# Let’s Explain the Confusing Term: Bulk Density Ratio

A couple of months ago I used the term “Bulk Density Ratio” and said that it was a subject for another day. So today is the day.

The term bulk density ratio describes the relationship of a material or substance mass as found in a particular sample vs its theoretical mass, assuming “complete compactness” and no voids of any type.

For example, Pea gravel is made up of small particles of stone, and a solid block of stone usually weighs approximately 168 lbs per cubic foot ( 2.7 times the weight of water, an SG of 2.7).

When we measured a particular sample of pea gravel we found that it weighed 108 lbs per cubic foot (1.76 times the weight of water). But stone is stone!! Why the difference?

Clearly, the difference is the pea gravel sample is full of voids between the stones. The ratio of solid stone to the sample of pea gravel is 168 lbs / 108 lbs or 1.55

Said differently, pea gravel occupies 1.55 times more space than solid rock for the same mass of product. This ratio is referred to as the “Bulk Density Ratio”.

If we take the weight of the pea gravel sample and put it over the weight of a sample of the same volume of solid stone and then convert it to a percentage (108/168 X 100 = 64%) we find that stone occupies 64 % of the space. Assuming it is a dry sample, air must occupy the balance of 36% of the sample’s volume.

Great information but how is it useful in the pump world? Well, the answer to that question is that Bulk Density Ratio is the key to calculating production rates when moving products like sand or gravel that are often measured by volume. The easiest way to explain this is by using an example.

You are a contractor and your job is to remove a sand bar made up of coarse sand that is 100 meters wide by 100 meters long by 5 meters thick, or 50,000 m3 of material. If you can pump at a rate of 800 m3/hr of slurry with a density of 1.23, how many hours must you operate?

You can assume the coarse sand has a dry Sg of 2.7. But the pumpage is not all sand, it is a slurry with water occupying the space between the solids. The formula below can help you determine the percent solids, by volume.

*Cv** =( **Sm-Sl**)/(Ss- **Sl**) = (1.23 – 1.0)/(2.7 – 1.0) = .135 or 13.5 %*

- Cw = Percent solids by weight
- Cv = Percent solids by Volume
- Ss = Sg of the dry solid
- Sm = Sg of the slurry
- Sl = Sg of the liquid

At a slurry flow rate of 800 m3/hr this equates to .135 x 800 m3 or 108 m3 of “solid” rock per hour, but the end product is not solid!! This is where you need to know a Bulk Density Ratio to properly estimate production by volume.

Applying the bulk density ratio of 1.55 for coarse sand would mean the contactor is removing the sand bar at a rate of 108 x 1.55 or, 168 m3/hr. Based on this rate of production, the project of moving 50,000 cubic meters being pumped at a rate of 168 cubic meters per hour will take 297hrs to complete.

Hopefully, this short blog helps to clear up some of the confusion around this subject, but if you still have some questions or need help on a specific project please feel free to contact our very competent applications team.

Bye for now

RJ