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GATE 2025 CE (CE1) – Question 43

Irrigation · Canals, design of weirs on permeable foundation, cross drainage structures · 2 marks · Multiple select

Lacey's regime equations, followed in India for making scour calculations while designing hydraulic structures across alluvial channels, are given below. Regarding these equations, which of the following statements is/are true:

$$D = 0.470 \times \left[\frac{Q}{f_s}\right]^{1/3}$$

$$P = 4.75 \times \sqrt{Q}$$

$$f_s = 1.76 \times \sqrt{d}$$

where $Q$ is discharge and $f_s$ is silt factor.

  1. D is the depth of scour below the existing riverbed
  2. P is the Lacey's waterway width
  3. d is the average grain size diameter of the bed material in centimetres
  4. D is the depth of scour below the design flood level

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Correct answer: (B) P is the Lacey's waterway width; (D) D is the depth of scour below the design flood level

Explanation

In scour calculations the regime depth from this equation is measured down from the design flood level, not from the existing bed, so D is true and A is false. $P = 4.75\sqrt{Q}$ is the regime perimeter, which is taken as the waterway width, so B is true. In Lacey's silt factor $f_s = 1.76\sqrt{d}$ the mean grain size $d$ is in millimetres, not centimetres, so C is false.