GATE AG 2008 • Q33 MCQ • 2 Marks

Section 4: Soil and Water Conservation Engineering

Hydrology

Subtopic: Stream flow measurement

Question Statement:

A 50 g L⁻¹ solution of a tracer was discharged into a stream at a constant rate of 20 mL s⁻¹. At a downstream section, the tracer was completely mixed and attained an equilibrium concentration of 10 parts per billion. Assuming the background concentration as zero, the stream discharge is

Options:

  • (A) 100 m³ s⁻¹
  • (B) 200 m³ s⁻¹
  • (C) 800 m³ s⁻¹
  • (D) 1000 m³ s⁻¹

Official Answer Key:

A

Step-by-Step Solution & Explanation

Mass balance (constant-rate injection method): C₁Q₁ = C₂(Q+Q₁) ≈ C₂Q (since Q₁≪Q). C₁=50 g/L=50 kg/m³, Q₁=20×10⁻⁶ m³/s → mass rate = 50×20×10⁻⁶ = 1×10⁻³ kg/s. C₂ = 10 ppb (by mass) = 10×10⁻⁹×1000 kg/m³(water) = 1×10⁻⁵ kg/m³. Q = mass rate/C₂ = 1×10⁻³/1×10⁻⁵ = 100 m³/s.

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