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 to 2 decimals). Read more

Steps to Solve

1. Convert Flow Rates to Compatible Units

First, we need to convert the discharge of contaminated water from cubic meters per day to cubic meters per second (m³/s).

The contaminated water flow rate is given as:

$$ \text{Flow rate} = \frac{300\ \text{m}^3}{\text{day}} $$

There are 86400 seconds in a day, so we have:

$$ \text{Flow rate in m}^3/\text{s} = \frac{300}{86400} = 0.0034722\ \text{m}^3/\text{s} $$

2. Calculate the DO Contribution from Each Source

Next, we calculate the contribution of Dissolved Oxygen (DO) from both the stream and the contaminated water.

• The DO level of the stream is 8.5 mg/L, and the flow rate is 0.04 m³/s.
• The DO level of the contaminated water is 4 mg/L with a flow rate of 0.0034722 m³/s.

The mass of DO from the stream is:

$$ \text{DO}\text{stream} = (\text{Flow rate}\text{stream}) \times (\text{DO level}_\text{stream}) = (0.04\ \text{m}^3/\text{s}) \times (8.5\ \text{mg/L}) = 0.34\ \text{mg/s} $$

The mass of DO from the contaminated water is:

$$ \text{DO}\text{contaminated} = (\text{Flow rate}\text{contaminated}) \times (\text{DO level}_\text{contaminated}) = (0.0034722\ \text{m}^3/\text{s}) \times (4\ \text{mg/L}) = 0.0138888\ \text{mg/s} $$

3. Calculate Total Mass of DO After Mixing

Now, sum the contributions from both sources:

$$ \text{Total DO} = \text{DO}\text{stream} + \text{DO}\text{contaminated} = 0.34 + 0.0138888 = 0.3538888\ \text{mg/s} $$

4. Calculate Total Flow Rate After Mixing

Calculate the total combined flow rate after mixing:

$$ \text{Total flow rate} = \text{Flow rate}\text{stream} + \text{Flow rate}\text{contaminated} = 0.04 + 0.0034722 = 0.0434722\ \text{m}^3/\text{s} $$

5. Calculate Resultant DO Level

Finally, calculate the resultant DO level in mg/L by dividing the total DO by the total flow rate:

$$ \text{Resultant DO} = \frac{\text{Total DO}}{\text{Total flow rate}} = \frac{0.3538888\ \text{mg/s}}{0.0434722\ \text{m}^3/\text{s}} \approx 8.13\ \text{mg/L} $$

Rounding to two decimal places gives us:

Resultant DO ≈ 8.13 mg/L.