Density Measurement
For Density Measurement, Precision is Key
Density is a measure of the mass to volume or weight to volume ratio of a material. This is an important property for systems that relate weight to volume for mixing or dispensing purposes. Volume measurements using traditional methods such as measuring cups or spoons, or even measuring pipettes, are imprecise. Knowing the density of a liquid or coating allows us to instead measure out precise volumes by weight or mass using a high-resolution scale. To do this, the density of the material must be known. The question is, how can we precisely measure the volume of a material to calculate its density in the first place? The answer is density cups.
Precise Volumes
Density cups are manufactured to a very precise volume. By filling this container to that precise volume and then weighing it, we can calculate the density of any liquid. One of the major problems with filling a container to a precise volume is the meniscus. Liquids tend to be cohesive, meaning the individual molecules attract each other. Therefore, when we fill a container to the very, very top, we can often see a small mound of liquid that extends above the rim of the container. This is called the meniscus:
How to Use a Density Cup
The meniscus means that the volume of the liquid in the container is slightly larger than the volume of the container itself. To solve this, density cups have a precisely fitted lid with a small hole in the center and a rim that extends slightly into the cup. The cup is filled with more liquid than is needed, and when the lid is placed on top the excess material will flow out of the hole. Wipe away the excess and voila - the cup is filled precisely with the appropriate amount of liquid.
The liquid is then weighed in grams, which can be achieved either by zeroing the scale before filling the cup or by using a tare weight, which ensures that only the mass of the liquid is measured. One thing to note is that bubbles in the liquid can throw off a density measurement. If a material must be shaken or mixed vigorously, which can cause bubbles in the liquid, it is often a good idea to do the mixing well in advance of the density measurement, so the bubbles have time to settle out.
Once the mass in grams is known it’s a simple calculation to arrive at the density. For US density cups, which have a volume of 83.2 ml, simply divide the mass of the liquid in grams by 10 to achieve the density in pounds per gallon (lbs/gal). US Mini Weight Per Gallon Cups have one tenth the volume (8.32 ml); with these cups the mass of the liquid in grams is exactly equal to the density in lbs/gal, and they also have the benefit of requiring less material for measurement. For imperial or ISO density cups which have a volume of either 50 or 100 ml, simply divide the mass of the liquid in grams by the volume of the cup to achieve the density in grams per ml (g/ml, or g/cm^3). Once the density of the liquid is known, any desired volume can easily be converted to a mass or weight and measured out with a scale.
| Determination of Density and Specific Gravity | |||
| Model | Volume (ml) | Density | Specific Gravity (relative to water) |
| U.S. Standard Cup: | 83.2 | [weight full (g) - weight empty (g)] x 0.1 = lbs/gal | [weight full (g) - weight empty (g)] x 0.01202 = specific gravity |
| U.S. Mini Cup: | 8.32 | [weight full (g) - weight empty (g)] = lbs/gal | [weight full (g) - weight empty (g)] x 0.1202 = specific gravity |
| ISO Cup: | 100 or 50 | [weight full (g) - weight empty (g)] / volume (ml) = g/cm3 | specific gravity = density |
| British Imperial Cup: | 100 | [weight full (g) - weight empty (g)] / volume (ml) = g/cm3 | specific gravity = density |
| 1 ml = 1 cm3; 1 liter = 1000 ml; specific gravity of
water = 1 g/ml 1000 ml = 0.2646 U.S. gallon; 1 U.S. gallon = 3.785 liter |
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