Question Bank • QB_IDE_005 NAT • 2 Marks

Section 5: Irrigation and Drainage Engineering

Irrigation Water Conveyance and Application Methods

Subtopic: Design and evaluation of irrigation methods

Question Statement:

In a sprinkler irrigation test with 4 catch cans, the depths of water collected are $10\text{ mm}$, $12\text{ mm}$, $14\text{ mm}$, and $8\text{ mm}$. Christiansen's Uniformity Coefficient ($CU$) expressed in percentage is ________ (answer in integer).

Answer Key:

82

Step-by-Step Solution & Explanation

Christiansen's Uniformity Coefficient is: $CU = 100 \left( 1 - \frac{\sum |x_i - \bar{x}|}{n \cdot \bar{x}} \right)$ 1. Mean depth $\bar{x}$: $\bar{x} = \frac{10 + 12 + 14 + 8}{4} = \frac{44}{4} = 11\text{ mm}$ 2. Absolute deviations $|x_i - \bar{x}|$: • $|10 - 11| = 1$ • $|12 - 11| = 1$ • $|14 - 11| = 3$ • $|8 - 11| = 3$ $\sum |x_i - \bar{x}| = 1 + 1 + 3 + 3 = 8\text{ mm}$ 3. Uniformity Coefficient: $CU = 100 \left( 1 - \frac{8}{4 \times 11} \right) = 100 \left( 1 - \frac{8}{44} \right) = 100 \left( 1 - 0.1818 \right) = 81.82\% \approx 82\%$
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