The scour depth D of a river during flood, may be calculated from the Lacey’s equation A. D = 0.47 $$\left( {\frac{{\text{Q}}}{{\text{f}}}} \right)$$ B. D = 0.47 $${\left( {\frac{{\text{Q}}}{{\text{f}}}} \right)^{\frac{1}{2}}}$$ C. D = 0.47 $${\left( {\frac{{\text{Q}}}{{\text{f}}}} \right)^{\frac{1}{3}}}$$ D. D = 0.47 $${\left( {\frac{{\text{Q}}}{{\text{f}}}} \right)^{\frac{2}{3}}}$$

The correct answer is: D. D = 0.47 $${\left( {\frac{{\text{Q}}}{{\text{f}}}} \right)^{\frac{2}{3}}}$$

Lacey’s equation is a formula used to calculate the scour depth of a river during flood. The equation is:

$$D = 0.47 \left( \frac{Q}{f} \right)^{\frac{2}{3}}$$

where:

• $D$ is the scour depth, in meters
• $Q$ is the discharge of the river, in cubic meters per second
• $f$ is the friction factor, which is a dimensionless number that depends on the type of bed material and the flow conditions

The equation is based on the assumption that the scour depth is proportional to the square root of the discharge and the cube root of the friction factor. This assumption is based on experimental data, and it has been shown to be accurate for a wide range of conditions.

The equation can be used to estimate the scour depth of a river during flood. However, it is important to note that the equation is only an approximation, and the actual scour depth may be different from the value calculated by the equation. The equation should be used with caution, and it is always best to consult with a professional engineer when designing a river or stream.

The other options are incorrect because they do not represent the correct formula for Lacey’s equation.