The correct answer is $\frac{{\text{Q}}}{{{\text{L}} \times {\text{D}}}}$.
The settling velocity of a particle is the velocity at which it settles in a fluid. It is a function of the particle’s density, the fluid’s density, and the fluid’s viscosity.
In a sedimentation tank, the discharge $Q$ is the volume of fluid that flows through the tank per unit time. The length $L$ and width $B$ of the tank are the dimensions of the tank in the flow direction and the transverse direction, respectively. The depth $D$ of the tank is the dimension of the tank in the vertical direction.
The settling velocity of a particle in a sedimentation tank is given by the following equation:
$$v_s = \frac{Q}{L \times D}$$
where $v_s$ is the settling velocity of the particle, $Q$ is the discharge, $L$ is the length of the tank, and $D$ is the depth of the tank.
Option A is incorrect because it does not include the factor $L$. Option B is incorrect because it does not include the factor $D$. Option C is incorrect because it does not include the factor $Q$. Option D is incorrect because it does not include the factor $D$.