1

FLUID MECHANICS

ASSIGNMENT

Presented To:

Dr. JAWAD SARWAR

Prepared by:

QAISER NAWAZ

2017-ME-65

DEPARTEMENT OF MECHANICAL ENGINEERIG

UNIVERSITY OF ENGINEERING AND TECHNOLOGY

1

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.

1

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

1

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 .

1

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:

? =

1

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

1

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