GATE AG 2014 • Q44 NAT • 2 Marks

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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