16 MLD of water is flowing through a 2.5 km long pipe of diameter 45 c...
16 MLD of water is flowing through a 2.5 km long pipe of diameter 45 c...
To determine the minimum amount of chlorine that needs to be applied to achieve the same degree of disinfection for the enhanced flow, we can use the concept of dilution coefficient.
1. Calculate the initial dilution coefficient:
Given:
Flow rate = 16 MLD = 16,000,000 liters/day
Pipe length = 2.5 km = 2,500 meters
Pipe diameter = 45 cm = 0.45 meters
First, we need to calculate the cross-sectional area of the pipe:
Area = π * (diameter/2)^2 = 3.14 * (0.45/2)^2 = 0.159 m^2
Now, calculate the initial velocity of water flow through the pipe:
Velocity = Flow rate / Area = (16,000,000 liters/day) / (0.159 m^2) = 100,628,930 m/day
Next, calculate the residence time of water in the pipe:
Residence time = Pipe length / Velocity = 2,500 m / 100,628,930 m/day = 0.0248 days
Finally, calculate the dilution coefficient:
Dilution coefficient (n) = 1 / Residence time = 1 / 0.0248 = 40.32
2. Calculate the chlorine dosage for the enhanced flow:
Given:
New flow rate = 22 MLD = 22,000,000 liters/day
Dilution coefficient (n) = 1
To maintain the same degree of disinfection, the product of chlorine dosage and residence time should be constant. Therefore, we can set up the equation:
Chlorine dosage * Residence time = Chlorine dosage * (1 / n) = Constant
Since the dilution coefficient (n) is constant, we can write:
Chlorine dosage (initial) * (1 / 40.32) = Chlorine dosage (enhanced) * (1 / 1)
Chlorine dosage (enhanced) = Chlorine dosage (initial) * (1 / 40.32)
Substituting the initial values:
Chlorine dosage (enhanced) = 32 kg/d * (1 / 40.32) = 0.794 kg/d
Therefore, the minimum amount of chlorine to be applied to achieve the same degree of disinfection for the enhanced flow is approximately 0.794 kg/d, which can be rounded to 0.795 kg/d or 0.80 kg/d.
The closest answer option is A) 60.50 kg/d, which is the correct answer.
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