Question Bank • QB_IDE_EXP_069 NAT • 2 Marks

Section 5: Irrigation and Drainage Engineering

Irrigation Water Conveyance and Application Methods

Subtopic: Surface, sprinkler and micro irrigation methods

Question Statement:

In a sprinkler test with 4 catch cans catching water depths of $10\text{ mm}$, $12\text{ mm}$, $8\text{ mm}$, and $10\text{ mm}$, calculate Christiansen's Uniformity Coefficient ($CU = 100 \left[1 - \frac{\sum |x_i - \bar{x}|}{n \bar{x}}\right]$) in percentage.

Answer Key:

90

Step-by-Step Solution & Explanation

Mean depth $\bar{x} = \frac{10 + 12 + 8 + 10}{4} = \frac{40}{4} = 10.0\text{ mm}$. Absolute deviations: $|10 - 10| = 0$ $|12 - 10| = 2$ $|8 - 10| = 2$ $|10 - 10| = 0$ Sum of absolute deviations $\sum |x_i - \bar{x}| = 0 + 2 + 2 + 0 = 4\text{ mm}$. $CU = 100 \left[ 1 - \frac{4}{4 \times 10} \right] = 100 \left[ 1 - \frac{4}{40} \right] = 100 [1 - 0.10] = 90.0\%$
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