Irrigation Water Conveyance and Application Methods
Subtopic: Design of irrigation channels and underground pipelines
Question Statement:
A permanent matured orchard has a tree spacing of 4 m × 5 m. Each tree has a shading area of 40 % to be irrigated with the 'pig tail' pattern multi-exit drip emitters. The effective wetting geometry of each emitter is 2 m × 2 m. The emitters have discharge constant and exponent of 0.3 and 0.6, respectively. The coefficient of variation of emitter discharge is 0.06. The average and minimum operating pressures are 120 kPa and 100 kPa, respectively. The emission uniformity of the emitters is ________ %.
Official Answer Key:
83 to 86
Step-by-Step Solution & Explanation
Area per tree = 4 × 5 = 20 m²; shaded (to be wetted) area = 0.40 × 20 = 8 m².
Area wetted per emitter = 2 × 2 = 4 m² ⇒ number of emitters per plant, n = 8/4 = 2.
Discharge ratio from the emitter equation q = k H^x with x = 0.6:
q_min/q_avg = (100/120)^{0.6} = (0.8333)^{0.6} = 0.8964.
Emission uniformity: EU = 100 (1 − 1.27 C_v/√n)(q_min/q_avg)
= 100 (1 − 1.27 × 0.06/√2)(0.8964) = 100 (1 − 0.0539)(0.8964)
= 100 × 0.9461 × 0.8964 = 84.8 % — within the official range 83–86.
The discharge constant k = 0.3 is not needed since only the ratio of discharges is required.
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