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 0.3 mm/s particle will settle?

To determine the percentage of the 0.3 mm/s particles that will settle in the sedimentation tank, we need to follow these steps:

### Step 1: Calculate the surface area of the tank
The surface area \( A \) of the tank is calculated by multiplying the length and the width of the tank:

\[
A = \text{Length} \times \text{Width} = 28 \, \text{m} \times 6.5 \, \text{m} = 182 \, \text{m}^2
\]

### Step 2: Determine the flow rate through the tank
We need to choose an average flow rate within the given range of 5.0 to 5.5 ML/d. For this calculation, let's choose a flow rate \( Q \) of 5.25 ML/d (midpoint of the range). Convert this flow rate to cubic meters per second (m³/s):

\[
Q = 5.25 \, \text{ML/d} = 5.25 \times 10^6 \, \text{L/day} = 5.25 \times 10^3 \, \text{m}^3/\text{day}
\]
\[
Q = \frac{5.25 \times 10^3 \, \text{m}^3/\text{day}}{24 \times 60 \times 60 \, \text{seconds/day}} = 0.0607 \, \text{m}^3/\text{sec}
\]

### Step 3: Calculate the overflow rate (surface loading rate)
The overflow rate \( v_o \) (also known as the surface loading rate) is given by:

\[
v_o = \frac{Q}{A} = \frac{0.0607 \, \text{m}^3/\text{sec}}{182 \, \text{m}^2} = 0.0003334 \, \text{m/s}
\]

### Step 4: Determine the settling velocity of the particle
The settling velocity \( v_s \) of the particle is given as 0.3 mm/s:

\[
v_s = 0.3 \, \text{mm/s} = 0.0003 \, \text{m/s}
\]

### Step 5: Calculate the percentage of particles that will settle
The percentage of the particles that will settle is given by the ratio of the settling velocity to the overflow rate:

\[
\text{Percentage settled} = \frac{v_s}{v_o} \times 100 = \frac{0.0003 \, \text{m/s}}{0.0003334 \, \text{m/s}} \times 100 \approx 89.98\%
\]

So, approximately **89.98%** of the particles with a settling velocity of 0.3 mm/s will settle in the tank.

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Would you like further details or explanations on any part of this process?

### Related Questions:
1. How does the depth of the tank affect the settling process?
2. What factors influence the choice of flow rate for the sedimentation tank?
3. How would changing the flow rate to 5.0 ML/d affect the percentage of particles settling?
4. How does the particle size relate to the settling velocity?
5. What would happen if the particle's settling velocity were lower than the overflow rate?
6. How does the width of the tank impact the surface loading rate?
7. What methods can be used to increase the percentage of particles that settle?
8. How does the sedimentation tank design change for different types of particles?

**Tip:** When designing sedimentation tanks, always ensure that the overflow rate is less than the settling velocity of the target particles for effective removal.

Learn how to calculate the percentage of particles settling in a sedimentation tank based on flow rate, tank dimensions, and particle settling velocity. Use our detailed step-by-step solution to understand the process. Suitable for professionals and graduate-level students.

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