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FLUID MECHANICS
ASSIGNMENT
Presented To:
Dr. JAWAD SARWAR
Prepared by:
QAISER NAWAZ
2017-ME-65
DEPARTEMENT OF MECHANICAL ENGINEERIG
UNIVERSITY OF ENGINEERING AND TECHNOLOGY

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To determine the density of the water in the container, density of
container and that of the whole system
1. ABSTRACT
Water is an essential component for life. So it is very important to have an idea about
its physical parameters like melting point, boiling point, density etc.
In this paper, we will measure the density of water by measuring its mass and volume ,
density of pot into which water has to be taken and then by finding the total mass and total
volume of the whole system (water and pot), we will find out the density of system. Then
we will compare these values with the original values and measure the error in our
measurement as the method we are going to use to measure the density has definitely some
uncertainty.
2. INTRODUCTION
Density( ?)of amaterial is defined as the ratio of the mass of the substance and its
volume.it can be useful in identifying the substances.it is aconvenient property since it
provides arelation between mass and the volume of the substance.
V
m ? ?
Mass and volume are the extensive properties,depends on amount, while the
density is intensive property. Typically, density is reported as g/ml, g/cm 3or kg/m 3.In order
to determine the density, the mass and volume should be determined ,if experimentally.
Mass of the substance can be measured by using weight balance or electronic balance while
volume of the substance such as the liquid can be measured by using container such as
beaker, pot, flask etc.
Methods for determining or delivering precise volumes include :
? volumetric pip pets and pycnometers;
less precise methods include
? bu rretts, graduated cylinders, and graduated pi ppets.
In this experiment, we will measure masses and volumes to determine density.

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3. KEY WORDS
1. Water
2. Density
3. Combined system
4. Errors in measurements
4. WATER and Its DENSITY
Water is acompoud made up of oxygen and hydrogen atoms. Due to a
highly electro-positive and highly electronegative atom in water molecule, hydrogen
boding is present among the molecules of the water. This bonding makes water more
denser since it becomes incompressible.
But it doesn ‘tmeans that its density is constant but varies with the change in
different factors. For example, its density is maximum at 40C that is 1cm 3.density of water
decreases when temperature goes up or down from 40C. but it is the density of the pure
water.
For ocean water ,its density is 1027kg/m 3.
If we want to find the specific volume, the reciprocal of density gives the Specific volume.
5.FACTORS EFFECTING THE DENSITY
5.1. TEMPERATURE
The temperature is the most important factor which effects the density of a
substance most effectively. We know that as he temperature of the liquid increases, the
molecular motion increases since the kinetic energy of the molecules gets increase.
Increase in temperature increases the volume of the liquid according to the equation:
nRT PV ?
Since increase in volume causes decrease in the density of the liquid, so
density of water will decrease with increase of temperature. Also from the relation:
RT
P ? ?
This relation shows that the density is inversely proportional to temperature.
From the table given below, the value of the density of water decreases as we
move from 40C to 30 0C. the density of water at 40C is 1g/cm 3but at 10 0cit is
0.9997g/cm 3and also at 30 0C is 0.9957g/cm 3

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5.2. PRESSURE:
Pressure has the direct relation with the density of substance. From the relation:
RT
P ? ?
The increase in pressure brings molecules close together which result in decrease
in volume and increase in density and vice versa.
But in fluid mechanics, we consider all liquids as incompressible.
6.CONCEPT OF COMBINED DENSITY OF WATER WITH OTHER MATERIALS
In science or precisely say fluid mechanics, the concept of density is not as simple as
one thinks. There are various problems which an engineer may encounter in which there is
aconcept of combined density .Combined density is actually the density of water as well
as density of other materials. But it is not simple to obtain the value of combined density
by just adding the individual density, but it is much complicated in some cases. The
combined density is obtained by finding the total mass of the system and total volume of
the system, then by applying the formula of density, we can find the combined density or
density of system.
7. METHODS TO DETERMINE DENSITY
In the modern technology, there are various methods to find the density of liquids as follow:
? Direct measurement of mass and volume
? Indirect volume measurement
? Estimated density using Archimedes principle
? X-Ray Scanning
? By using hydrometer etc .

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7. PROBLEM SOLVING TECHNIQUES
7.1. PROBLEM STATEMENT
We have to find
i. Density of water
ii. Density of beaker material
iii. Density of the system(consisting of water and beaker)
7.2. SCHEMATIC
Figure: Beaker with water (system)
The beaker is half filled with the water. In order to find the density of the water in the
beaker we must have its mass and volume. In case of the density of the beaker, we have to
find the mass as well as the volume of the beaker material. The whole mass and volume of
the beaker will give the density of the system.
7.3. ASSUMPTIONS AND APPROXIMATIONS
? The cylinder is half filled with water.
? The cylinder is pure cylindrical.
? The density of the system remains constant due to incompressiblity.
? We are performing the task at 20 0C and 1 atm.
? Air in the system is being ignored.
? The empty portion of the system is being considered as vacuum.
7.4. PHYSICAL LAWS
The density of substance is given by:
? =

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Physical laws that hold during solving our problem include:
? Newton ‘sLaw of inertia is applicable as there is no external unbalanced force on
either water or beaker. So, the system will be in equilibrium during the experiment.
? Newton ‘s3rd law holds as the force applied by the water molecules on the beaker
must be equal to the re active force applied by beaker on water molecules in order to
maintain equilibrium.
? Archimedes principle holds as buoyancy force acts on the beaker when it is
immersed into the beaker.
7.5. PROPERTIES
? The density of the water remains constant sice there is negligible change in temperature
ad pressure.
? The water is amphoteric and neutral compound. The pH of water remains constant since
we are not adding impurities in water.
? Water has strong hydrogen bonding among its molecules.
7.6. OBSERVATIONS AND CALCULATIONS
MASSES
Mass of beaker = 55.34 g
Mass of system = 95.91 g
(beaker+water)
Mass of water = 95.91 -55.34 = 40.57 g
VOLUMES
Volume of beaker:
h = 8 cm hi= 7.75 cm
ro= 2 cm ri= 1.75 cm
hr V 2 ??
Vo = 100 cm 3 Vi = 74.56 cm 3
Volume of the material of the beaker = 100 -74.56 = 25.43 cm 3
DENSITIES
Density of water :
ter volumeofwa
r massofwate
water ? ?
014.1 40
57. 40
3 ? ? cm
g
water? g/cm 3

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Density of empty beaker :
ker
ker
ker a volumeofbe
massofbea
emptybea ? ?
kerea densityofb? 176.2 43. 25
34. 55 ? ? 3 /cm g
Density of system :
stem volumeofsy
em massofsyst
system ? ?
3 3 / 96.0 100
91. 95 cm g cm
g
system ? ? ?
7.7. RESULTS
The density of water at 20 0C is 0.9982 g/cm 3
% error in the density of water = 1.55 %
The density of pyrex glass from beaker is made is 2.23 g/cm 3
% error in the density of material of the beaker = 2.42 %
8. DISCUSSION COMMENTS
Now its time to discuss the faults and comments on the report.
1. The density of water varies with change in temperature and pressure.
2. There are errors in the densities of water and the material of the beaker due to
i. Errors while taking readings
ii. Impure water
iii. Variation in conditions
iv. The beaker may not be symmetrical
3. The errors can be reduced if
v. Readings and calculations are properly carried out
vi. Water being used is pure
vii. Reduce the effects of the outer conditions

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