Calculate the water distribution efficiency, if the depths of penetration along the length of a border strip at an interval of 20 m are 1.5 m, 1.8 m and 2.1 m respectively.

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SSC JE CE Previous Year Paper 18 (Held On: 25 JAN 18 Morning)
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  1. 0.6667
  2. 0.8333
  3. 0.8889
  4. 0.9767

Answer (Detailed Solution Below)

Option 3 : 0.8889
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Concept:

Water distribution efficiency \(= {{\rm{\eta }}_{\rm{d}}} = \left[ {1 - \frac{{\rm{y}}}{{{{\rm{d}}_{\rm{w}}}}}} \right] \times 100{\rm{\;}}\left( {{\rm{in\;\% }}} \right)\)

\({{\rm{d}}_{\rm{w}}} = \frac{{{{\rm{d}}_1} + {{\rm{d}}_2} + \ldots + {{\rm{d}}_{\rm{n}}}}}{{\rm{n}}},\) dw = average depth of water stored

\({\rm{y}} = \frac{{y_1 \ + \ y_2\ + \ ......\ +\ y_n}}{n}\), y = Average of absolute value of deviations

y1, y2,......., yn = absolute deviations from average depth of water stored

Calculation:

\({\rm{d_w}} = \frac{{1.5 + 1.8 + 2.1}}{3} = 1.8\)

y1 = 0.3 m, y2 = 1.8 – 1.8 = 0, y3 = 2.1 – 1.8 = 0.3 m

\({\rm{y}} = \frac{{0.3 + 0.3 + 0}}{3} = 0.2\)

\({{\rm{\eta }}_{\rm{d}}} = \left( {1 - \frac{{0.2}}{{1.8}}} \right) = \frac{8}{9} = 0.8889\)
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