GATE 2024 AG – Question 41

Irrigation and Drainage Engineering · Irrigation Water Conveyance and Application Methods · 2 marks · Multiple choice

Border-irrigation stored depths at 12 locations are50,49,48,47,46,45,44,43,42,41,40,39 mm. Find Christiansen uniformity coefficient in percent.

93.26
91.66
89.70
36.28

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Show answer and explanation

Correct answer: (A) 93.26

Explanation

Mean depth is $(50+39)/2=44.5$ mm. Absolute deviations occur in pairs. Their total is $2(.5+1.5+2.5+3.5+4.5+5.5)=36$ mm. Thus $CU=100[1-\sum|x_i-\bar x|/(n\bar x)]=100[1-36/(12\cdot44.5)]=93.2584\%$. Hence **93.26%,A**.

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