A coal washery discharges 300 m3/day of contaminated water in a stream having a flow rate of 0.04 m3/s. The DO level of the stream and the contaminated water are 8.5 mg/L and 4 mg/... A coal washery discharges 300 m3/day of contaminated water in a stream having a flow rate of 0.04 m3/s. The DO level of the stream and the contaminated water are 8.5 mg/L and 4 mg/L, respectively. Neglecting the impact of temperature, the resultant DO, in mg/L, of the stream just after mixing is _____ (round off up to 2 decimals). Read more

Steps to Solve

1. Convert the flow rate of the stream to daily volume

Convert the flow rate of the stream from cubic meters per second (m³/s) to cubic meters per day (m³/day):

[ \text{Flow rate of stream} = 0.04 , \text{m³/s} \times 86400 , \text{s/day} = 3456 , \text{m³/day} ]

2. Calculate the total volume after mixing

Add the volume of contaminated water being discharged to the daily volume of the stream:

[ \text{Total Volume} = 3456 , \text{m³/day} + 300 , \text{m³/day} = 3756 , \text{m³/day} ]

3. Calculate the total amount of dissolved oxygen before mixing

First, calculate the total dissolved oxygen (DO) in both the stream and the contaminated water:

• For the stream: [ \text{DO (stream)} = 8.5 , \text{mg/L} \times 3456 , \text{m³/day} = 29376 , \text{mg/day} ]

• For the contaminated water: [ \text{DO (contaminated water)} = 4 , \text{mg/L} \times 300 , \text{m³/day} = 1200 , \text{mg/day} ]

Add these amounts to get the total DO:

[ \text{Total DO} = 29376 , \text{mg/day} + 1200 , \text{mg/day} = 30576 , \text{mg/day} ]

4. Calculate the resultant DO level after mixing

Use the total DO and total volume to find the resultant concentration in the mixed water:

[ \text{Resultant DO} = \frac{\text{Total DO}}{\text{Total Volume}} = \frac{30576 , \text{mg/day}}{3756 , \text{m³/day}} ]

Now convert the volume from cubic meters to liters:

[ \text{Total Volume in Liters} = 3756 , \text{m³/day} \times 1000 , \text{L/m³} = 3756000 , \text{L/day} ]

Now calculate the resultant DO:

[ \text{Resultant DO} = \frac{30576 , \text{mg/day}}{3756000 , \text{L/day}} \approx 8.14 , \text{mg/L} ]

5. Round off the resultant DO to two decimals

Rounding off to two decimal places, we get:

[ \text{Resultant DO} \approx 8.14 , \text{mg/L} ]