This lesson is authored in North American operator units — million gallons per day, milligrams per litre, pounds per day — because the constant at its centre is a convention of that system and does not survive translation. Every operator certification exam on the continent asks it in this form.

$W = Q\,C \times 8.34$ — W equals Q C times eight point three four. $W$ is the mass loading in pounds per day: the weight of pollutant arriving, not its concentration. $Q$ is the flow in MGD, millions of gallons per day. $C$ is the concentration in mg/L — of BOD here, but the same relation prices TSS, chlorine demand or a chemical dose without changing a symbol.

The 8.34 is the weight of a US gallon of water in pounds, and here is why it belongs. A milligram per litre is one part per million by weight. A million gallons of water weighs 8.34 million pounds. One part per million of that is 8.34 pounds. So each mg/L in each MGD is 8.34 lb/d, and the constant is not a fudge factor at all — it is the weight of the water doing the carrying.

Two relations ride alongside it. Removal efficiency is $E = \dfrac{C_i - C_e}{C_i} \times 100$, where $C_i$ is the influent concentration and $C_e$ the effluent — subscript i is what came in, subscript e is what left. Note it needs no flow: as long as the same water goes in and out, the concentrations tell the whole story. Secondary treatment is expected to hit 85 to 95% BOD removal.

Population equivalent is $PE = \dfrac{W}{w}$, where $W$ is the total load in lb/d and $w$ is one person's daily share, 0.17 lb of BOD per capita per day in North America. It is the fairest sentence in the trade: it lets a town charge a food processor for what it actually behaves like. And it carries the sharpest trap in the chapter — Europe uses 60 g per capita per day, which is 0.132 lb, and the two figures disagree by 30%. A PE quoted without its convention has told you nothing.