# Density, Specific Weight and Thermal Expansion Coefficient

## Applications of Specific Gravity

The following formula is used to calculate the specific gravity of a material.

SG = ρ / ρW

Where SG = specific gravity, ρ = density of the material (kg/m3), ρW = density of water ( kg/m3). The reference density of water at 4oC (39oF) is used as the reference as these are the conditions of maximum density.

There is a wide range of instruments designed to measure the specific gravity of a material. The hydrometer can be used to measure the specific gravity of any liquid. The device is designed to float freely at the liquid surface with a protruding stem giving a reading corresponding to the specific gravity of the liquid.

Specific Gravity has a wide range of applications including:

1. Pharmaceuticals: The specific gravity is used to find out the purity of a drug since each of the constituents has a distinct specific gravity.
2. Determining the additives used in a base material: Specific gravity is used to find out the amount of additives used in a base material which might affect the performance and stability of the base material.
3. Urine Specific Gravity: The Urine Specific gravity (USG) is measured and used mostly in veterinary sciences to understand whether water is excreted or conserved in an appropriate fashion.
4. Calculating volume of a fluid: The fluid’s volume can be calculated using the specific gravity of the fluid and the weight. Conversely the weight can be calculated if the volume is known.
5. Other applications of specific gravity include fluid mechanics, buoyancy and the brewing industry.
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A fluid is a continuous medium; i.e., a substance
that is continuously distributed throughout a region in space. Because
a fluid is a continuous medium, it would be rather awkward to analyze
the fluid as a single entity with a total mass, m,total weight,
W, or total volume, V.

It is more convenient to analyze
the fluid in terms of the mass of fluid contained in a specified
volume. is defined as mass
per unit volume
. Density is a property that applies to solids as
well as fluids.

The most commonly used units for density are kg/m3
in the SI system and slug/ft3 in the English system. Values
for density can vary widely for different fluids.

For example, the
densities of water and air at 4�C and 1 atm pressure are
approximately 1000 kg/m3 (1.94 slug/ft3) and
1.27 kg/m3 (0.

00246 slug/ft3), respectively.
Densities of liquids are higher than those of gases because the
intermolecular spacing is smaller. Physical properties vary with
temperature and pressure to some extent.

For liquids, density does not
vary significantly with changes in temperature and pressure, but the
densities of gases are strongly influenced by changes in temperature
and pressure.

A fluid property that is similar to density is . Specific weight is defined as weight per unit
volume
. The mathematical definition for specific weight, <img src="https://www.eng.fsu.

The most commonly used units for specific weight
are N/m3 in the SI system and lbf/ft3
in the English system. Note that the unit for specific weight in the
English system is not lbm/ft3.

The unit lbm
is a unit of mass, not a unit of weight. A quick inspection of
Equation 7-1 and Equation 7-2 reveals that specific weight is
essentially the same property as density with mass replaced by weight.

A formula that relates density, ,
and specific weight, <img src="https://www.eng.fsu.

edu/~chandra/courses/eml3004c/book/Chapter13/Images/gamma.gif» border=»0″ width=»9″ height=»13″>,
may be obtained by noting that the weight of a unit volume of fluid is
W=mg, where g is the local gravitational
acceleration.

Using the standard value of gravitational
acceleration, g=9.807 m/s2, water at 4�C has a
specific weight of

Doing the same calculation in English units, noting
that the standard value of gravitational acceleration is g=32.174
ft/s2, water at 4�C (39.2�F) has a specific weight of

The rationale for finding the density and specific
weight of water at 4�C in the foregoing discussion is that 4�C is a
reference temperature on which is based. Specific gravity is defined as the ratio
of the density of a fluid to the density of water at a reference
temperature
.

Typically, the reference temperature is taken as 4�C
because the density of water is maximum (about 1000 kg/m3)
at this temperature. The mathematical definition for specific gravity,
sg, is

Because specific gravity is a ratio of two
properties with the same units, it is a dimensionless quantity.
Furthermore, the value of sg does not depend on the system of
units used.

Using English units, we obtain the same value.

Specific gravity may also be defined as the ratio
of the specific weight of a fluid to the specific weight of water at a
reference temperature
. This definition, which is derived by
combining Equation 7-4 and Equation 7-3, is expressed as

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