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In Control: Density Measurement,
Theory and Practice
by Dan Capano, DTS, Inc.
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What is Density?
The density of a sample of a
material is defined as the quantity of mass of the material to a
given volume of the sample. The material becomes denser as the
amount of material per unit volume rises. It can be said that the
molecules of a dense material are "packed" more tightly
together than the equivalent weight of a lighter material. Recall
the question "which weighs more, a ton of feathers or a ton
of steel?" While these items obviously weigh the same, their
mass to volume ratio differs greatly. The steel is denser, of
course, than the feathers because of a drastically higher quantity
of mass to unit volume.
The measurement of the density of a
process material is a common requirement of many processes. The
control of the density of primary sludge in a wastewater treatment
plant is a common example; controlling pulp density is essential
in the pulp & paper industry; the production of ice cream also
relies upon accurate measurement and control of density.
Density & Specific Gravity
Density and Specific Gravity are
often used interchangeably. While Density is a straight Mass to
The density of a material is
measured in g/cc (grams per cubic centimeter) or lbs./ft3 . While
ordinary paper has a range of density between .7 - 1.15 g/cc
(44-72 lbs/ft3 ), Lead has a density of about 11 g/cc (687
Specific Gravity (SG) is defined as
the ratio between the density of a given volume of a material to
the density of the same volume of water; the specific gravity of a
gas is the ratio of the molecular weight of a given sample to an
equivalent volume of standard air:
SG = D1/D2
Specific Gravity is used to
describe the density of a liquid. Several different scales are
used to measure specific gravity, depending upon the application
and range of SG of the process liquids being measured. Specific
Gravity is used to control the batching of liquid components of a
product. For a given ingredient, the relationship between specific
gravity and the quantity of the material to be added is
predictable and can be controlled. This allows accurate mixing and
Density of a material is affected
by temperature and pressure. For most applications, though, the
effects of pressure are negligible and will not be considered.
Temperature, however, does introduce measurable variations in
density, particularly in liquids and gases. Measurements of
Density and specific gravity must be corrected for variations in
Several methods are used to measure
density. As with any instrument, all factors must be considered
before deciding upon the method most suited for the application.
Among these factors are:
- Display and Transmitter options
- Pipeline or Vessel application
- Process material characteristics
Most vendors offer instruments that
are compliant with requirements for installation in hazardous
environments. This item will have a significant impact on the cost
of the unit, read the specifications carefully for required
enclosure. Displays and transmitters will also have an impact on
cost; Displays can be locally or remotely mounted. Transmitters
can be integral or remote. All offer standard electrical
connections for power and signal; data interfaces are also
available. Pipeline mounts require either in-line or
Certain instruments lend themselves
to specific types of physical installation in order to effect that
particular method of measurement. Vessel mounting can be
accomplished utilizing standard fittings. Instrument vendors are a
wealth of information on these items and will be happy to discuss
Process material characteristics is
most important to consider when deciding upon a densitometer.
Slurries and aggressive fluids or solids will tend to degrade the
relatively sensitive measurement apparatus. For light slurries and
liquids, insertion types may be used. In certain applications, it
may not be possible to pull the instrument for calibration or
repair because of lost production, contamination or hazardous
material. In this case, a "non-contact" type of
densitometer is used.
The use of a densitometer
eliminates the need for separate flow, temperature and pressure
measurements in order to derive density. The proper application of
a densitometer offers accurate and complete control of the
process, virtually eliminating delays and lost production.
Following is a general description of the common methods of
all mass flowmeters can be used as densitometer, if the volumetric
flow rate is kept constant. In all mass flowmeters, it is the mass
of the process material that exerts a physical force upon the
measuring apparatus, causing a measurable change . Most types of
mass flowmeter are not suited to this type of duty, however.
Thermal mass flowmeters may be used to measure the density of a
gas and possibly some liquids. It would be inadvisable to use this
type of device in a slurry. The Coriolis mass flowmeter is widely
used as a densitometer on clean liquids and light slurries.
Coriolis densitometers operate by
measuring the vibration and twist of a U-shaped tube. This is
essentially the same principle used in measuring mass flow; a true
mass flow meter measures mass flow over time. As the density of
the material changes, it affects the frequency of vibration of the
tube. This is a measurable quantity. The change in frequency is
proportional to the density of the material. The effects of
pressure are negligible; temperature compensation must be used
however. Coriolis densitometers are relatively expensive and
cannot be used for viscous fluids or heavy slurries. These units
are typically used in the chemical, food and beverage industries
on clean fluids with little solids content.
types of instruments have found widespread use because of the
range of application conditions on which they may be used. All
instruments in this category work similarly to the Coriolis
described above. A vibrating element is introduced into the
process material; the damping of the vibration is proportional to
the density of the measured material. This measurement is
referenced to the element's natural frequency. Several types of
instruments based upon vibration are in common use:
- Vibrating Tube: A tube of known
mass is vibrated at its natural frequency. As the tube is
filled with the process fluid, the frequency will be damped
proportionate to the density of the material. Other variables,
such as specific gravity, molecular weight, Brix (see below)
and concentration can be derived from this measurement if
- Vibrating Spool: Similar to the
Vibrating tube, but utilizing a vibrating spool piece inserted
into a pipeline. These instruments are useful for interface
detection in pipelines.
- Tuning Fork: Typically inserted
into a process vessel. Consists of a vibrating element
immersed in the process material. The figure below shows this
type of unit, suitable for insertion into a tank or pipeline.
Gas density may also be measured
using this method. A vibrating chamber filled with a reference gas
is driven at it's natural frequency. As gas flows past the
chamber, the change in gas density will cause damping of the
chamber vibrations, which are proportional to the density of the
Nuclear non-contact densitometers
are used in application where it is impossible or undesirable to
break a pipeline or containment in order to install an instrument.
This approach allows for continuous containment of the process
material. This is required when the system is sanitary or the
material is hazardous, or when discharging the pipeline would
result in lost production or a hazardous condition.
densitometers measure density by measuring the strength of emitted
Gamma radiation as it passes through the process material.
Absorption of the radiation is directly proportional to the
material density. The unit uses a Cesium or Cobalt source on one
side of the pipe, and a scintillation counter on the other. The
unit is strapped on to the pipe as a unit. Other units are
available for use with open conveyors; the source is place above
the belt with the detector mounted below. This type of application
is useful in such industries as cement production and bulk loading
Nuclear densitometers are extremely
accurate and stable, but can be costly. The use of a radioactive
source requires permitting and regular monitoring and emergency
procedures. This type of densitometer is well suited to use in
applications dealing with hazardous or aggressive liquids or
slurries. With no part of the instrument exposed to the process
material, and no other wearing parts, there is little chance for a
lost time failure.
It is possible to measure the
density of a liquid by using a large capacitor. To do so, the
capacitor must be inserted into the process liquid. The capacitor
is usually some arrangement of concentric tubes made of conducting
material. As the liquid fills the annular space, the dielectric
constant of the capacitor changes, causing a change in the
capacitance of the sensor. The capacitance is proportional to the
dielectric constant, which is proportional to the density. This
capacitor is connected to an external bridge, which measures the
change. This type of sensor is used only with non-conductive
fluids such as petroleum products. The cost of these units varies;
instruments can be ordered in a wide variety of configurations to
suit different applications.
This type of instrument relies upon
the application of calibrated floats. Float buoyancy is a function
of liquid density; a rise or drop in liquid density will cause the
float ot rise or drop accordingly. The position of the float
relative to the instrument scale is an indication of fluid
density. Floats may be attached to calibrated weights, these are
referred to as chain-loaded, or chain-balanced, densitometers.
Other types use sophisticated electromagnetic suspension
techniques to eliminate skin-effect errors. Pickup coils embedded
in the walls of the instrument sense the position of the float.
The most basic type of displacer
system is a series of calibrated plastic or ceramic weights that
become buoyant at certain densities. A cable attached to a torque
arm or lever suspends the weights. As the weights become buoyant,
less weight is exerted on the lever, which moves in the opposite
direction. This arm activates a switch or series of switches,
which in turn initiate the appropriate actions.
Other type of units use calibrated
floats to obscure light from a series of discrete optical sensors.
This unit operates similarly to the unit described above.
Displacement units require a clean process fluid, though the
suspended weight variety may be used in certain dirty, but
Hydrometers represent the simplest
and most economical method of measuring density. A hydrometer is a
calibrated glass float, which incorporates a scale for direct
reading. Typically, a hydrometer is "spun" into a sample
and eventually stabilizes at a certain height relative to the
liquid surface. The SG is read directly forma the scale on the
tube. Hydrometers may be calibrated in one of several specialized
- Alcoholometer: This hydrometer
is used for testing alcoholic solutions. The scale is
calibrated is percent of alcohol by volume
- Ammoniameter: For testing
Ammonia solutions. The scale is calibrated in 0°-40°.
- Barkometer: Used in the tanning
industry. The scale is 0°-80°
- Baume': Two types are in use-
Heavy Baume', for liquids heavier than water; and Light Baume',
for liquids lighter than water. Scales are available to 90°
- Brix: Used in the sugar industry
for determining the percentage of sugar in solution. Degrees
Brix is percent sugar.
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