Irrigation Water Conveyance and Application Methods
Subtopic: Design and evaluation of irrigation methods
Question Statement:
The performance of a border irrigation event was evaluated by taking soil moisture measurements at 12 locations along the border from the upstream end. The computed irrigation depths at those locations were 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, and 39 mm. The Christiansen Uniformity Coefficient (CU) for the event, in %, is __________. (Rounded off to 2 decimal places)
Options:
(A) 93.26
(B) 91.66
(C) 89.70
(D) 36.28
Official Answer Key:
A
Step-by-Step Solution & Explanation
The Christiansen Uniformity Coefficient is:
CU = 100 [1 − Σ|xᵢ − x̄|/(n · x̄)]
Step 1 — mean depth. The values form an arithmetic series from 39 to 50:
x̄ = (39 + 50)/2 = 44.5 mm
Step 2 — sum of absolute deviations. The deviations are symmetric about the mean:
±0.5, ±1.5, ±2.5, ±3.5, ±4.5, ±5.5
Σ|xᵢ − x̄| = 2 × (0.5 + 1.5 + 2.5 + 3.5 + 4.5 + 5.5) = 2 × 18 = 36 mm
Step 3 — substitute:
CU = 100 [1 − 36/(12 × 44.5)] = 100 [1 − 36/534]
= 100 [1 − 0.067416]
= 93.26 %
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