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 0.5 mm/s particle will settle?


To determine the percentage of particles with a settling velocity of 0.5 mm/s that will settle in the sedimentation tank, we need to compare the particle's settling velocity with the overflow rate (also known as surface loading rate) of the tank.

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

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

Where:
- \( Q \) is the flow rate in m³/s.
- \( A \) is the surface area of the sedimentation tank in m².

### Step 2: Convert Flow Rate to m³/s
First, we need to convert the flow rate from ML/d to m³/s. Assuming we choose an average flow rate \( Q = 5.25 \) ML/d:

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

Convert from m³/d 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, we can 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 (\( OR \)):

\[
\text{Percentage Settling} = \left(\frac{\text{OR}}{V_s}\right) \times 100
\]

Given that \( V_s = 0.5 \text{ mm/s} \):

\[
\text{Percentage Settling} = \left(\frac{0.3336 \text{ mm/s}}{0.5 \text{ mm/s}}\right) \times 100 \approx 66.72\%
\]

### Final Answer:
Approximately **66.72%** of the particles with a settling velocity of 0.5 mm/s will settle in the sedimentation tank.

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Would you like to go over more details or have any questions? 

Here are 8 related questions you might find useful:
1. How does increasing the flow rate affect the percentage of particles that settle?
2. What is the effect of tank depth on particle settling?
3. How does particle size relate to settling velocity?
4. What assumptions are made in this calculation for particle settling?
5. How would reducing the tank width affect the sedimentation efficiency?
6. What is the significance of the overflow rate in sedimentation tank design?
7. What are some methods to improve the settling efficiency of a sedimentation tank?
8. How would the settling percentage change if the particle settling velocity were 0.2 mm/s?

**Tip:** Regularly monitor and clean sedimentation tanks to maintain their efficiency and prevent clogging, which can reduce the effective surface area and settling efficiency.

Learn how to calculate the percentage of particles with a settling velocity of 0.5 mm/s that will settle in a sedimentation tank with dimensions 3.5 m depth, 6.5 m width, and 28 m length, at an average flow rate of 5.25 ML/d. Detailed step-by-step solution including the overflow rate calculation and percentage settling formula.

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