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HYDRAULICS OF MICROIRRIGATION Dr K Yell Reddy, FIE Principal Scientist & Project Manager AP Water Management Project

Tube Section Section (internal) A = 3.14 x r 2 Example: pipe PVC with diameter (external) 24 mm ; thickness 2mm A: the internal radius will be (24- (2x2mm) / 2) =10 mm the section will be 10 x 10 x 3.14= 314 mm2 or 3.14 cm2

Water Flow in Pipes V = L / t (m/sec) Q = A x V (m3/h or cm3/sec) Velocity = Length / time V = L / t (m/sec) Flow rate = Section x Velocity Q = A x V (m3/h or cm3/sec) Example :in a pipe of 8” the flow rate is 100 m3/h flow velocity ?? Internal section 8” (20 cm de diameter) is 10 x 10 x 3.14=314 cm2 The flow rate 100m3/h or 100 000 liter/3600 sec =27777 cm3/sec the velocity V=Q/A will be 27777 / 314 = 88.46 cm/sec or 0.9 m/sec

Water Flow in Pipes Q = A x V (m3/h or cm3/sec) Flow rate = section x Velocity Q = A x V (m3/h or cm3/sec) The flow rate will change ?? The velocity will change ?? Q = A1 x V1= A2 x V2= A3 x V3 (m3/h or cm3/sec) the flow rate is constant

Pressure the pressure is the force applied by a liquid on a surface P = F / A kg (or lb) bar (or psi) cm2 (or sq.inch) elgad1@netvision.net.il

P = F / A Pressure head (on bottom of 10 meters water) the pressure is defined in kg per cm2 here the volume will be of 10m on 1 cm2 , or 1000cm x 1cm or 1000 cm3 =1liter =1kg the pressure will be of 1kg/cm2= 1 At 10m 1 At= 1kg/cm2 1psi= 1 lb/inch2 1At=14.22 psi P = F / A

Pressure and hydrostatic B no friction 37 m Pressure 10 At. A 20 m Sea level

Pressure and hydrostatic Pressure = 10 At – ((37-20) / 10) = 8.3 At B no friction 37 m Pressure 10 At. A 20 m Sea level

Pressure due to gravity pipe of 5000 m slope 1.2% A B 100 C 1200m D 1300 m Pressure at: A . B . C . D . E E 2400 m 1.2%

Pressure due to gravity Pipe of 5000 m slope 1.2% A 100 B 1200m C 1300 m 1.2m D 14.4m 2400 m E 15.6m Pressure at: 28.8m 1.2% A: 0 atm B: 0.12 atm C: 0.12+1.44=1.56 atm D: 0.12+1.44+1.56=3.12 atm E: “’+2.88= 6 atm (5000 x1.2%=60m=6 atm.)

HEAD LOSS ΔH = the total energy drop of a pipe section k = constant for a given pipe size and type of flow Q = discharge rate ΔL = pipe section length m = an exponent

Hazen-Williams equation Among all the equations, the Hazen-Williams formula is commonly and most frequently used (Keller and karmeli, 1975; Jeppson, 1982). The Hazen-Williams formula for smooth pipe (C=150) can be shown as where, ΔH = energy drop by friction for a given pipe length (ΔL), m Q = discharge rate, l s-1 ∆L = length of pipe, m D = inside diameter of the pipe, cm The above equation modified into the following form is used in computation of frictional head loss

where, Hf = frictional head loss, m L = length of pipe, m Q = flow rate, l h-1 D = internal diameter of pipe, mm C = a constant having different values for different pipe materials and sizes (Hazen-Williams constant) For PVC pipes the following values of C are generally used C = 130 ( D < 17 mm ) C = 140 ( 17  D < 21 mm ) C = 150 ( D  21 mm ).

Darcy-Weisbach equation where, D = internal diameter of pipe, m V = velocity of flow, m s-1 g = acceleration due to gravity, m s-2 f = Darcy’s frictional factor Hf and L are equal to ΔH and ΔL as defined earlier Considering discharge in place of velocity and taking g = 9.81 m s-2 in the above, we get,

The Blasius formula Re = Reynolds number where, Q = flow rate in pipe, l h-1 k = a constant equal to 3600 η = kinematic viscosity of water, m2 s-1 D = internal diameter of pipe, mm

For laminar flow (Re 4000) For turbulent flow, the Blasius equation is (4,000  Re 1,00,00) For fully turbulent flow (Re  1,00,000)

Temperature effect ηT = kinematic viscosity of water at temperature, T oC T = temperature of water in oC η20 = kinematic viscosity of water at 20 oC (1.003 x 10-6 m2 s-1)

von Bernuth (1990) listed out the following advantages by insertion of the Blasius friction factor into the Darcy-Weisbach eqution It is theoretically sound and dimensionally homogeneous. Both the Blasius and D-W equations have theoretical base. It is very accurate for plastic pipe when Reynolds numbers are less than 100,000. The Reynolds number limit is non-restrictive for irrigation-system design using smaller than 80 mm. It is conveniently written in readily available terms: flow rate, length, and diameter. It can be easily corrected for viscosity changes directly.

Types of Emitters Flow regime (Reynolds number) 1. Laminar flow 2. Partially turbulent flow 3. Fully turbulent flow Lateral connection 1. In-line 2. On-line Q vs H Pressure Compensating Non-Pressure Compensating

Emitting Pipes Dripper

Integral Emitter

Emitter flow Q = emitter flow rate, l h-1 k = constant of proportionality H = pressure head at emission point, m x = emitter flow exponent ‘x’ is typically between between 0.0 to 1.0 For laminar flow condition x=1.0, fully turbulent flow x=0.5, and for perfect pressure compensating x=0.0

Uniformity Concept For typical field layouts the actual emitter discharge rates vary considerably and depend upon i)      Emitter characteristics ii)      Variability in manufacturing and aging of emitters iii)   Frictional head losses throughout the pipe distribution network iv)     Elevation differences throughout the field v)      Number of clogged emitters in the system vi)   Number and degree of partially clogged emitters in the system and vii) Variation in the water temperature throughout the system.

Emitter flow variation Pressure variations(%) for different emitter flow variations and x-values x-value Emitter flow variation 5% 10% 15% 20% 25% 0.1 40 65 80 89 94 0.2 23 41 56 67 76 0.3 16 30 42 52 62 0.4 12 33 43 51 0.5 10 19 28 36 44 0.6 8 24 31 38 0.7 7 14 21 27 34 0.8 6 18 0.9 5.5 11 17 22 1.0 5 15 20 25

. Comparison of pressure heads along the lateral obtained with DW and HW equations

Christiansen Uniformity Coefficient (CUC) where, CUC = Christiansen uniformity coefficient n = number of emitters along the lateral qi = discharge of emitter i qave= average emitter discharge

Emission uniformity (EU) where, EU=design emission uniformity in percent n = number of emitters per plant Cv = manufacturer’s coefficient of variation Qmin = minimum emitter discharge rate, l h-1 Qave = average emitter discharge rate, l h-1 General Criteria > 90% : Excellent 80-90% : Good 70-80% : fair < 70% : poor

Pipeline Selection Constant diameter pipes Velocity limit criterion (1.5 m/s) Critical flow method

Fig. Moisture availability to crops in different irrigation methods 5 10 20 15 Days Drip method Sprinkler method Surface method Wilting point (15 atm) Field capacity (1/3 atm) Moisture content Fig. Moisture availability to crops in different irrigation methods

Layout of Drip Irrigation System LEGEND 1 Water source 7 Flow control valve 2 Pumpset 8 Submain 3 Fertilizer applicator 9 Lateral pipe 4 Filter 10 Emitter/dripper 5 Watermeter 11 Endcap 6 Mainline 1 2 3 4 5 6 7 10 11 8 9

Drip Irrigation Layout GW recharge pit

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