# Specific Gravity

## Definition

Specific gravity (S.G.) is the ratio of a substances density to that of a reference substance. For liquids and solids the reference substance is almost always water at 4oC where it has its maximum density of 1g/cm3.

Taking this into account, the specific gravity (S.G.) of a fluid is the ratio of the liquids density to the density of water as shown below: $Latex formula$

S.G. – Specific gravity of fluid to be measured
Pf – Density of fluid to be measured (g/cm3)
Pw – Density water(g/cm3)

Note any units for density can be used as long as both they are the same for the fluid and water, as the ratio of the two values will always be the same.

This gives fluids that are more dense than water, an S.G. value >1, and fluids that are less dense than water an S.G. value <1.

## Measuring Specific Gravity

Primarily, there are 2 ways in which S.G. can be measured as mentioned below:

### Hydrometer

A hydrometer is a device which can be used to directly determine the S.G. of a fluid requiring only a small sample of the fluid.

By filling a cylindrical container with the fluid being tested and placing the hydrometer into the container so that it becomes suspended in the fluid, the S.G. of the fluid can be read from where the fluid surface touches the scale on the hydrometer.

For an accurate reading, make sure the hydrometer is fully suspended in the fluid i.e. it does not touch the sides or bottom of the container and that it has been calibrated correctly. The hydrometer can be calibrated by using water as the fluid being tested at the standard condition of 4oC and checking whether the S.G. reading is 1.

### Calculation with Density/Weight

From the definition of S.G., if we know the density of the fluid we can directly calculate the S.G. of the fluid by dividing this value by the density of water at the same conditions. Since density is equal to mass over volume, the S.G. can also be calculated by dividing the mass of the fluid by the mass of water for the same volume of fluid and water.

## Combination of Multiple Liquids with Different Specific Gravity

When multiple liquids of varying S.G. are mixed together, the product is a new liquid with its own S.G. which is different to the components which formed it. The S.G. of the mixture can be found as follows: SGi – Specific gravity of species i
xi – Mass fraction of species i

As an example, consider two liquids, A and B, where A has a S.G. of 1.0 and B has a S.G of 1.5 and are mixed together at a ratio of 2:3 by weight, that is 40% of the product is made up of A and the remaining 60% of the product is made up of B.

The S.G. of the product can be calculated as follows: $Latex formula$

## Effect on Mixing

It is important to know the S.G. of the liquids being mixed when deciding what type of mixer shall be used. This is because the S.G. of the liquids has an effect on the power requirements to achieve proper mixing.

For Newtonian fluids, as S.G. increases, the power needed for mixing also increases and so if S.G. was not accounted for when determining the type of impeller and gearbox required for the mixer, it is likely that the required power would be underestimated and as a result, damage the mixer.

## Liquid/Liquid Mixing

In applications where two or more liquids are to be mixed, the difference in S.G. can be an important factor. Even if the two components are miscible, if there is a large difference S.G. they will tend to split into two separate layers. If one component has a lower S.G. than the other, it will tend to float on the top of the main bulk of the fluid and will be difficult to incorporate into the product. If the product has a higher S.G. it will tend to fall to the bottom and again be difficult to incorporate into the bulk fluid.

The larger the difference in S.G. between two components the greater the mixing intensity required to effectively mix them. Mixing can also be aided by the addition of a second impeller near the top of the fluid level which is used to intentionally to create a small vortex. This draws the lighter component down from the surface of the fluid into the main bulk.

A similar idea is achieved with using a low level “kicker” impeller at the base of the tank to kick the heavier component up into the bulk of the fluid.

## Solid/Liquid Mixing

In solid suspension applications the difference in S.G. can pose even greater problems. If the solid will not eventually dissolve in the fluid, then the mixer has to constantly work to keep the solids suspended throughout the liquid. This can mean that high intensity agitation is required, with large motors and high impeller speeds required to ensure that the solids remain suspended.

As with liquid/liquid blending, placing a second impeller at the top of the mixing tank can help to draw lighter components into the bulk of the fluid where the main impeller can disperse them throughout the liquid. And low level kicker type impellers can be used to help kick heavy solids off of the base of the tank where they are more easily entrained in the flow from the main impeller and carried up into bulk fluid.

## Brix Scale (°bx)

One common way of measuring the S.G. of a fluid indirectly, is from the degrees Brix of the fluid. One degree Brix (1°bx) is defined as 1 gram of sucrose in 100 grams of aqueous solution. For fruit juice concentrates and other sugary products, the sugar content is likely to be provided by the manufacturer, and from this the S.G of the fluid can be found.

## Background

Named after the 19th century scientist Adolf Brix, the Brix scale was originally devised for brewers to find out the sugar content of their product. The brewer would first measure the specific gravity of the product, and then using a set of published data tables, look up the equivalent concentration of sucrose by percentage mass. The data was gathered by preparing pure sucrose solutions of known strength and measuring their specific gravities and percentage sucrose by mass.

Nowadays, the Brix scale is still used by industries such as sugar, winemaking and fruit juice as a means of comparison of relative sugar content.

## Conversion between Brix and Specific Gravity

For the purposes of designing a mixer we would wish to convert the Brix value back to S.G. and this can be done with the original look up tables,
or with the formula given below:

Converting Brix (°bx) to Specific Gravity (SG): $Latex formula$

Converting Specific Gravity (SG) to Brix (°bx): $Latex formula$

Note that these are empirical relationships and should not be used for values of greater than 40°bx or 1.18 SG.

##### Plot of Degrees Brix vs Specific Gravity
Specific
Gravity Degrees Brix
##### Plot of Degrees Brix vs Sugar Content
Sugar Content
(g/l) Degrees Brix

John Whittle MEng (Hons)

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