Question Bank • QB_IDE_EXP_015 NAT • 2 Marks

Section 5: Irrigation and Drainage Engineering

Irrigation Water Conveyance and Application Methods

Subtopic: Design and evaluation of irrigation methods

Question Statement:

Catch cans placed in a sprinkler test grid recorded application depths of $8, 10, 12, 10$ and $10\text{ mm}$ (mean depth $= 10.0\text{ mm}$). Using Christiansen's Uniformity formula $CU = 100 \left(1 - \frac{\sum |x_i - \bar{x}|}{n \bar{x}}\right)$, the Christiansen Uniformity Coefficient $CU$ in percentage is ________ (round off to 1 decimal place).

Answer Key:

92

Step-by-Step Solution & Explanation

1. Mean depth $\bar{x} = \frac{8 + 10 + 12 + 10 + 10}{5} = \frac{50}{5} = 10.0\text{ mm}$. 2. Deviations $|x_i - \bar{x}|$: $|8 - 10| = 2$ $|10 - 10| = 0$ $|12 - 10| = 2$ $|10 - 10| = 0$ $|10 - 10| = 0$ Sum of deviations $\sum |x_i - \bar{x}| = 2 + 0 + 2 + 0 + 0 = 4.0\text{ mm}$. 3. Christiansen Uniformity Coefficient $CU$: $CU = 100 \left(1 - \frac{4.0}{5 \times 10.0}\right) = 100 \left(1 - \frac{4.0}{50.0}\right) = 100 (1 - 0.08) = 92.0\%$
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