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Total energy loss assessment for trickle lateral lines equipped with integrated in-line and on-line emitters

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Abstract

The accurate evaluation for the pressure head distribution along a trickle (drip) irrigation lateral, which can be operated under low-pressure head, dictates to precisely determine the total energy (head) losses that incorporate the combined friction losses due to pipe and emitters and, the additional local losses, sometimes called minor losses, due to the protrusion of emitter barbs into the flow. In routine design applications, assessment of total energy losses is usually carried out by assuming the hypothesis that minor losses can be neglected, even if the previous experimental studies indicated that minor losses can become a significant percentage of total energy losses as a consequence of the high number of emitters (with reducing the emitter spacing) installed along the lateral line. In this study, first, simple mathematical expressions for computing three energy loss components—minor friction losses through the path of an integrated in-line emitter, the local pressure losses due to emitter connections, and the major friction losses along the pipe—are deduced based on the backward stepwise procedure, which are quickly implemented in a simple Excel spreadsheet, to rapidly evaluate the relative contribution of each energy loss component to the amount of total energy losses. An approximate combination formulation is finally proposed to evaluate total energy drop at the end of the lateral line. For practical purpose, two design figures were also prepared to demonstrate the variation of total friction losses (due to pipe and emitters) with emitter local losses, and the variation of pipe friction losses with emitter minor friction losses, versus different emitter spacing ranging from 0.2 to 1.5 m, and various total number of emitters, regarding two kinds of the integrated in-line emitters. Comprehensive comparison test covering two design applications for different kinds of integrated in-line and on-line emitters indicated that the present mathematical model is simple, can be easily adaptable, but sufficiently accurate in all design cases examined, in comparison with the alternative procedures available in the literature.

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Abbreviations

c :

Coefficient in Eq. 4

D i :

Lateral pipe inner diameter (mm, m)

D g :

Inner diameter of an integrated in-line/on-line emitter (mm, m)

f :

The Blasius friction factor for the range of Reynolds number, 2,000 < R < 36,000

f e :

Friction coefficient for the emitter flow

g:

Acceleration due to gravity (m s−2)

h f(e) :

Friction loss through individual in-line emitter (m)

H av :

Average pressure head (m)

Hin, H1:

Operating inlet pressure head or pressure head at the first upstream emitter (m)

H (N) :

Pressure head at the first emitter from the downstream closed end (m)

I :

Integer, counted from 1 to N

j e :

Emitter friction loss per unit emitter length (m/m)

K :

Constant given by Eq. 8

L g :

Longitudinal length of integrated in-line emitter (mm, m)

L e :

Length of the lateral line between the first and last emitters (m)

N :

Total number of emitters along the lateral

ND:

Nominal diameter of the lateral pipe (mm, m)

Q n :

Nominal flow rate (L h−1 or m3 s−1)

Q av :

Average flow rate (L h−1 or m3 s−1)

Q in :

Total flow rate accumulated by all emitter outflows (L s−1)

q n :

Emitter outflow at the downstream closed end (L h−1 or m3 s−1)

q i :

Individual emitter outflow (L h−1 or m3 s−1)

Q :

Total lateral inflow rate (L h−1 or m3 s−1)

R :

Reynolds number

R g :

Reynolds number for the flow occurred in the integrated in-line emitter

S :

Emitter spacing (m)

UC:

Christiansen uniformity coefficient (%)

V g :

Flow velocity inside the emitter (m s−1)

V :

Flow velocity in the pipe (m s−1)

∆H T :

Total energy (head) losses at the end of the lateral line (m)

∆H f :

Total friction losses due to pipe and emitters (m)

∆H l :

Summation of local losses due to emitter connections (m)

∆H f(e) :

Summation of friction losses through the paths of integrated in-line emitters (m)

∆H f(p) :

Total friction losses along the lateral line (m)

Φe(l,f) :

The ratio of total emitter local losses to the total emitter friction losses (m)

Φ l :

The amount of total emitter local losses as percentage of total energy losses (m)

Φ f :

The ratio of total friction losses to the total emitter local losses (m)

ν :

Kinematic viscosity of water at standard temperature, ν = 1.01 × 10−6 (m2 s−1)

λ:

Local pressure loss caused by the presence of emitter (m)

α:

Local loss coefficient

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Acknowledgments

The author would like to express his appreciation to Editor, Associate Editor and four anonymous Reviewers whose clear comments and constructive criticisms contributed greatly to the quality of the present work. Specifically, Associate Editor Dr. Peter Waller from Arizona State University is gratefully appreciated for his high contribution on its language edition. The Scientific and Technological Research Council of Turkey (TUBITAK) is also acknowledged for supporting the researcher’s time at Texas A&M University by the fellowship and grants program (2219).

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  1. Gürol Yildirim

    Present address: Biological and Agricultural Engineering Department (BAEN), Texas A&M University (TAMU), College Station, TX, USA

Authors and Affiliations

  1. Faculty of Engineering, Hydraulics Division, Civil Engineering Department, Aksaray University, 68100, Aksaray, Turkey

    Gürol Yildirim

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Correspondence to Gürol Yildirim.

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Communicated by P. Waller.

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Yildirim, G. Total energy loss assessment for trickle lateral lines equipped with integrated in-line and on-line emitters. Irrig Sci 28, 341–352 (2010). https://doi.org/10.1007/s00271-009-0197-5

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