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GATE 2021 CE (CE2) – Question 43

Water and Waste Water Quality and Treatment · Unit processes and operations · 2 marks · Multiple choice

A sand filter has grain diameter 0.4 mm, shape factor 0.84, specific gravity 2.55, bed depth 0.70 m and initial porosity 0.35. Backwashing expands porosity to 0.65. Terminal settling speed is 4.5 cm/s. Choose required backwash velocity.

  1. 5.79×10⁻³ m/s
  2. 6.35×10⁻³ m/s
  3. 0.69 cm/s
  4. 0.75 cm/s

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Correct answer: (B) 6.35×10⁻³ m/s

Explanation

The commonly used empirical expanded-bed estimate is $v_b=v_t\epsilon^{4.5}$. Substituting vt=0.045 m/s and ε=0.65 gives 0.006476 m/s. The nearest listed value is **6.35×10⁻³ m/s (B)**. The roughly 2% mismatch should be reviewed against the intended empirical exponent/correlation; it is not an exact numerical equality.