Solids Concentration: Why does 2% solids equal 20,000 mg/L?

A common way of describing the thickness or “soupiness” of sludge is % solids. Percent solids is a measure of the amount of solid material in a wastewater sample. As this number increases, the sludge becomes less watery and thicker to the point you can hold it in your hand (with gloves of course). You’ll commonly come across this measurement if you’re ever doing any problems involving anaerobic digesters, sludge thickening, or dewatering. Here’s the difference between sludge’s consistency at different % solids:


2% solids sludge collected from an anaerobic digester.

Dewatered sludge at around 15 – 25% solids.
Also known as “cake” or biosolids. Smells pretty earthy.
(Photo credit: Sustainable Sanitation Alliance / CC-BY-4.0)

While percent solids is a nice way of describing solids content, it’s not readily useable for most wastewater calculations. Wastewater problems typically will require you to convert % solids to mg/L in the beginning. Luckily, the conversion is simply:

1 % solids = 10,000 mg/L

Therefore, 2% solids equals 20,000 mg/L (soupy), 15% solids equals 150,000 mg/L (thicker), and so on.

But something that bothered me for the longest time is why 1% solids equals 10,000 mg/L, and not simply 1000 mg/L or anything else for that matter? The answer is that going from % solids to mg/L is a units conversion. It’s a simple conversion, but I’ve never seen this covered in a textbook, so here’s an example of the conversion below:

1.) For poop’s sake, let’s assume we’re working with 2% solids. We know 2% solids is another way of saying 2 lb solids/100 lb wastewater (English) or 2 kg solids/100 kg wastewater (Metric). This is always true, unless the problem specifically states that % solids is on a volumetric basis (for the P.E. exam this isn’t likely).

2.) The next step is to convert this to mg/L using the density of water and any relevant unit conversions:

(English Units)
 
(Metric Units)
*Note: The wastewater (sludge), consisting of solids and water, is assumed to have the same density as normal water (1 kg/L or 62.4 lb/ft3), but this isn’t strictly true.

And that’s it! Just clever manipulation of the units. Whenever you see % solids, multiply that number by 10,000 to convert to mg/L., and vice versa.