chapter 1 fluid mechanics

1FLUID MECHANICS

CHAPTER 1

LECTURER: Sarah Asif

[email protected]

2SYLLABUS

1.0 INTRODUCTION TO HYDRAULICS

1.1 Units and dimensions

1.2 Ideal and Newtonian fluid

1.3 Properties of fluid: density, specific weight,

specific gravity, viscosity, bulk modulus,

shear force, surface tension and

capillarity.

31.0 Introduction

- This subject is focus on scientific study related to

fluid flow in closed conduit (e.g pipe) and open

channel (e.g river).

4Fluid engineering applications is enormours; which are flow

in pipelines and channels, movements of air and blood

in the body, air resistance, wind loading on buildings,

motion of projectiles, jets, shock waves, lubrication,

combustion and irrigation.

The knowledge of fluid mechanics and hydraulics is required

to properly design water supply systems, wastewater

treatment facilities, spillways, pumps, turbines, air

conditioning systems and etc.

Contd

1.0 Introduction

51.1 Units and Dimension

Notes: British Gravitational (BG) system used English unit, while

System International (SI) used metric units.

Quantity Dimension SI BG

Mass M kg Lb

Length L m ka

Time T S s

Temperature oC oF

61.2 Ideal & Newtonian Fluid

Fluid can be divided into 2 (two) :

1) Liquid

- Able to flow and does not have specific form.

- Change to another form or shape if shear force

involved.

- Assumed as uncompressible fluid.

(Compressibles value has been ignored - too small)

Contd


2) Vapor / gas

- Compressible fluid.

- Density of gas/vapor is different based on

temperature and pressure required.

Contd


Ideal Fluid

Known as perfect fluid

This fluid has no friction, surface tension and

compressiblity.

Although this fluid does not exist in reality, a lot

of researchers used it in analysis and

calculation of fluid.

Contd


Real Fluid

In real fluid, either liquid or gas, tangential or shearing

forces always develop whenever there is motion relative

to a body, thus creating fluid friction.

Newtonian fluid

is a fluid for which the constant of proportionality

(where, shear stress proportional to the time rate of

(angular) deformation) does not change with rate of

deformation.

Contd

10


Real Fluid

Water, air, gasoline, and oils (Newtonian fluids)

Blood and liquid plastics (non-Newtonian fluids)

Contd

11

Density ()

Depends on temperature and pressure

Density = mass per unit volume or = m/V

SI Unit = kg/m3.

Example: density of water = 998 kg/m3 1000 kg/m3

1.3 Properties of FluidContd

12

Specific Weight ()

Specific weight = weight per unit volume or

= W/V N/m3 or

= g N/m3

Example: specific weight of water

= 1000 x 9.81 = 9.81 kN/m3

where, accelaration of gravity = 9.81 ms-2

Contd

1.3 Properties of Fluid

13

Specific Gravity (s.g)

Specific gravity = specific weight of substance/

specific weight of water at 4oC

s.g = substance / water at 4o

C

Where, specific weight of water is 9.81 kN/m3

Contd1.3 Properties of Fluid

14

Relative Density (rd)

The relative density of a substance /liquid is

defined as the ratio of its mass density to the mass

density of water taken at atmospheric of 4C.

Contd

water

sub

waterofDensity

substance ofDensity

(Formula for rd and sg are similar if gravitys value is same)


15

Contd

Example 1 :

A reservoir of glycerin as a mass of 1200 kg and a

volume of 0.952 m3. Find the glycerins weight (W), mass density ( ), specific weight ( ) and

specific gravity (s.g)


16

W = mg = (1200)(9.81) = 11770N atau 11.77kN

= m/V = 1200/0.952 = 1261 kg/m3

= g = (1261)(9.81) = 12.37 kN/m3 (atau W/V)

s.g = substance / water at 4oC = 12.37k/9.81k = 1.26

Contd

Answer 1:


17

Answer :

W = 4905 N, = 1587 kg/m3, =15.57 kN/m3,

s.g =1.59

Contd

A reservoir of carbon tetrachloride (CCl4) has a

mass of 500 kg and a volume of 0.315 m3. Find the

carbon tetrachlorides weight, mass density, specific weight and specific gravity.


Question 1

18

Specific Volume (vs)

Defined as the reciprocal of the mass density or

volume per unit mass

SI Unit is m3/kg

Contd

1

sv


19

Contd

If the specific volume of a certain gas is 0.73 m3/kg,

calculate its specific weight.


Example 2 :

vs = 0.73 m3/kg = 1/vs = 1/0.73 =1.37 kg/m

3

= g = 1.37 x 9.81 = 13.44 N/m3

Answer 2 :

20

Viscosity

is a property that represents the

internal resistance of a fluid to

motion or the fluidity.

The force a flowing fluid exerts

on a body in the flow direction is

called the drag force, and the

magnitude of this force depends

on viscosity.


21

Viscosity

To obtain a relation for viscosity,

consider a fluid layer between

two very large parallel plates (or

equivalently, two parallel plates

immersed in a large body of a

fluid) separated by a distance.


22

Viscosity

Now a constant parallel force F is applied to the

upper plate while the lower plate is held fixed. After

the initial transients, it is observed that the upper

plate moves continuously under the influence of

this force at a constant velocity V.

The fluid in contact with the upper plate sticks

to the plate surface and moves with it at the same

velocity.


23

Viscosity

Force which are needed to make a constant flow is

where is dynamic viscosity,


y

AuF

rate stressshear

stressshear /

yu

AF

The shear stress acting on this fluid layer is ( = F/A) where

A is the contact area between the plate and the fluid.

Note that the fluid layer deforms continuously under the

influence of shear stress.

24

The shear stress can also shows as

SI Unit = Ns/m2 or kg/ms or Pa.s or Poise

(10 Poise = 1Ns/m2)

Contd

dy

du


25

Kinematic viscosity is defined as the ratio of

dynamic viscosity to mass density,

SI units : m2/s or stokes

(10,000 stokes = 1 m2/s)

Contd

density

viscositydynamic


26


Example 3 :

A plate separated by 0.5 mm from a fixed plate

moves at 0.5 m/s under a force per unit area of 4.0

N/m2. Determine the viscosity of fluid between the

plates.

27


Answer 3 :

dy

du

4.0 N/m2

0.5 m/s

0.0005 m

2/004.00005.0

5.0)0.4( mNs

du

dy

28

Compressibility and Bulk Modulus

All fluid are compressible when subjected to

applied forces, they will exprience a reduction

in volume.

Volume reduction in gases are much more

compressible compared to liquids. Hence, gases

are much more compressible compared to

liquids.


29

The change in volume which accompanies the

change in pressure is given;

where, K is the bulk modulus of substance

Bulk modulus is limitation for substance to

resist compressibility.


V

dVKdp

30

The bulk modulus for solids

and liquids remains fairly

constant over the ranges of

pressure and volume changes.

Liquids are considered

incompressible as the volume

change is very small.

K unit = N/m2


31

Contd

Example 4 :

A liquid compressed in a cylinder has a volume of

1000 cm3 at 1 MN/m2 and a volume of 995 cm3 at 2

MN/m2. What is its bulk modulus of elasticity (K)?

MPa2001000/)1000995(

12

VV

pK

Answer 4:


32

Question 2

Answer :

K = 13.2 MPa

Contd

If K for water is 22 GPa, what pressure required to

reduce a volume by 0.6 percent.


33

Surface Tension ( )

This property takes place at the interface between a

liquid and a gas, i.e., at the liquid surface, and at

the interface between two immiscible liquids.

The out of balance attraction force between

molecules forms an imaginary surface film which

exerts a tension force in the surface.

Contd


34

This force acts in the plane of the surface, normal to any line drawn in the surface and its tends to reduce the surface area of liquid body.

Effect of surface tension is to reduce the liquid area to minimum level and increase the internal forces thus, surface tension force must be in equilibrium.

= 0.073 N/m for air-water interface

= 0.480 N/m for air -mercury interface


35

Unit : N/m

For interior of liquid cylinder,

A spherical droplet,

The pressure difference between 2 surfaces of soap

bubbles,


RP

RP

2

RP

4

36

An atomizer forms water droplets 45m in diameter. Find the excess pressure within these droplets for

water at 30oC.

Example 5 :


PaxR

P 63292/)1045(

)0712.0(226

Answer 5 :

37

Question 3

Answer :

P = 67.5 Pa

Contd

What is the pressure difference between the inside

and outside of a cylindrical water jet when the

diameter is 2.2 mm and the temperature is 10oC


38

Capillarity

When a liquid comes into contact with a solid

surface, then the adhesion forces between solid and

liquid as well as the cohesion forces within the liquid

must be considered. It is also because of surface

tension of liquid.

If adhesion forces > cohesion forces, the

meniscus in glass tube will show maximum curve

,i.e, mercury.


39

While, if cohesion forces > adhesion forces, the

meniscus will behave differently, i.e. water


40

Increasing of liquids level in tube can be estimated if angle, which is between wall and liquid are

known. Here is the formulae;


rh

cos2

Where : - angle

- specific weight

- surface tension

r - radius

41

Find the capillary rise in the tube for a mercury-air-

glass interface with 130oC if the tube radius is 1mm

and the temperature is 20oC.

Example 6 :


Answer 6 :

mr

ho

005.0)1000/1)(81.9)(13570(

)130)(cos514.0(2cos2

42

Question 4

Answer :

h = 14.8 mm

Contd

Find the capillary rise in the tube for a water-air-glass interface ( =0o) if the tube radius is 1 mm and the temperature is 20oC. Given w = 0.0728 N/m


43


Next slides (pg 44- pg 48) are show the properties of

air, water dan common gases at standard sea-level

atmosphere pressure.

44

1.3 Properties of Fluid (Appendix)

ContdTable A.1: Properties of air at standard sea-level atmosphere pressure

Temperature oC

Density, kg/m3

Specific weight,

N/m3

Dynamic viscosity,

Ns/m2

Kinematic Viscosity,

m2/s

0 1.29 12.7 1.72 10-5 13.3 10-6

10 1.25 12.2 1.77 10-5 14.2 10-6

20 1.20 11.8 1.81 10-5 15.1 10-6

30 1.16 11.4 1.86 10-5 16.0 10-6

40 1.13 11.0 1.91 10-5 16.9 10-6

50 1.09 10.7 1.95 10-5 17.9 10-6

60 1.06 10.4 1.99 10-5 18.9 10-6

70 1.03 10.1 2.04 10-5 19.9 10-6

80 1.00 9.80 2.09 10-5 20.9 10-6

90 0.972 9.53 2.19 10-5 21.9 10-6

100 0.946 9.28 2.30 10-5 23.0 10-6

45

1.3 Properties of Fluid (Appendix)Contd

Table A.2: Properties of water at standard sea-level atmosphere pressure

TemperatureoC

Density, kg/m3

Specific weight, N/m3

Dynamic viscosity, Ns/m2

Surface tension*, N/m

0 1000 9810 1.75 10-3 0.0756

10 1000 9810 1.30 10-3 0.0742

20 998 9790 1.02 10-3 0.0728

30 996 9770 8.00 10-4 0.0712

40 992 9730 6.51 10-4 0.0696

50 988 9690 5.41 10-4 0.0679

60 984 9650 4.60 10-4 0.0662

70 978 9590 4.02 10-4 0.0644

80 971 9530 3.50 10-4 0.0626

90 965 9470 3.11 10-4 0.0608

100 958 9400 2.82 10-4 0.0589

* Contact

with air

46


Fluid

TempDensity,

Specific gravity, sg

Viscosity,

Surface tension,

Bulk Modulus,

K

oC kg/m3 10 3

Ns/m2N/m 106 N/m2

Benzene 20oC 876 0.88 0.65 0.029 1030

Tetrachloride Carbon

20oC 1588 1.594 0.97 0.026 1100

Raw oil 20oC 856 0.86 7.2 0.03

Gasoline 20oC 680 0.68 0.29

Glycerine 20oC 1258 1.26 1494 0.063 4344

Hydrogen

257oC 73.7 0.074 0.021 0.0029

Table A.3: Properties of fluid at standard sea-level atmosphere pressure

47


Table A.3: Properties of fluid at standard sea-level atmosphere pressure

Fluid

TempDensity

,

Specific weight,

sg

viscosity,

Surface tension,

Bulk Modulus,

K

oC kg/m3 10 3

Ns/m2N/m 106N/m2

Kerosene 20oC 808 0.81 1.92 0.025

Mercury 20oC 13550 13.56 1.56 0.51 26200

Oxygen 195oC 1206 1.21 0.278 0.015

SAE 10 oil 20oC 918 0.92 82 0.037

SAE 30 oil 20oC 918 0.92 440 0.036

Water 20oC 998 0.999 1.00 0.073 2171

Sea water 20oC 1023 1.024 1.07 0.073 2300

48

1.3 Properties of Fluid (Appendix)

Contd

Table A.4: Physical properties of common gases at standard sea-level atmosphere pressure

Gas

Chemical formula

Molar Mass, M

Density,

Viscosity,

Gas Constant, R

kg/ kg-mol kg/m3 106 Ns/m2 m2/(s2K)

Air 28.96 1.205 18.0 287

Carbon dioxide

CO2 44.01 1.84 14.8 188

Carbon monoxide

CO 28.01 1.16 18.2 297

Helium He 4.003 0.166 19.7 2077

Hydrogen H2 2.016 0.0839 9.0 4120

Methane CH4 16.04 0.668 13.4 520

Nitrogen N2 28.02 1.16 17.6 297

Oxygen O2 32.00 1.33 20.0 260

Water Vapour

H2O 18.02 0.747 10.1 462

49

1.3 Summary of Fluids Properties

Surface Tension

Viscosity

Bulk Modulus

Density

Specific Gravity

Capillarity

Compressibility

Relative Density

Properties

of Fluid

Value of fluid

properties are

vary in different

temperatures

chapter 1 fluid mechanics

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