Question

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:

• A. \( D = 0.470 \times \left( \frac{Q}{f_s} \right)^{1/3} \)
• B. \( P = 4.75 \times \sqrt{Q} \)
• C. \( f_s = 1.76 \times \sqrt{d} \)
• D. \( D \) is the depth of scour below the design flood level.

Hint:

Lacey’s regime equations are useful for designing structures like bridges and weirs in alluvial channels. Understanding the relationships between discharge, particle size, and silt factor is key to accurate scour prediction.

Answer 1

The Correct Option is B, D

According to Lacey's regime equations, we have the following relationships for designing hydraulic structures across alluvial channels: - The equation for the depth of scour is: \[ D = 0.470 \times \left( \frac{Q}{f_s} \right)^{1/3} \] where \( D \) is the depth of scour, \( Q \) is the discharge, and \( f_s \) is the silt factor. - The equation for the perimeter is: \[ P = 4.75 \times \sqrt{Q} \] where \( P \) is the perimeter and \( Q \) is the discharge. - The equation for the silt factor is: \[ f_s = 1.76 \times \sqrt{d} \] where \( f_s \) is the silt factor and \( d \) is the diameter of the particle. Thus, the correct statements are (B) and (D). The depth of scour \( D \) is calculated based on the discharge and silt factor, and \( P \) is the perimeter based on the discharge.