Density and Specific Gravity

Definitions
Density is the weight per unit volume of a particular substance. The substance may be in the liquid, solid, or gas phase.

Specific gravity is defined as the density of a particular substance compared to the density of a "standard substance."

Density
We see from our definition that the density of a particular substance is determined by calculating its weight per unit volume. Our most familiar example of "density" would be our well-used water weight/volume conversion. "Water weighs 8.34 pounds for each gallon of volume." It's "density" can be calculated in the following manner:

Some other water and wastewater treatment plant examples:
1) "Caustic soda" (sodium hydroxide) (NaOH), at a strength of 50 percent, 5 gallons weighs in at 64 pounds.
a) Calculate the density in pounds per gallon units.

We first place our "destination units" on the page, and then arrange our given information accordingly, and then do the math:

b) Calculate density in pounds per cubic foot units. We first place our "destination units" on the page, and then arrange our given information accordingly, and then do the math:

2) A full, five gallon pail of a certain polymer weighs 58.6 pounds. The polymer is poured out, and then the clean, empty pail is weighed. It weighs three pounds. Calculate the density of polymer in pounds per gallon, and in pounds per cubic foot units.

In both of these, we first need to subtract out the weight of the pail, and find the weight of just the polymer:

(58.6 lbs pail and poly) - (3 lbs pail) = 55.6 pounds of polymer

a) Density, in pounds per gallon units.Ok, I will say this for the last time, and then you will remember what to do!!We first place our "destination units" on the page, and then arrange our given information accordingly, and then do the math. Ok, its said for the last time!

b) Density, in pounds per cubic foot units:

 

Summary Statement on Density
Density, by definition may be expressed in any weight per unit volume. Other units of density may be grams per liter (grams/L); grams per cubic centimeter (grams/cc); ounces per cubic inch (ounce/cu inch), etc.

What is the density of wood? Answer: "Not more than air, after the tree has been gutted by a lightning strike!"

 

Specific Gravity
When we examine the definition, we see that we are comparing the density of a specific substance to a specified, "standard density." (By "standard," we mean that it is a "generally acceptable" or "generally used" reference or gauge by which all other substances will be compared against.)

An example is the statement "The sludge has a specific gravity of 1.31." What does that mean? The density of sludge, and most of the liquids we use in water, and in wastewater treatment is compared with the density of water. We may weigh a gallon of sludge and find it to weigh 10.9254 pounds. It's density, in pounds per gallon units is therefore 10.9254 pounds per gallon. The specific gravity of the sludge is found by dividing the density of the sludge by the density of water:

Please note that all of the units cancel out, which is why there are "no units" for specific gravity.

 

An example using other density units:
The density of alum is 83.616 lb/cubic foot. Determine the specific gravity.

Specific gravity may be less than 1.0 examples include some light boils, fuels light gasoline, and some polymers. This next problem will illustrate this case: A polymer has a density of 3.92 lb/gal. Calculate the specific gravity.

The principal use of specific gravity is in solids handling and in chemical processes.

Calculate the number of pounds of sludge per day to be pumped given the following information:
Sludge density 65.824 pounds per cubic foot.
Continuous sludge pumping rate, at 75 gallons per minute.

We first need to find what a gallon of sludge weighs (find its density):

We can now find the number of pounds of water and solids (sludge) we will pump in one day of continuous pumping:

Your turn!
The sludge pumps are operating at 55 gallons per minute. The sludge has a density of 73.612 pounds per cubic foot.
1) Calculate the specific gravity. (Ans: 1.18 spec. gravity)
2) How many pounds of sludge are pumped each day? (Ans: 779,423 lb/day)

 

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