GATE AG 2007 • Q80 MCQ • 1 Mark

Section 4: Soil and Water Conservation Engineering

Hydrology

Subtopic: Hydrograph analysis, unit hydrograph theory and application

Question Statement:

A 4-h unit hydrograph (UH) is used to derive an S-hydrograph. The ordinates of the 4-h UH are given in the table below: | Time (h) | 0 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | |---|---|---|---|---|---|---|---|---|---|---|---|---| | 4-h UH ordinates (m³ s⁻¹) | 0 | 20 | 80 | 130 | 150 | 130 | 90 | 52 | 27 | 15 | 5 | 0 | Equilibrium discharge and its time of occurrence for the derived S-hydrograph are:

Options:

  • (A) 150 m³ s⁻¹ and 16 h
  • (B) 380 m³ s⁻¹ and 16 h
  • (C) 699 m³ s⁻¹ and 40 h
  • (D) 699 m³ s⁻¹ and 44 h

Official Answer Key:

C

Step-by-Step Solution & Explanation

The S-hydrograph is built by successively summing the UH ordinate table (equivalent to superposing the UH lagged by 4 h, repeatedly): running cumulative sums of the 4-h UH ordinates (0,20,80,130,150,130,90,52,27,15,5,0) give 0,20,100,230,380,510,600,652,679,694,699,699 at t=0,4,...,44 h. The S-curve first becomes constant (equilibrium) at t=40 h, where it reaches 699 m³/s, remaining unchanged at t=44 h (confirming equilibrium was reached at 40 h, not 44 h).

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