic gradient of a lateral is like a pipe with multiple outlets with even sections. Feature of lateral pipe: decreasing discharge along the flow. Calculation of head loss: 1.head loss is calculated as a pipe without outlets, 2.then outcome is multiplied by the coefficient F which depends on the number of outlets n.

Features of the lateral: the average head (h a ) along the lateral pipe is equal to the head (h s ) of selected equipment, the selected equipment is located on the first to fifths of a lateral pipe, as it seems: three quarter of lateral head loss dissipates along the first two fifth section. Lateral pipes dd d/2 manifold laterals

Lateral pipes A flat field, 360x360m, is irrigated with a hand moved aluminium lateral pipe (C=140). The laterals’ water szupply is from a submain crossing the center of field. The selected sprinkler is Naan 233/92 with nozzle of 4.5mm, the required pressure h s =25m  2.5bar,and the flow rate q s =1.44m 3 /hr. The space between sprinklers is d=12m apart, and the location of the first sprinkler is 6m away from the lateral inlet. The riser height to the sprinkler is 0.8m, and the diameter is ¾”. What a diameter of lateral is required? How much is the required pressure head at the lateral inlet?

Lateral pipes 1.The topography 2.The number of sprinklers is as follows: 360 m submain lateral

Lateral pipes 3.The length of lateral pipe is as follows: 4.The flow rate of the lateral pipe is: 5.The maximum head loss (20%) throughout the field is as follows:

Lateral pipes For a 2” aluminium pipe the hydraulic gradient out of a table or a ruler is J=165‰. 6.The head loss in 2” plain aluminium pipe is: 7.The head loss for 15 sprinklers is as follows where coefficient F 15 =0.363: Since  h f   h max the diameter of lateral pipe is too small.

Lateral pipes For a 3” aluminium pipe the hydraulic gradient out of a table or a ruler is J=25‰. 8.The head loss of a 3” plain aluminium pipe is 9.The head loss for 15 sprinklers is as follows where coefficient F 15 =0.363: Since  h f   h max the diameter of lateral pipe is good. The reserved head loss for the head loss of submain is the difference of  h f and  h max :  h max -  h f =5[m]-1.579[m]=3.421[m].

Lateral pipes The pressure head  h u at the lateral inlet is determined by the following expression where h u is the lateral inlet pressure head, h s is the pressure head of selected sprinkler (or dripper), h f is the head loss along lateral, h r is the riser height from the lateral to the sprinkler. 10.The required pressure head at the inlet of 3” lateral pipe is the following:

Lateral pipes Pressure requirement on slope Once a lateral is laid out along a slope with difference elevation between its two ends. The required pressure at the lateral inlet is computed as follows: where means the adjustment for upward slope, means the adjustment for downward slope.

Lateral pipes Following the previous example, let us take into consideration 2% downward slope and a 2% upward slope. 1.The difference elevation between the two ends of lateral is as follows: 2.Inlet pressure with 2% downward slope 3. Inlet pressure with 2% upward slope:

Lateral pipes The „20% Rule” In order to maintain up to 10% difference in flow rate between any emitters within a plot, then the pressure difference inside a plot should be up to 20%. The relationship between pressure and flow rate is as follows:, where Q is the flow rate, C, K are constant values depended on the type of emitter, Ais the cross section area of a nozzle, His the pressure head, xis the exponent which depends on the flow pattern inside a nozzle; usually x=0.5 for sprinklers, x=0 for emitter with flow regulator, x=0.5 for turbulence flow type like the labyrinth emitters, x<0.5 for very low flow rate emitter, and x=1 for laminar flow type emitter.

Lateral pipes The question is, what the expected difference discharge is between the two ends of the lateral sprinkler when the hydraulic gradient along the lateral pipe is 20%? 1. The flow rate of a sprinkler is as follows: 2.The relationship between two identical sprinklers which have a same constant K, and 20% pressure difference is the following:, and since

Lateral pipes A PE lateral pipe, grade 4, has n=10 micro-sprinklers at d s =10m apart. The selected sprinkler has a flow rate q s =120 l/h at h s =20m pressure head. The riser’s height is h r =0.15m. What is the appropriate diameter of pipe? 1.Length of lateral: 2.The total flow rate for one lateral is as follows: 3.The maximum allowable head loss in the entire plot is:

Lateral pipes 4.The hydraulic gradient out of a slide rule or monograph for a 20mm PE pipe and Q=1.3m 3 /h is J=19%, and coefficient F 10 = Since  h f >  h therefore, a larger pipe is required. 5.Let the larger pipe is a 25mm PE pipe which has hydraulic gradient J=6.2% at Q=1.2m 3 /h. Since  h f <  h therefore, the pipe is useful.

Lateral pipes 6.The required pressure at the lateral pipe inlet is

References Azenkot, A.(1998):”Design Irrigation System”. Ministry of Agricul- ture Extension Service (Irrigation Field service), MASHAV Israel Dr. Avidan, A.(1995):”Soil-Water-Plant Relationship”. Ministry of Agriculture Extension Service (Irrigation Field service), CINADCO, Ministry of Foreign Affairs, MASHAV, Israel Sapir, E.-Dr. E. Yagev (1995):”Drip Irrigation”. Ministry of Agricul- ture and Rural Development, CINADCO, Ministry of Foreign Affairs, MASHAV, Israel Sapir, E.-Dr. E. Yagev (2001):”Sprinkler Irrigation”. Ministry of - culture and Rural Development, CINADCO,Ministry of Foreign Affairs, MASHAV, Israel Eng. Nathan, R. (2002):”Fertilization Combined with Irrigation (Fertigation)”. Ministry of Agriculture and Rural Development, CINADCO,Ministry of Foreign Affairs, MASHAV, Israel