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GATE 2025 CE (CE1) – Question 31

Water and Waste Water Quality and Treatment · Unit processes and operations · 1 mark · Multiple select

The Surface Overflow Rate (SOR) in a rectangular sedimentation tank is 45 m$^3$/m$^2$/d. Minimum diameters of spherical inorganic and organic particles expected to be completely removed in this tank are calculated. Assume that Stoke's law is applicable. Which of the following options is/are correct:

Specific gravity of inorganic particles = 2.65

Specific gravity of organic particles = 1.20

Acceleration due to gravity ($g$) = 9.81 m/s$^2$

Kinematic viscosity ($\nu$) = $1 \times 10^{-6}$ m$^2$/s

  1. Minimum diameter of inorganic particles is 24 µm
  2. Minimum diameter of organic particles is 69 µm
  3. Minimum diameter of inorganic particles is 15 µm
  4. Minimum diameter of organic particles is 55 µm

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Correct answer: (A) Minimum diameter of inorganic particles is 24 µm; (B) Minimum diameter of organic particles is 69 µm

Explanation

A particle is fully removed if its settling velocity is at least the overflow rate, $v_s = \frac{45}{86400} = 5.21 \times 10^{-4}$ m/s. Stokes' law gives $v_s = \frac{g(G_s - 1)d^2}{18\nu}$, so $d = \sqrt{\frac{18\nu v_s}{g(G_s - 1)}}$. For inorganic particles $d = \sqrt{\frac{18 \times 10^{-6} \times 5.21 \times 10^{-4}}{9.81 \times 1.65}} = 24.1$ µm. For organic particles $d = \sqrt{\frac{18 \times 10^{-6} \times 5.21 \times 10^{-4}}{9.81 \times 0.20}} = 69.1$ µm. So A and B are correct.