Chapter1 - Introduction and Basic Concepts

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u

What is fluid mechanics?, Applications, The no slip

condition, Classifications of fluid flow, Liquid and gases, , , , , ,and conversion factors



Objectives

Understand the basic concepts of fluid mechanics

Recognize the various types of fluid flow problems encountered in practice

JUST Department of Chemical Engineering Fluid Mechanics – ChE 343 1-2



Introduction

Mechanics: Physical science that deals with both stationary and movin bodies under the influence of forces

Statics: Branch of mechanics that deals with bodies at rest

Fluid Mechanics: the science that deals with the behavior of fluids at,

interaction of fluids with solids or other fluids in boundaries




Categories

Hydrodynamics: Study of fluid motion that are practically

incompressible (i.e. liquid, specially water, and gases at low speed

Hydraulics: deals with liquid flows in pipes and open channels

Gas dynamics: Deals with flow of fluids undergo density changes

Example: flow of gases through nozzles at high speeds

such as aircraft, rockets, and automobiles at high or low speed

Other categories:

, ,

occurring flow




What Is a Fluid

Fluid: A substance in the liquid or gas phase

Distinction between a solid and a fluid is made on the basis of the substance’s

ability to resist an applied shear (or tangential) stress that tends to change its shape

¾ Consider the weight force in the drawing which tends to pu t e rope a part

Stress : ratio of applied force to area

Tensile stress : tensile force per unit cross-sectional area

Compressive force : weight force that tends to crush the

columnCompressive stress: compressive force divided by

the cross-sectional area




¾ Consider the system in which glue is used to hold a weight

Shear force : weight force that tends to make one surfaceslide parallel to an adjacent surface

Solids Fluids

- Can permanently resist large shear

forces

- Can not permanently resist large

shear forces no matter how small

- en su ec e o a s ear orces ey

move a short distance (elastic

deformation ) and then stop moving

- en su ec e o a s ear orces

they keep moving as long as the force

is applied



A lication AreasFluid mechanics is widely used both in every day activities and in the design

modern engineering systems from vacuum cleaner to supersonic aircraft.

Fluid mechanics is used extensively

in the design of artificial hearts

Natural flows and wheather

Boats



Aircraft and spacecraft Power plant

Wind turbine Piping, plumping, and Industrial applications



Basic Ideas in Fluid Mechanics The principle of conservation of mass

The first law of thermod namics Desired

The second law of thermodynamics

Newton’s law of motion F = ma

forces,

velocities,etc.

¾ Experimental data and dimensional analysis

Method of solution: Form equations and solve analytically or

numerically



The No-Slip Condition

Consider the flow of a fluid in a stationary pipe or over a solid surfacethat is nonporous

All experimental observations indicate that a fluid

in motion comes to a complete stop at the surface

No-slip

condition

Consequences of no-slip condition:

e ayer t at st c s to t e sur ace s ows t e a acent u ayer because of viscous forces between the fluid layers, which slow

.

Development of velocity profile- Boundary layer

- Surface dra skin friction dra



Internal versus External Flow

External low: F ow o anunbounded fluid over a surfacesuch as a late a wire or a i e

Internal flow: Flow in a pipe or ductwhere the fluid is com letel

bounded by solid surfaces

Compressible versus Incompressible Flow

Incom ressibilit : a roximation of flow when the densitremains constant throughout (i.e. no change in volume)

Com ressible: when densit chan es with ressure.




Laminar versus Turbulent Flow

Lam nar: H g y or ere umotion characterized bysmooth la ers

Eg . Flow of high-viscosity fluids such

as oil at low velocity

Turbulent: Highly disordered fluid motion characterized by velocity

uctuat onsSteady versus Unsteady Flow

Steady: implies no change at a point with time

Unstead or Transient: im lies chan e with time

Uniform: implies no change with time and location over aspecified region




Liquids and Gases

Fluids in common are in two types: liquids and gases which aredifferent on molecular level.

n qu s , mo ecu es are c oseto each other and are held to ether b si nificant forcesof attraction

In Gases , molecules arere at ve y ar apart an avevery weak forces of attraction

• ,

differences become less and less, until the liquid

and the gas become identical at the critical point

• Imagine what could happen when raising the

piston that holds a fluid, gas or liquid , which

com letel fills the s ace below the iston !!!




System and Control Volume

System, Surrounding, and Boundary

System: Quantity of matter of fixed mass and

identity upon which attention is focused for study”

excluding the system)

system from its surrounding

The system’s thermodynamic state is defined by macroscopic

properties that can be measured (such as pressure).

The macroscopic properties are described in terms of fundamental scientific

dimensions: Length, time, mass, temperature etc. (ChE 204)




Closed and Open Systems

Closed System (or control mass): fixed amount of mass with no mass across its boundary

Moving

may enter and leaveBoundary

Fixed

Boundary

2 kg

3 m3

Heating

Isolated system: No energy crossing the

boundar

Gas2 kg 1 m3

Energy

Open System (or control volume): selected region in space where both mass and

energy can cross e oun ary o a con ro vo ume

Usually encloses device that involves massmass

Control

Control

surface , ,

Control surface: boundary of a control volume

masso ume




Properties of Fluids

Intensive and Extensive Properties

Intensive thermodynamic variables: are those variables which are

independent of the size or amount of the substance (eg., T and P ) Extensive thermodynamic variables: are those variables which

depend on the size or amount of the substance (eg., V , m and n )

Note: Intensive variables are functions of T , P and composition




Density and Specific Gravity

Density is defined as mass per unit volume. That is

m= k /m3

9 How can we measure the density of a liquid?

9

9 What about the density of materials which

contain holes inside?

Imagine what happens when we measure thedensity of a large block of Swiss cheese and

point inside the block

9 Density of a substance is a function of temperature and pressure:Proportional to pressure and inversely with temperature

nRT PV =9 Density of ideal gases: or P W )(

= ρ




Specific gravity, or relative density, is defined as the ratio of the

ens y o a su s ance o e ens y o some s an ar su s ance a a specified temperature (usually water at 4oC)

C4atO,H o2

ρ =SG

o e a o a su s ance s a

dimensionless quantity

9 o some su stances

at 20oC

9 u s ances w ess

than 1 are lighter than water,

water




Force and Wei ht

Based on Newton’s second law of motion: F ma=

Unit of force: kg m s-2 = [N]According to SI system

Be aware of the engineeringunit for force lb : see the

m = 1 kga = 1 m/s2

F = 1 N

textbook 1 lbf = 4.4482216 N

m = 32.174 Ibm a = 1 ft/s2 F = 1 lbf

Weight properly refers to the force of gravity on a body



Viscosity

scos y measures e u res s ance o ow• What happens if we tip glass of water on a table

⇒ Honey has more resistance to flow (more

viscosity) than water • Consider two long, solid plates separated by a

thin film of fluid

ow 0, e ve oc y pro e s near.

This is demonstrated experimentally. oo

V V y=

Shear rate = rate of strain =o

ody y=

a body in the flow direction

Shear stress, τ = F/A Viscosity =τ

μ = 2

N.s⎡ ⎤⎢ ⎥




Newtonian versus Non-Newtonian Fluids

The equation dV

dyτ μ = says that the shear stress τ is linearly proportional to

the velocity gradient dV/dy

μ is independent of shear rate.

Examples: gases and simple formula liquids.

-

suspended particles or dissolved molecules

which are large compared with the size of yp ca u mo ecu es.



Three Common Types of Non-Newtonian Fluids

• Bingham fluids: They resist a small stress but flow easily under larger shear stresses.

.

• Pseudoplastic fluids (by far the most common): μ decreases as shear rate

increasesExamples: mud, most slurries, blood, polymer solutions.

• Dilatant fluids (uncommon): viscosity increases with increasing velocity gradient

Such behavior is called shear thickening

Exam les: starch sus ensions

Kinematic Viscosity =ν

= viscosity/density = μ / ρ

2m⎡ ⎤

⎢ ⎥



Surface Tension

Surface tension is the tendency of the surface of a liquid to behave like astretched elastic membrane.

Surface tension is caused by the attractive forces in liquids.

The fluid tries to take a shape that would have the greatest number of molecules

near the center, a sphere. The fluid tries to minimize its surface area.

Surface tension = force of one film/length or F

l σ =

N

m

⎡ ⎤⎢ ⎥

, .



Pressure

Normal force exerted by a fluid per unit area of the acting surface

Unit: in SI s stem N m-2 = Pa

= F P

In English engineering system: force per square inch (psi)

Example: for vertical column, under the influence of gravity A

The force acting on the system is the weight of the fluid

∴ F = W = mg = ( ρ V ) g = A h ρ g

mg

h

= = = F A h ρ g P ρ gh A

Other units of pressure:

1 atm = 101,325 Pa = 101.325 kPa = 0.101325 MPa = 760 mmHg5 m height

P top ?

ar = a = . a m Room

P bottom ?



Important!!

¾ Thermodynamics deals with absolute pressure which is

different than the au e readin :

Gauge reading = Absolute pressure – Atmospheric pressure

Pressure above atmospheric

Atmospheric pressure (1 atm)

Vacuum au e readin (-ve)

Pressure gauge reading (+ve)

Pressure below atmospheric

Absolute ressure less

Barometer

reads

atmospheric

Absolute

pressure

(> atm)

Datum (zero pressure)

than atmospheric



Units and Dimensions You use values, units and dimensions all the time:

Grocer List

1 carton of milk (value: 1; units: carton; dimensions: volume

(length3

)) 1/4 pound burger (value: 0.25; units: pounds; dimensions:mass)

VALUE:

. .

UNITS:

The units tell what that quantity represents. For example: 5.2 liters .

DIMENSIONS :

The dimensions are the measurable properties that the units represent. For example: a liter is a unit of volume (units are a specific example of a

dimensional quantity).

, , , , , ,



Benefits of units

Diminished possibility of errors in your calculations,

Reduced intermediate calculations and time in

problem solving, A logical approach to the problem rather than

rememberin a formula and substitutin numbers into

formula,

numbers you use



Relation between the basic dimension (in boxes) and various

Density

Volumetric

Flow

Mass

Flow

Time MassVolume

Area Velocity

Acceleration Force

Diameter



S stems of Units

System Length Mass Time Force Customary Name Conversion Factor gc

SI m kg s m Newton kg ms2 2 N s

CGS cm g s cm dyn g cmg

s

2 2

dyn s

FPS ft lbm s ft oundal lbm ft m

s232 2

2.

lbf s



SI Units

Physical Quantity SI Unit

Velocit m

s

Acceleration

EnergyJ kg

m

s=

2

2

s2 Power W

J

skg

m

s= =

2

3

s

PressurePa

N

m

kg

m s= =2 2

m3 V scos ty

Jg

m s=

N kgs

=2

m

s



Auxiliary Units

Physical Quantity Unit Symbol Definition

Length micron μm 10 6− m

Mass Metric ton t 3

Volume Liter L 10 3 3− m

Pressure bar bar 10

5

Pa

Viscosity Poise P 1− kg

m s

Kinematic Viscosity Stokes St 4

2

− ms



Prefixes for Fractions and Multiples

Factor Name Symbol Factor Name Symbol

10 12− pico p 1012 tera T

10− nano n 10 g ga

10 6− micro μ 106 mega M

10 3− milli m 103 kilo k

Commonl Used Conversion Factors See tables in the first and last pages of the textbook.



Units Al ebra Treat units as algebraic entities:

add/subtract them if the are of the same units 3 cm - 1 cm =2 cm

multiply/divide them anytime

(3 N . 4 m = 12 N.m OR 5.0 km/2.0h = 2.5 km/h) But you cannot cancel or merge units unless they are identical

3 m2/60 cmÆ 3 m2/0.60 m Æ 5 m

EXAMPLES:

Al ebraic e uationy

= ⎞⎛

"Unit" equation

x ⎠⎝ ( ) dollars

e sdozen

dollarseggsdozen =

⎟

⎟ ⎞

⎜

⎜⎛

"Unit" equationcm3cm2cm1 =+



Conversion of Units A measured quantity can be expressed in terms of any units having the

appropriate dimension.

Example: Velocity (ft/s, miles/h, km/h, cm/yr, etc.)

Units with same dimensions -> easily inter-converted/ OR

defined in terms of a ratio:

EXAMPLE: s)millimeter 10 per centimeter (1 mm10cm1 ⎟

⎠ ⎞⎜

⎝ ⎛

22

)centimeter per smillimeter 0(1 cm1

mm10⎟ ⎠ ⎞

⎜⎝ ⎛

2cm1

mm

cm1

mm=⎥⎦⎢⎣

.



Conversion of Units Convert from one set of units to another:

multiply the given quantity by the conversion factor (new unit/old unit).

Example:

Convert 36 mg to its equivalent in grams: ⎞⎛ g1m36 ⎠⎝ mg1000

Example:

Convert 36 mg to its equivalent in grams: ( ) g.0360mg1000

g

mg36 =⎟⎟ ⎠⎜⎜⎝

Example:

Convert 46 ft/min into its equivalent in m/s:

46 ft 1 m 1 min

min 3.281 ft 60 s= 0.2336 m/s

Chapter1 - Introduction and Basic Concepts

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Transcript of Chapter1 - Introduction and Basic Concepts