An In-Depth Report on Density Measurement Methods & Analysis

This report provides a comprehensive overview of various methods used for measuring the density of liquids and solids, including the measurement of mass and volume, displacement method (Archimedes' principle), hydrometer, pycnometer, and digital density meter. Each method is discussed in detail, outlining the principles, procedures, suitability, advantages, and disadvantages. The report includes examples of how to apply each method and emphasizes the importance of accurate measurements for obtaining reliable density values. The report concludes by referencing various sources that were used to compile the information.

Introduction
Density, or more precisely, density of volumetric mass, a substance is its mass per unit volume.
The most commonly used symbol for density is ρ (Greek letters rho in lowercase), although
Latin letters may also be used. Mathematically, density is defined as a mass divided by volume.
In all material circumstances, density is a physical parameter that performs a significant part,
whether solid, fluid or gas. The density of solids and fluids is the focus of this study. This report
explains what "density" is, how these parameters are defined and measured, the density
measurement history, the different accessible techniques and also how to achieve the highest
density outcomes using a good density measurement technology. The general Equation for
calculating density is as given below
ρ= Mass
volume [ k g
m3 ]
The actual density ρ in kg / m3 or g / cm3 of liquid is defined as the mass m divided by its
volume V. The mass is related to weight in vacuum and is not dependent on external conditions
such as buoyancy in air or gravity.
Aims and objectives
The objectives of the report are as listed below
1. Research and analyse the methods listed below used in finding density for liquid and
solids. These methods include;
1.1 measurement of mass and volume then calculate
1.2 displacement
1.3 hydrometer
1.4 pycnometer
1.5 Digital density metre
2. Set out the strengths and weakness of each method
3. Evaluate the suitability of method in finding density for both liquid and solids
Density measuring Methods
The various methods used in measuring density have been discussed as follows1;
1. measurement of mass and volume then calculate
This method generally gives the raw definition of density. It involves measuring the mass and
volume of liquid/solid using the available techniques then calculate the density
procedure
1 "Lab 1 - Density Determinations and Various Methods to Measure Volume", in Webassign.net, , 2019,
<http://www.webassign.net/question_assets/ucscgencheml1/lab_1/manual.html> [accessed 30 June 2019].

consider the solid and liquid to be used as show on picture, the first approach is to measure the
masses of the quantities
Figure 1 measuring the mass of the solid and liquid 2
the second activity is to measure the volume of the given solid and liquids
Figure 2 measuring volume of the liquid
Results
solid
Mass of solid rock = 38.718 grams
Volume of solid rock was measured as, volume = 20 cm3
Liquid
Measured Mass of liquid =100grammes
Measured Volume of liquid = 100mm3
Calculations
To find density, we use the formulae provided below
2 "How to Measure Mass & Density", in Sciencing, , 2019, <https://sciencing.com/measure-mass-density-
7820720.html> [accessed 30 June 2019].

Density ( ρ ) = Mass
volume [ k g
m3 ]
For liquids
ρ=100
100 [ g
cm3 ]
Densityofliquidρ=1 [ g
c m3 ]
For solid
ρ=38.718
20 [ g
cm3 ]
ρ=1.9359 [ g
cm3 ]
Suitability
This method is suitable for measuring density of liquids and solids
advantages
1. can be used for both liquids’ gases, this is because both the mass and volume of
liquids and can be evaluated. The fact that there are so many instruments that can be
used to get the quantities
2. No tech skills needed, just simple mathematics for calculation
Disadvantages
1. Too tedious, since it involves calculations
2. Finding volume for irregular solids makes it not always relevant density in solids
3. The mass of container used in keeping the liquid should be known first, this add more
unnecessary steps needed

2. Displacement
Archimedes began to find density by displacement of water. Density calculation using the
formula D= m μv, where D is the density , m is the mass and v the volume. Find the mass on an
equilibrium scale and use the transfer of water to discover an uneven object quantity. The
volume of displaced water the quantity of water that rises when an object placed in water. The
displaced water is equivalent to the object volume. If a cynically submerged object displaces the
water level from 40 ml to 90 millilitres, the volume shift of 50 ml is equivalent to that of the
cubic centimetres for the object.
Figure 3 finding mass of the object
Example
Procedure
Find mass-A balance scale must be used to detect mass. Most mass scales counter a known mass
with an unidentified object. For example, three beams and real balances, such as the classical
scale seen in an assay desk.
Find volume- use a standard formula to find the volume of ordinary geometric objects. The
volume of the box is equal to the length by width times the height. However, not every object
matches the formula. For objects with this irregular shape, use the water displacement method to
find the volume of the object.

Figure 4 finding volume of solid using displacement
The volume of the solid will be found as follows
Volume = final volume – initial volume
Volume= 66cm3 -46cm3
Volume = 20cm3
densityρ=38.178
20 [ g
cm3 ]

ρ=1.9359 [ g
cm3 ]
Suitability
can only be used for solids
reason; solids are the only matter that can displace liquids of greater density than them
Advantages
1. Can be used for both regular and irregular solids
Disadvantages
1. Not all solids can submerge in water, hence not suitable for all solids
2. Parallax problem when reading the flask can results to inaccurate results
3. Hydrometer
Hydrometer is a measurement instrument based on the notion of buoyancy for the relative
densities of liquids. They are normally calibrated and passed with one or more gravitational
scales.
Hydrometers generally include a closed hollow glass tube with the widest boom, ballast for
stability, plume or mercury, and a tight rod for measurement. The fluid to be tested, which is
usually in uniform cylinder, is poured into a hygrometer and slowly lowered into the fluid until it
settles freely. The point at which the fluid surface touches the rod of the hydrometer is linked to
the relative density. There are a number of scales in the hydrometer along the stem depending on
density-related characteristics.
Example
To find density of a liquid, we need to have a hygrometer for specified liquid

Figure 5 required hydrometer and a jar for the hydrometer
The liquid to be tested is transferred to the hydrometer cylinder and the hydrometer is lowered
softly into the liquid until it floats free of charge. This records where the fluid's surface touches
the rod of the hydrometer.
Figure 6 leave the hygrometer to settle
Take the reading which corresponds to the plane of intersection of horizontal liquid and the stem

Figure 7 correct hydrometer reading
Suitability
Suitable for finding relative density of liquids
Advantage
only a single measurement is done to find relative density
disadvantage
Through cleaning of hydrometer surface needed, which is a waste of time
4. Pycnometer
Pycnometer density determination is a highly accurate technique. It utilizes a workable fluid of
established density, such as water. We will use distilled water that is shown in table 1 at
temperatures based on densities. The pycnometer (Figure 8) is a glass bottle with the floor glass
stopper fitted closely with the capillary hole.

Figure 8 picture of pycnometer
Example of use
Procedure
fill the vessel with pure water.
Volume of water if found using equation below 3
Where m represents weight of water
Secondly, we repeat the procedure by pouring in the density of unknown liquid, the weight of
unknown liquid is also determined
the volume of liquid poured remains the same as that of water
The next step is to compare the two equations, given that they all have same volume
The results give the density of unknown liquid.
Suppose volume of water = 10cm3
Volume of water = volume of liquid
Mass of liquid = 20g
3 C Vámossy, S Davidson & Z Zelenka, "Comparison of density determination of liquid samples by density
meters", in Metrologia, vol. 53, 2016, 07007-07007.

Mass of water = 10g
Densityofliquidρ=20
10 [ 1 ]
Densityρ=2 [ g
cm3 ]
Suitability
Suitable for liquids
Advantages
Can be used for both liquids and solids, though suitable for liquids
Disadvantages
Cannot be used for solids that dissolves in water
More work done, involves too many measurements
5. Digital density meter
A density meter is an instrument that measures the density of a liquid sample. Digital density
meters are used in the pharmaceutical, petroleum, chemical and food and beverage industries for
quality control and in research and development. The density meter works by measuring the
oscillation of a glass tube containing a sample. There is also a digital density meter that can
measure specific gravity and refractive index of the matter. There are density meters available
which are portable or bench models, which can measure liquids, gases, or both, and have a built-
in thermostat or need a water bath to maintain temperature. Some other variations include the
sample volume needed, the speed of testing, and the ability to take and store images.

Figure 9 image of digital density meter
Example of use
The oscillation tube technology is used in digital density meters to evaluate a sample density
very precisely in a brief period of time. The sample is injected into a U-shaped glass tube and
oscillated at a certain frequency. When the tube is filled in with the sample, this frequency
changes: the higher the sample mass, the lower the frequency. This frequency is measured and
density transformed4.
Distilled water is used to calibrate the machine.
Suitability
Can be used for both liquid and solids
Advantages
1. Can be used for large scale activities, i.e. commercial purposes
2. Fast measurements
3. Can be automated
4 C Vámossy, S Davidson & Z Zelenka, "Comparison of density determination of liquid samples by density
meters", in Metrologia, vol. 53, 2016, 07007-07007.

Disadvantages
1. Expensive
2. It’s a new technique, not available to all