A town has an existing horizontal flow sedimentation tank and it wishes to remove particles that have settling velocities of 0.1 mm/s. The treatment sedimentation tank has the following dimension:

•               Depth 3.5 m

•               Width 6.5 m

•               Length 28 m

Choose an average flow rate for the tank between 5.0 and 5.5 ML/d.                                                    

 a)           What percentage of the 0.1 mm/s particle will settle?

To determine the percentage of particles with a settling velocity of 0.1 mm/s that will settle in the sedimentation tank, we will use the same method as before. Here's the step-by-step calculation:

### Step 1: Calculate the Overflow Rate (Surface Loading Rate)
The overflow rate (OR) is given by the formula:

\[
\text{Overflow Rate (OR)} = \frac{\text{Flow Rate (Q)}}{\text{Surface Area (A)}}
\]

### Step 2: Convert Flow Rate to m³/s
Let's assume an average flow rate of \( Q = 5.25 \) ML/d.

Convert from ML/d to m³/s:

\[
Q = 5.25 \times 10^6 \text{ L/d} = 5.25 \times 10^3 \text{ m³/d}
\]

Convert to m³/s:

\[
Q = \frac{5.25 \times 10^3 \text{ m³/d}}{86400 \text{ s/d}} \approx 0.0607 \text{ m³/s}
\]

### Step 3: Calculate the Surface Area of the Tank
The surface area \( A \) is the product of the length and the width of the tank:

\[
A = \text{Length} \times \text{Width} = 28 \text{ m} \times 6.5 \text{ m} = 182 \text{ m²}
\]

### Step 4: Calculate the Overflow Rate (OR)
Now, calculate the overflow rate:

\[
\text{OR} = \frac{Q}{A} = \frac{0.0607 \text{ m³/s}}{182 \text{ m²}} \approx 0.0003336 \text{ m/s} = 0.3336 \text{ mm/s}
\]

### Step 5: Determine the Percentage of Particles that Settle
The percentage of particles that settle is determined by comparing the particle's settling velocity (\( V_s \)) with the overflow rate (\( OR \)):

Given that \( V_s = 0.1 \text{ mm/s} \) and \( OR = 0.3336 \text{ mm/s} \), since the settling velocity \( V_s \) is less than \( OR \), the percentage of particles that settle is:

\[
\text{Percentage Settling} = \left(\frac{V_s}{\text{OR}}\right) \times 100 = \left(\frac{0.1 \text{ mm/s}}{0.3336 \text{ mm/s}}\right) \times 100 \approx 29.98\%
\]

### Final Answer:
Approximately **29.98%** of the particles with a settling velocity of 0.1 mm/s will settle in the sedimentation tank.

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Would you like to explore more details or have any questions? 

Here are 8 related questions you might find useful:
1. What modifications can be made to increase the percentage of particles that settle?
2. How does the flow rate impact the percentage of particles that settle?
3. What happens if the settling velocity is greater than the overflow rate?
4. How would decreasing the tank length affect the settling efficiency?
5. What is the role of tank depth in sedimentation efficiency?
6. How does particle shape influence settling velocity?
7. What are the factors that influence the design of a sedimentation tank?
8. How would you calculate the percentage settling for particles with a different velocity?

**Tip:** Understanding the overflow rate is crucial in sedimentation tank design as it directly affects the settling efficiency of particles.

Learn how to calculate the percentage of particles with a settling velocity of 0.1 mm/s that will settle in a sedimentation tank with dimensions 3.5 m depth, 6.5 m width, and 28 m length. Understand the impact of flow rate and overflow rate on sedimentation efficiency.

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