Final answer:
The average filtration rate for the filter unit is approximately 0.000079 L/m² sec. The quantity of water used for backwashing is 36.45 m³, and the percentage of treated water that is used in backwashing is about 0.152% of the total volume filtered in 24 hours.
Step-by-step explanation:
The student is asked to calculate the average filtration rate and the quantity and percentage of treated water used in backwashing a filter unit during a 24-hour period. The dimensions of the filter unit are 4.5 m by 9 m, it filters 10000 m²/d and it is backwashed at a rate of 10 L/m².sec for 15 minutes. To find the average filtration rate (in L/m² sec), we take the total volume filtered in a day and divide it by the filter area and the number of seconds in a day. For the quantity of water used in backwashing, we multiply the backwash rate by the filter area and the duration of backwashing in seconds. Finally, we calculate the percentage of the treated water used for backwashing by comparing the volume of backwashed water to the total volume filtered in a day.
To calculate these values:
- Total volume filtered (in liters) = 10000 m²/d × 1 d/24 hr × 1 hr/3600 s × 1000 L/m² = 277.78 L/s
- Total filter area = 4.5 m × 9 m = 40.5 m²
- Average filtration rate (L/m² sec) = Total volume filtered ÷ (filter area × seconds per day) = 277.78 L/s ÷ (40.5 m² × 86400 s) ≈ 0.000079 L/m² sec
- Backwash volume (m³) = Backwash rate × filter area × backwash time (sec) = 10 L/m².sec × 40.5 m² × (15 min × 60 s/min) = 36450 L = 36.45 m³
- Percentage of treated water used = (Backwash volume ÷ Total volume filtered) × 100 = (36.45 m³ ÷ (10000 × 24) m³) × 100 ≈ 0.152%
Please note that the average filtration rate is quite low because it is calculated over a 24-hour period including the time the filter is not in operation (during backwash).