BOD5 threshold covered by basic sewer charges/taxes
Cthreshold
300 mg/L
Operating cost for removing BOD5 above the threshold
—
$0.25/kg BOD5 removed
Find. The annual dollar surcharge the industry pays for the portion of its BOD5 load that exceeds the basic-charge threshold.
Approach. Only the BOD5 concentration ABOVE the 300 mg/L threshold is subject to a surcharge (the first 300 mg/L is already covered by basic sewer charges/taxes); convert that excess concentration to a daily mass load using the given flow, scale to an annual mass, then apply the given unit removal cost.
Excess BOD5 mass load per day. Since 1 mg/L = 1 g/m3, the daily excess mass is $Q \times C_{excess}$, converted from grams to kilograms:
$$m_{excess} = \frac{800\ \text{m}^3/\text{d} \times 335\ \text{g/m}^3}{1000\ \text{g/kg}} = 268\ \text{kg/d}$$
Annual excess BOD5 mass. Scaling the daily excess load to a full year of continuous operation:
$$M_{annual} = 268\ \text{kg/d} \times 365\ \text{d/yr} = 97{,}820\ \text{kg/yr}$$
Annual surcharge. Applying the given operating cost per kg of BOD5 removed to the annual excess mass:
$$\boxed{\text{Surcharge} = 97{,}820\ \text{kg/yr} \times \$0.25/\text{kg} = \$24{,}455/\text{yr}}$$
Final results
Quantity
Value
Excess BOD5 concentration above threshold
335 mg/L
Excess BOD5 mass load
268 kg/d
Annual excess BOD5 mass
97,820 kg/yr
Annual surcharge
$24,455/yr
Check: assumes 365 days/year of continuous operation at the stated flow and concentration (no explicit operating-schedule data given), and that the surcharge applies strictly to the excess mass above 300 mg/L (the first 300 mg/L of BOD5 concentration is treated as fully covered by the basic sewer charge/tax, per the question's own wording).
