A sedimentation basin with a 30-meter diameter and an average water depth of 3.0 meters treats a wastewater flow of 0.3 cubic meters per second. Calculate the overflow rate and detention time.

To calculate the overflow rate and detention time for the sedimentation basin, we’ll need to use two different formulas:

1. The overflow rate (also known as the surface loading rate) is the flow rate of water entering the basin (in cubic meters per second, m³/s) divided by the surface area of the basin (in square meters, m²).

2. The detention time (also known as the retention or hydraulic residence time) is the volume of the basin (in cubic meters, m³) divided by the flow rate (in cubic meters per second, m³/s).

First, let’s find the overflow rate:

Overflow Rate = Flow Rate / Surface Area

The surface area (A) of the circular basin is calculated using the formula for the area of a circle: A = π * radius².

The radius of the basin is half of the diameter, so the radius is 30 meters / 2 = 15 meters.

Surface Area (A) = π * (15 m)² Surface Area (A) = π * 225 m² Surface Area (A) = 3.14159265 * 225 m² Surface Area (A) ≈ 706.85775 m²

Now we can calculate the overflow rate:

Overflow Rate = 0.3 m³/s / 706.85775 m² Overflow Rate ≈ 0.0004244 m³/s/m²

To convert this to a more standard unit used in sedimentation process design, we'll multiply by 86,400 to get cubic meters per day per square meter (m³/day/m²):

Overflow Rate ≈ 0.0004244 m³/s/m² * 86,400 s/day Overflow Rate ≈ 36.6644 m³/day/m²

Next, let’s calculate the detention time:

Detention Time = Volume of Basin / Flow Rate

The volume of the basin is the product of the surface area and the average water depth,

Volume of Basin = Surface Area * Average Depth

Volume of Basin = 706.85775 m² * 3.0 m Volume of Basin = 2120.57325 m³

Now, calculate the detention time:

Detention Time = 2120.57325 m³ / 0.3 m³/s Detention Time ≈ 7068.5775 seconds

To convert the detention time to hours, we divide by the number of seconds in an hour (3,600 seconds per hour):

Detention Time ≈ 7068.5775 s / 3,600 s/hour Detention Time ≈ 1.96349 hours

So, the overflow rate is approximately 36.6644 m³/day/m² and the detention time is approximately 1.96349 hours.

Extra: The overflow rate is an important design parameter used to size sedimentation basins. It determines how quickly water flows over a unit area of the settling basin surface. A lower overflow rate can lead to more effective solids removal because it gives particles more time to settle out of the water before exiting the basin.

The detention time is also a critical parameter in sedimentation basin design as it indicates the average time a particle (and the water) will stay in the basin. Longer detention times can be advantageous, allowing more time for particles to settle, but excessively long times may lead to another issue such as resuspension of settled particles or algal growth in the basin.

Both the overflow rate and detention time help engineers to strike a balance between efficient sedimentation and practical space and cost considerations in the design of water treatment facilities.