Explanation:
The superficial velocity in a stratified bed is the velocity at which the fluid moves through the bed, considering the void spaces between the particles. It is an important parameter in the design and operation of fluidized beds and other similar systems.

In a stratified bed, the particles are arranged in layers or strata based on their settling velocities. The particles with higher settling velocities settle at the bottom, while the particles with lower settling velocities are present in the upper layers.

Terminal settling velocity:
Terminal settling velocity is the velocity at which a particle settles under the influence of gravity in a fluid. It is determined by the size, shape, and density of the particle, as well as the properties of the fluid.

Porosity:
Porosity is a measure of the void space in a material. In the context of a stratified bed, porosity refers to the proportion of void space between the particles. It is calculated as the ratio of the volume of void space to the total volume of the bed.

Relationship between superficial velocity and terminal settling velocity:
The superficial velocity in a stratified bed can be related to the terminal settling velocity and porosity.

The superficial velocity is the average velocity of the fluid through the bed, taking into account the void spaces between the particles. It can be calculated by dividing the total volumetric flow rate of fluid by the cross-sectional area of the bed.

The terminal settling velocity of the particles at the bottom of the bed determines the overall flow behavior of the bed. The particles settle under the influence of gravity, and as they settle, they displace the fluid and create void spaces. The fluid then flows through these void spaces.

Porosity and superficial velocity:
The porosity of the bed affects the superficial velocity. A higher porosity means there are more void spaces through which the fluid can flow. Therefore, a higher porosity leads to a higher superficial velocity.

To calculate the superficial velocity, we multiply the terminal settling velocity by a factor related to porosity.

The correct answer is option 'D' because the superficial velocity is equal to the terminal settling velocity multiplied by (porosity)4.5. This relationship takes into account the effect of porosity on the superficial velocity in a stratified bed.