1. Introduction:
This question is related to settling velocity and surface loading in the context of chemical engineering. We are given the settling velocity of 1 cm per second and we need to determine the corresponding surface loading in liters per day per square meter.

2. Understanding the problem:
To solve this problem, we need to understand the definitions of settling velocity and surface loading.

- Settling velocity: Settling velocity is the speed at which particles in a fluid settle under the influence of gravity. It is a measure of the rate at which particles settle in a given medium.
- Surface loading: Surface loading refers to the rate at which a substance is applied to a specific surface area. In this case, it represents the rate at which particles settle on a specific surface area.

3. Calculation:
To calculate the surface loading, we need to convert the settling velocity from cm per second to liters per day per square meter.

- Conversion of settling velocity:
1 cm per second = 0.01 m per second (as 1 m = 100 cm)
= 0.01 * 60 * 60 seconds per hour (as there are 60 seconds in a minute and 60 minutes in an hour)
= 36 m per hour

- Conversion of surface loading:
Surface loading is calculated as the product of settling velocity and the density of the particles.
Let's assume the density of the particles is ρ kg/m^3.

Surface loading = settling velocity * density
= 36 m/hour * ρ kg/m^3

To convert this to liters per day per square meter, we need to multiply by appropriate conversion factors:
1 m^3 = 1000 liters
1 day = 24 hours

Surface loading = (36 m/hour * ρ kg/m^3) * (1000 liters/m^3) * (24 hours/day)
= 864,000 ρ liters per day per square meter

4. Conclusion:
Therefore, the surface loading corresponding to a settling velocity of 1 cm per second is 864,000 liters per day per square meter.