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Design of microirrigation subunit of minimum cost with proper operation

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Abstract

Matlab software named PRESUD (Pressurized Subunit Design) was developed to identify the optimum microirrigation subunit design using the annual water application cost per unit of irrigated area (C T). This is defined as the cost per cubic meter of water applied to the soil for crop use, calculated as the sum of investment, maintenance, energy, and water (C w) costs. In this study, only rectangular subunits are considered, using an iterative method for calculating the lateral and manifold pipelines. The infrastructure necessary for water delivery to the subunit inlet was taken into account in the price of water. The results indicate that C w is the most important factor in C T, which includes the investment and energy costs for moving water from the source to the subunit inlet. Other important factors, in order of importance, are the emission exponent (x), coefficient of variation of emitter manufacturer (CVqmf), and emitter spacing (s e). The minimum water application cost for a typical subunit to irrigate vegetable crops such as pepper is obtained with a subunit of 0.3–0.5 ha, with 80 m of paired lateral pipe length of 16 (13.6 mm) PE 0.25 MPa diameter, and 50 (44 mm) PE 0.4 MPa of manifold pipe diameter. The cost of a typical drip irrigation subunit design for a crop, such as grapevines on trellises, is equivalent to 25 % of the C T of a typical subunit to irrigate vegetable crops, such as pepper.

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Abbreviations

A:

Investment annuity (€ T−1)

C a :

Investment annuity per unit of irrigated area (€ L−2T−1)

C e :

Energy cost per unit of irrigated area (€ L−2T−1)

C i :

Total investment cost (€)

C m :

Maintenance cost (€ L−2T−1)

CRF:

Capital recovery factor

C T :

Total annual cost of water application (€)

CVqmf :

Coefficient of variation of emitter manufacturer (dimensionless)

CVq :

Total coefficient of variation of flow rate (dimensionless)

CVqh :

D q q −1ah  = coefficient of variation of emitter flow due to pressure variation (dimensionless)

CVh :

σh h −1a  = coefficient of variation of pressure (dimensionless)

C w :

Cost of irrigation water (€ T−1 L−2)

D :

Inner diameter of pipe (L)

D l :

Nominal diameter of lateral (L)

D m :

Nominal diameter of manifold (L)

D q :

Standard deviation of the emitter flow due to the pressure variation (dimensionless)

e :

Number of emitters per plant

ee:

Annual rate of escalation in energy costs

E a :

General application efficiency for the irrigation system (dimensionless)

E p :

Efficiency of pumping system (dimensionless)

Enc :

Energy rates (€ kWh−1)

EU:

Emission uniformity (dimensionless)

F :

The Christiansen’s reduction factor for s 0 = s, with s 0 as the distance between the inlet point and the first emitter

F G :

The Christiansen’s reduction general factor

h e :

Inlet pressure head of the emitter (L)

h a :

Average pressure head in the subunit (L)

h f :

Pipe head loss with constant flow rate (L)

h fL :

Lateral pipe head loss (L)

h fS :

Manifold pipe head loss (L)

h mh :

Minimum pressure head in the subunit (L)

h 0 :

Lateral pipe inlet head (L)

H 0 :

Pressure head required at the inlet of the microirrigation subunit (L) and flow rate (Q 0s, in m3 s−1)

i :

Interest rate (dimensionless)

K :

Emission coefficient (L3−x T−1)

L :

Pipe length (L)

L a :

Lateral pipe length uphill of the manifold (L)

L l :

Lateral pipe length (L)

L m :

Manifold pipe length (L)

m :

Flow exponent in the head loss equation

n :

Number of emitters in the lateral

N :

Useful life (T)

O t :

Annual operating time of the irrigation system (T T−1)

P :

Power consumed for irrigation water application (kW)

P l :

Lateral pipe price (€ L−1)

P m :

Manifold pipe price (€ L−1)

P w :

Water price (€ L−3)

q a :

Average emitter flow in the subunit (L3 T−1)

q ah :

Average emitter flow due to the variation of pressure in the subunit (L3 T−1)

q h :

Emission rate (L3 T−1)

q mh :

Minimum emitter flow in the subunit due to the pressure (L3 T−1)

Q 0 :

Inflow rate to the pipe (L3 T)

Q 0s :

Inflow rate to the microirrigation subunit (L3 T)

q u :

Emission rate by unit of length (L3 T)

R :

Reynolds number

R g :

Gross annual crop irrigation water requirement (L3 L−2 T−1)

R n :

Net annual crop irrigation water requirement (L3 L−2 T−1)

S :

Irrigated area (L−2)

s e :

Emitter spacing (L)

s l :

Lateral pipe spacing (L)

s 0 :

Distance between the inlet point and the first emitter

S 0 :

Slope (L L−1)

Tr:

Transpiration relationship

US:

Uniformity index

x :

Emission exponent

σh :

Standard deviation of the emitters pressure in the subunit (m)

ν:

Water kinematic viscosity (L2 T−1)

Δh :

Difference in pressure head in the irrigation subunit (% of h a)

Δq :

Difference in emitter flow in the irrigation subunit (% of q a)

ΔZ :

Differences in elevation in the pipe (lateral or manifold)

Ψ(r L):

Function of r L = La L−1

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Acknowledgments

The authors wish to express their gratitude to the Spanish Ministry of Education and Science (MEC), for funding the PET2008_0175_02, and AGL2011-30328-C02-01 projects. They also wish to thank Mondragón Solutions for their support by providing the data and products needed to perform the study.

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Authors and Affiliations

  1. Regional Centre of Water Research (CREA), UCLM, Ctra. de las Peñas, km 3.2, 02071, Albacete, Spain

    F. Carrión, J. M. Tarjuelo & M. A. Moreno

  2. Instituto de Desarrollo Regional, UCLM, Campus Universitario s/n., 02071, Albacete, Spain

    D. Hernández

Authors
  1. F. Carrión
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  2. J. M. Tarjuelo
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  3. D. Hernández
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  4. M. A. Moreno
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Corresponding author

Correspondence to M. A. Moreno.

Additional information

Communicated by K. Stone.

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Carrión, F., Tarjuelo, J.M., Hernández, D. et al. Design of microirrigation subunit of minimum cost with proper operation. Irrig Sci 31, 1199–1211 (2013). https://doi.org/10.1007/s00271-013-0399-8

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  • DOI: https://doi.org/10.1007/s00271-013-0399-8

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