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Relative Density (Specific Gravity)
Relative density, also called specific gravity (SG), is the ratio of the density of a substance to the density of a reference substance. For liquids and solids, the reference is almost always water at 4 °C, where it reaches its maximum density of 1 g/cm³.
The specific gravity of a fluid is therefore the ratio of its density to the density of water:
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SG – specific gravity of the fluid ρf – density of the fluid (g/cm3) ρw – density of water (g/cm3) |
Hydrometer
A hydrometer gives a direct reading of the specific gravity of a fluid and needs only a small sample.
Fill a cylindrical container with the fluid to be tested and place the hydrometer in it so that it floats freely. The SG is read on the hydrometer scale at the point where the fluid surface meets the stem.
For an accurate reading, the hydrometer must float freely, without touching the sides or bottom of the container, and must be correctly calibrated. To calibrate it, use water at 4 °C as the test fluid and check that it reads an SG of 1.
Calculation from Density or Mass
If the density of the fluid is known, its SG is obtained by dividing it by the density of water under the same conditions. As density equals mass divided by volume, SG can also be calculated by dividing the mass of the fluid by the mass of the same volume of water.
Mixtures of Liquids with Different Densities
When liquids with different specific gravities are mixed, the result is a new liquid with its own SG, different from that of each component. The SG of the mixture is calculated as follows:
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SGi – specific gravity of component i xi – mass fraction of component i |
For example, take two liquids, A with an SG of 1.0 and B with an SG of 1.5, mixed in a 2:3 ratio by weight: the product contains 40% A and 60% B.
.png "Mixture specific gravity calculation")
The SG of the product is calculated as follows:
Effect on Mixing
The specific gravity of the liquids must be known in order to select the right mixer, because SG affects the power needed to achieve proper mixing.
For Newtonian fluids, the power required increases with SG. If SG is not taken into account when selecting the impeller and gearbox, the power requirement will probably be underestimated and the mixer may be damaged.
Liquid–Liquid Mixing
When two or more liquids are mixed, the difference in SG can be a major factor. Even if the components are miscible, a large difference in SG makes them separate into two distinct layers. The lighter component tends to float on the surface and is difficult to incorporate; the heavier component tends to sink to the bottom and is just as difficult to draw into the bulk liquid.
The greater the difference in SG between two components, the higher the mixing intensity needed to blend them. Mixing can be improved by adding a second impeller near the liquid surface to create a small, controlled vortex that draws the lighter component down into the bulk.
In the same way, a low-level “kicker” impeller at the bottom of the tank lifts the heavier component into the bulk of the fluid.
Solid–Liquid Mixing
In solids suspension, differences in SG can cause even greater problems. If the solids do not dissolve, the mixer must work continuously to keep them in suspension. This may require high-intensity agitation, with large motors and high impeller speeds.
As with liquid–liquid mixing, a second impeller near the surface helps draw lighter solids into the bulk, where the main impeller disperses them. Low-level kicker impellers lift heavy solids off the tank bottom so that they are entrained in the flow of the main impeller.
Brix Scale (°Bx)
A common indirect way of determining the SG of a fluid is its Brix value. One degree Brix (1 °Bx) is 1 gram of sucrose in 100 grams of aqueous solution. For fruit juice concentrates and other sweetened products, the sugar content is usually given by the manufacturer, so the SG of the fluid can be determined.
Background
Named after the 19th-century scientist Adolf Brix, the Brix scale was originally designed to help brewers determine the sugar content of their product. The brewer first measured the density of the product, then used published tables to find the equivalent sucrose concentration as a percentage by mass. These tables were produced by preparing pure sucrose solutions of known concentration and measuring their density.
The Brix scale is still used today in the sugar, wine and fruit juice industries to compare relative sugar content.
Converting Between Brix and Specific Gravity
For mixer design, the Brix value has to be converted to SG. This can be done with the original conversion tables or with the formulas below:
| Conversion from Brix (°Bx) to specific gravity (SG): | .png)
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| Conversion from specific gravity (SG) to Brix (°Bx): | .png "Specific gravity to Brix formula")
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These are empirical relationships and should not be used above 40 °Bx or an SG of 1.18.
Brix vs specific gravity |
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| Specific gravity |  |
|---|---|
| Brix degrees |
Brix vs sugar content |
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| Sugar content (g/L) |  |
|---|---|
| Brix degrees |