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 what percentage of the 0.1 mm/s particles will settle in the sedimentation tank, we can use the following principles:

### Key Concepts:
1. **Overflow Rate (Surface Loading Rate, \( V_o \))**: This is the rate at which water flows over the top of the sedimentation tank. It is given by:
   \[
   V_o = \frac{Q}{A}
   \]
   where:
   - \( Q \) is the flow rate (in \( m^3/s \)),
   - \( A \) is the surface area of the tank (in \( m^2 \)).

2. **Surface Area (A)**: The surface area of the tank is the product of the width and length of the tank.
   \[
   A = \text{Width} \times \text{Length}
   \]

3. **Settling Velocity (V_s)**: The percentage of particles that will settle can be found by comparing the settling velocity (\( V_s \)) to the overflow rate (\( V_o \)). The percentage of particles that will settle is determined by the ratio \( \frac{V_s}{V_o} \), provided \( V_s \leq V_o \).

### Step-by-Step Solution:

1. **Convert Flow Rate to m³/s**:
   Let's take the average flow rate to be \( Q = 5.25 \) ML/d.

   \[
   Q = 5.25 \, \text{ML/d} = 5.25 \times 10^6 \, \text{L/d} = \frac{5.25 \times 10^6}{86400} \, \text{m³/s} \approx 60.76 \, \text{m³/s}
   \]

2. **Calculate the Surface Area of the Tank**:
   \[
   A = \text{Width} \times \text{Length} = 6.5 \, \text{m} \times 28 \, \text{m} = 182 \, \text{m²}
   \]

3. **Calculate the Overflow Rate \( V_o \)**:
   \[
   V_o = \frac{Q}{A} = \frac{60.76}{182} \approx 0.334 \, \text{m/s}
   \]

4. **Determine the Percentage of Particles that will Settle**:
   The settling velocity of the particles is given as \( V_s = 0.1 \, \text{mm/s} = 0.0001 \, \text{m/s} \).

   The percentage of particles that will settle is determined by:
   \[
   \text{Percentage Settled} = \frac{V_s}{V_o} \times 100\%
   \]
   \[
   \text{Percentage Settled} = \frac{0.0001}{0.334} \times 100\% \approx 0.03\%
   \]

Thus, approximately **0.03%** of the 0.1 mm/s particles will settle in the tank under the given conditions.

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Do you want more details or have any questions?

Here are some follow-up questions to consider:
1. What happens to particles with a settling velocity higher than the overflow rate?
2. How would increasing the depth of the tank affect the settling percentage?
3. What other factors could improve the settling of particles in the tank?
4. How would a change in flow rate impact the overflow rate and settling percentage?
5. What is the significance of the tank's width in the design process?
6. Can the shape of the tank influence the efficiency of particle settling?
7. How does temperature affect the settling velocity of particles?
8. What are the consequences of having too low of a settling percentage in water treatment?

**Tip:** Always ensure the flow rate is consistent with the design capacity of the sedimentation tank to optimize particle settling efficiency.

Learn how to calculate the percentage of 0.1 mm/s particles that will settle in a sedimentation tank with dimensions: Depth 3.5 m, Width 6.5 m, Length 28 m, and average flow rate between 5.0 and 5.5 ML/d. Follow a step-by-step solution using principles of hydraulics and fluid mechanics. Suitable for engineering students and professionals.

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