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 (ha ) along the lateral pipe is equal to

the head (hs ) 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

d d

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 hs=25m2.5bar,and the flow rate qs=1.44m3/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:

d

Lns

lat

360 m

360

msubmain

late

ral

pcsm

m15

12

180

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:

2)1( ddnL

sslat

qnQ su

hh s

100

%20max

mmm 17461214

hm

hm 33

6.2144.115

mm 525100

20

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 F15=0.363:

Since hf hmax the diameter of lateral pipe is too small.

1000

latL

hJ

Fhh f 15

1000latLJh

mm

71.281000

174165 000

mm 42.10363.071.28

Lateral pipesFor 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 F15=0.363:

Since hf hmax the diameter of lateral pipe is good.

The reserved head loss for the head loss of submain is the difference of hf and hmax:

hmax- hf =5[m]-1.579[m]=3.421[m].

1000LJh lat

Fhh f 15

mm35.4

1000

17425 000

mm 579.1363.035.4

Lateral pipes

The pressure head hu at the lateral inlet is determined by the following expression

where • hu is the lateral inlet pressure head,• hs is the pressure head of selected sprinkler (or dripper),• hf is the head loss along lateral,• hr 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:

hhhh rfsu 4

3

hhhh rfsu 4

3 m98.268.0579.14

325

Lateral pipes

Pressure requirement on slopeOnce 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.

24

3 zhhhh rfsu

2

z

2

z

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:

1002 Lz lat

24

3 zhhhh rfsu

mmmmmhu 244.25

2

48.38.0579.1

4

325

24

3 zhhhh rfsu

mmmmmhu 724.28

2

48.38.0579.1

4

325

mm 48.3100%2

174

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:

,

whereQ is the flow rate,C, K are constant values depended on the type of emitter,A is the cross section area of a nozzle,H is the pressure head,x is 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.

HKHgACQ x 2

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

HKQ

H

H

HKHK

Q

Q

1

2

1

2

1

2

HH 12 8.0

%9089.08.08.0

1

1

1

2 H

HQ

Q

Lateral pipes

A PE lateral pipe, grade 4, has n=10 micro-sprinklers at ds=10m apart. The selected sprinkler has a flow rate qs=120 l/h at hs=20m pressure head. The riser’s height is hr=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:

2

1 ddnL

sslat

1000

qnQ su

hh s

100%20

mmm 95

2

1010110

hmh

l3

2.11000

12010

mm 4202.0

Lateral pipes

4. The hydraulic gradient out of a slide rule or monograph for a 20mm PE pipe and Q=1.3m3/h is J=19%, and coefficient F10=0.384.

Since hf> 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=1.2m3/h.

Since hf<h therefore, the pipe is useful.

100LJh lat

hFh f 10

100LJh lat

hFh f 10

mm05.18

100

95%19

mm 93.605.18384.0

mm89.5

100

95%2.6

mm 261.289.5384.0

Lateral pipes

6. The required pressure at the lateral pipe inlet is

hhhh rfsu 4

3 mmmm 846.2115.0261.24

320

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