Recent Advances in Mechanical Engineering and Automatic Control
Hydrometer-Spring balance instrument
CLAUDE ZIAD BAYEH1, 2
1
Faculty of Engineering II, Lebanese University
2
EGRDI transaction on physics (2001)
LEBANON
Email: [email protected]
NIKOS E.MASTORAKIS
WSEAS (Research and Development Department)
http://www.worldses.org/research/index.html
Agiou Ioannou Theologou 17-2315773, Zografou, Athens,GREECE
[email protected]
Abstract: - The Hydrometer-Spring Balance is a new instrument introduced by the authors in physics in order to
simplify the manipulating of two instruments which are the Hydrometer that measure the density of the liquid
and the spring balance that measure the mass of an object inside and outside the liquid. So the new instrument
can be used instead of the two traditional instruments. The new instrument will be put in a graduated cylinder
filled with water and this will facilitate the measurement of the volume of the displaced water that is equal to
the volume of the object, so we can measure at the same time the mass of the object and its volume therefore we
can deduce the density of the object with respect to the density of water. The new instrument allows us to
measure also the density of other liquids such as alcohol, benzene, oil, milk, salt water, petroleum
products…with respect to the density of the water.
Key-words:-Buoyant force, Archimedes’ principles, Hydrometer, Spring balance, liquid, instrument.
container) in order to facilitate the calculation. The
“Hydrometer-Spring balance” can be found in many
scales and sizes according to the usage. In this paper
the authors develops the basic principle of the new
instrument and brief examples are given in order to
understand how this instrument works.
In the section 2, the Archimedes’s principle is
presented. In the section 3, Hydrometer-Spring
balance principle is presented with simple example.
And finally in the final section a conclusion is
presented.
1 Introduction
In physics, A hydrometer is an instrument used to
measure the specific gravity (or relative density) of
liquids; that is, the ratio of the density of the liquid to
the density of water. A hydrometer is usually made
of glass and consists of a cylindrical stem and a bulb
weighted with mercury or lead shot to make it float
upright. The liquid to be tested is poured into a tall
container, often a graduated cylinder, and the
hydrometer is gently lowered into the liquid until it
floats freely. The point at which the surface of the
liquid touches the stem of the hydrometer is noted.
Hydrometers usually contain a scale inside the stem,
so that the specific gravity can be read directly.
Varieties of scales exist, and are used depending on
the context.
In this paper, the authors developed a new instrument
called “Hydrometer-Spring balance” because it will
simplify the two instruments “Hydrometer” and
“Spring balance” into only one instrument.
This instrument is capable to measure the density of
the liquid and at the same time is can measure the
mass and weight of an object above and under the
liquid. This instrument can be helpful for measuring
sinking objects only and not for the floating objects
because the buoyant force is equal to the weight. We
should use also a graduate test tube (graduate tall
ISBN: 978-1-61804-142-5
2 Archimedes’s principle
Archimedes' Principle, law of physics that states that
when an object is totally or partially immersed in a
fluid, it experiences an upthrust (or buoyant force)
equal to the weight of the fluid displaced.
The principle is most frequently applied to the
behavior of objects in water, and helps to explain
floating and sinking, and why objects seem lighter in
water. It also applies to balloons in the air.
𝐹𝐹𝐵𝐵 = 𝑚𝑚𝑚𝑚 = 𝜌𝜌𝜌𝜌𝜌𝜌
(1)
With
𝐹𝐹𝐵𝐵 is the buoyant force or Upthrust
𝜌𝜌 is the density of the liquid or object (g/cm3 or
kg/m3)
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Recent Advances in Mechanical Engineering and Automatic Control
𝑉𝑉 is the Volume of liquid displaced or the volume of
the object that immersed in the liquid (cm3 or m3).
𝑔𝑔 = 9.81𝑁𝑁/𝑘𝑘𝑘𝑘 is the gravity constant.
•Buoyant force = weight ⇒ the object floats and
stationary
•Buoyant force > weight ⇒ the object moves up
•Buoyant force < weight ⇒ the object moves
down
Fig. 2: represents the Hydrometer instrument. This
instrument measures the density of a liquid.
3.2 Spring balance instrument
Fig. 1: represents an object immersed in a liquid and
two forces are applied on this object, the weight force
and the buoyant force.
The spring balance (spring scale apparatus) is simply
a spring fixed at one end with a hook to attach an
object at the other. It works by Hooke's Law, which
states that the force needed to extend a spring is
proportional to the distance that spring is extended
from its rest position. Therefore the scale markings
on the spring scale are equally spaced.
The warm liquid is less dense than the cold liquid.
3 Hydrometer instrument and Spring
balance instrument
3.1 Hydrometer instrument
A hydrometer is an instrument used to measure the
specific gravity (or relative density) of liquids; that
is, the ratio of the density of the liquid to the density
of water.
A hydrometer is usually made of glass and consists
of a cylindrical stem and a bulb weighted with
mercury or lead shot to make it float upright. The
liquid to be tested is poured into a tall container,
often a graduated cylinder, and the hydrometer is
gently lowered into the liquid until it floats freely.
The point at which the surface of the liquid touches
the stem of the hydrometer is noted. Hydrometers
usually contain a scale inside the stem, so that the
specific gravity can be read directly. Varieties of
scales exist, and are used depending on the context.
ISBN: 978-1-61804-142-5
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Recent Advances in Mechanical Engineering and Automatic Control
Fig. 3: represents the Spring balance instrument. This
instrument measures the mass of an object inside a
liquid.
4 Hydrometer-Spring balance principle
This instrument is invented by the authors. The
principle of the instrument “Hydrometer-Spring
balance” is very simple. It is composed by a graduate
stem that contains two scales, one for the density of
the liquid and the other for the mass of the object
posed on the plate (Figure 4).
It contains also a plate on the top of the graduate
stem in order to put an object and measure its mass
when the instrument is immersed in the water. The
scale of mass is presented in the left part of the stem.
It contains also in the bottom a head of lead in order
to put it upright when it is immersed in the water.
It contains also two hooks of thin aluminum that can
be fold in order to maintain the object under the
water.
The scales in the left part of the stem is to measure
the density of the liquid, when the instrument is
immersed in the liquid, the surface of the liquid will
be at the same level as indicated on the graduate
scale specified for the density. So we can read easily
the value of the density. (Refer to figure 5)
The density of the potable water is equal to 1 g/cm3.
And this is a reference for other liquids.
Fig. 4: represents the instrument “Hydrometer-Spring
balance”.
ISBN: 978-1-61804-142-5
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Recent Advances in Mechanical Engineering and Automatic Control
Fig. 5: represents the instrument “Hydrometer-Spring
balance” immersed in a liquid.
In figure 5, we can measure the density of the liquid.
For example it is equal to 1.2g/cm3.
The density of the water is equal to 1g/cm3.
Fig. 6: represents the instrument “Hydrometer-Spring
balance” immersed in a liquid with an object posed
on the plate.
4.1 Calculating the mass of an object
4.2 Calculating the volume of an object
To calculate the mass of an object we have to fill the
graduate tall container with water and immerse the
instrument in the water until indicate the value
1g/cm3 on the scale. Then we put an object on the
plate (Figure 6) and measure its mass in (g) as
indicated in the left part of the stem. For example it is
equal to 20g in the figure 6. (We look at the left part
of the stem when the graduate scale is for the mass)
𝑚𝑚𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 = 20𝑔𝑔
(2)
ISBN: 978-1-61804-142-5
To calculate the volume of an object we have to fill
the graduate tall container with water and immerse
the instrument in the water until indicate the value
1g/cm3 on the scale. At the same time we look at the
graduate scale of the tall container (figure 8).
In the figure 7, the volume indicated is equal to
101ml
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Recent Advances in Mechanical Engineering and Automatic Control
We can also calculate the apparent weight of the
object in the water with
𝑊𝑊𝑎𝑎 = 𝑚𝑚 ∗ 𝑔𝑔 = 10 ∗ 9.81 = 98.1 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁
Fig. 7: represents the instrument “Hydrometer-Spring
balance” immersed in a liquid.
The next step is to put the object under the water
folded by the hooks (figure 8), and the instrument
will descend until give the exact value of the volume
indicated on the graduate tall container.
For
example
𝑉𝑉𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 = 111 − 101 = 10𝑚𝑚𝑚𝑚 =
10𝑐𝑐𝑐𝑐3 (refer to figure 8)
Fig. 8: represents the instrument “Hydrometer-Spring
balance” immersed in a liquid with an object folded
by the hooks under the water.
5 Conclusion
Therefore,
We have calculated the mass of the object and the
volume of the object so it is easy to calculate the
density of the object using the following formula:
𝑚𝑚 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜
(3)
𝜌𝜌𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 =
The Hydrometer-Spring Balance is a new instrument
introduced by the authors in physics in order to
simplify the manipulating of two instruments which
are the Hydrometer that measure the density of the
liquid and the spring balance that measure the mass
of an object inside and outside the liquid. So the new
instrument can be used instead of the two traditional
instruments. The new instrument will be put in a
graduated cylinder filled with water and this will
facilitate the measurement of the volume of the
displaced water that is equal to the volume of the
object, so we can measure at the same time the mass
of the object and its volume therefore we can deduce
the density of the object with respect to the density of
𝑉𝑉𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜
In our example it is equal to:
𝑚𝑚 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜
20𝑔𝑔
= 2𝑔𝑔/𝑐𝑐𝑐𝑐3 =
=
𝜌𝜌𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 =
𝑉𝑉𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜
2000𝑘𝑘𝑘𝑘/𝑚𝑚3
10𝑐𝑐𝑐𝑐 3
We can also calculate the weight of the object with
𝑊𝑊 = 𝑚𝑚 ∗ 𝑔𝑔 = 20 ∗ 9.81 = 196.2𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁
ISBN: 978-1-61804-142-5
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Recent Advances in Mechanical Engineering and Automatic Control
water. The new instrument allows us to measure also
the density of other liquids such as alcohol, benzene,
oil, milk, salt water, petroleum products…with
respect to the density of the water. We can have
many sizes and volumes of this instrument according
to the utilization. As conclusion, this instrument
replaces two other instruments which are used to
determine the volume and mass and density of a
liquid or an object.
References:
[1] Mariam Rozhanskaya, I. S. Levinova, "Statics",
in Rashed, Roshdi; Morelon, Régis, Encyclopedia
of the History of Arabic Science, 1 & 3,
Routledge, ISBN 0-415-12410-7, pp. 614–642,
(1996).
[2] Charles Thomas Davis, The manufacture of
leather: being a description of all of the processes
for the tanning and tawing with bark, extracts,
chrome and all modern tannages in general use,
H. C. Baird & co., 1897.
[3] "Acidometer", The Free Dictionary. Farlex. 2003.
[4] Acott, Chris (1999). "The diving "Law-ers": A
brief resume of their lives.". South Pacific
Underwater Medicine Society journal 29 (1).
ISSN 0813-1988. OCLC 16986801. (1999)
[5] “The first Eureka moment”, Science 305: 1219,
(August 2004).
[6] CRC Press Handbook of tables for Applied
Engineering Science, 2nd Edition, 1976, Table 159
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