Solids Loading Calcs++

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Influent TSS: 50 mg/L = 0.05 g per liter = 0.00005 kg per liter.

Filtration Rate: 10 m³/m²·hr = 10,000 L per m² per hour.

Solids Loading Rate:  0.00005 kg/L×10,000 L/(m²\cdotphr)  =  0.5 kg/(m²\cdotphr). 0.00005 \text{ kg/L} \times 10{,}000 \text{ L/(m²·hr)} \;=\; 0.5 \text{ kg/(m²·hr)}.0.00005 kg/L×10,000 L/(m²\cdotphr)=0.5 kg/(m²\cdotphr). 

So each square meter of filter receives 0.5 kg of solids every hour.

Typical  Capacity: 3–6 kg/m² (we’ll assume 5 kg/m² as a mid-range      “breakthrough” point).

Time to Reach Capacity:

5 kg/m²  ÷  0.5 kg/(m²\cdotphr)  =  10 hours. 5 \text{ kg/m²} \;\div\; 0.5 \text{ kg/(m²·hr)} \;=\; 10 \text{ hours.}5 kg/m²÷0.5 kg/(m²\cdotphr)=10 hours. 

Hence, the filter can run ~10 hours before hitting ~5 kg/m² of solids load.

In reality, run length might be 6–12 hours (if we use the 3–6 kg/m² range). But ~10 hours is a good average.

One backwash every ~10 hours of filtration. That’s typically 2–3 cycles per day.

Backwash takes ~5–10 minutes per cycle, at 2.5× forward flow.

Backwash Rate: ~25 m³/m²·hr (2.5× the 10 m³/m²·hr).

Duration:  ~10 minutes = 1/6 hr.

Volume per backwash per m²:

25  ×  16  =  4.17 m³/m². 25 \;\times\; \frac{1}{6} \;=\; 4.17 \text{ m³/m².}25×61​=4.17 m³/m². 

• Over      10 hours, the filter processes 10 m³/m²·hr × 10 hr = 100 m³/m².
• Backwash Fraction: 4.17/100 = ~4% of the throughput.

The filter accumulates ~5 kg/m² of solids by 10 hours (assuming that’s our chosen capacity).

Each backwash flushes out ~4.17 m³/m² of water.

Average TSS in backwash: ~5 kg ÷ 4.17 m³ ≈ 1,200 mg/L 

Run Time: 8–12 hours is far more typical for rapid filtration. You’d see 2–3 backwashes a day.

Backwash Water Fraction: ~4–5% of treated flow, which is quite manageable.

Fewer Mechanical Cycles: 2–3 backwashes per day per filter is standard in many industrial or municipal filters.

Likely Feasible: A 50 mg/L TSS feed is still on the high side for direct media filtration. With robust piping/valves and enough filter units to rotate, you can maintain continuous output relatively easily. If TSS occasionally spikes above 50 mg/L, the system can handle it but you might see shorter runs or slightly higher backwash frequency.

Verdict: Spikes of 50 mg/L TSS are acceptable, but for continuous operation at > 30 mg/L pre-clarification is recommended.