Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Meteorological parameters and their measurement
Question Statement:
The day length (sunshine hours) on 31st May 2014 at a place in India (26°18’ N, 73°01’ E) will be___________.
Official Answer Key:
13.50 to 13.55
Step-by-Step Solution & Explanation
Day length depends on latitude φ and solar declination δ, and (to first order) not on longitude.
Day of year for 31 May (non-leap year) = 31+28+31+30+31 = 151.
Solar declination (Cooper's formula): δ = 23.45° sin[360(284+N)/365] = 23.45° sin[360×435/365] = 23.45° sin(428.99°) = 23.45° sin(68.99°) = 23.45°(0.9336) = 21.89°.
Sunset hour angle: cos(H) = −tanφ·tanδ, with φ = 26°18' = 26.30°:
cos(H) = −tan(26.30°)tan(21.89°) = −(0.4938)(0.4017) = −0.1984 ⇒ H = 101.44°.
Day length = 2H/15 = 2(101.44)/15 = 13.53 hours, within the accepted range.
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