FM-1

Fluid Mechanics (3-1) Instructor: Lec Hammad Aziz

Introduction to Fluid

Mechanics

Assessment

Category Total Weightage

Quizzes 06 12%

Sessional 02 35%=(15+20)%

Final 01 40%

Assignment 02 08%

Project 01 05%

Topics Covered S. No Topic Week

1 Introduction: Definition of a fluid, fluid properties, viscosity,

compressibility of fluids

1-2

2 Hydrostatics: Measurement of pressure, Pressure measurement devices,

hydrostatic forces on plane and inclined surface, buoyancy and stability

2-5

3 Principles of Fluid Motion: Description of fluid flow; continuity equation;

Euler and Bernoulli equations; Pitot total head and static tubes, venturi-

meters, orifice plates, restrictions on use of Bernoulli equation

6-7

4 Fluid Kinematics: Eulerian and Lagragian flow, acceleration field and

Reynolds transport theorem

8-9

5 Momentum Equation: Momentum equation for steady flow; applications

to jet flows, impinging flows in pipe bends; momentum theory of

propellers, differential analysis of fluid flow.

10-11

6 Dimensional Analysis: Buckingham Pi Theorem, Modelling and Similitude 12

7 Viscous and Compressible Flow: Laminar and Turbulent flow, Minor and

Major losses in pipes, Mach number and speed of sound, Isentropic and

Non isentropic flow, Rayleigh flow

13-14

8 Turbomachines: Hydraulic systems, centrifugal, axial and mixed flow

pumps, fans, turbines, compressors

15-16

Recommended Books

Fundamentals of Fluid Mechanics by Bruce

R. Munson, Donald F. Young and Theodore H.

Okiishi (SI Version)

Fluid Mechanics by Frank M. White

Fluid Mechanics by John F. Douglas, John A

Swaffield

Fluid Mechanics-Fundamentals and

Applications by Yunus A Cengel

Engineering Fluid Mechanics by Donal F.

Elger

Introduction to Fluid Mechanics

At the end of this chapter, you should be able to;

a. Understand the basic concepts of fluid mechanics

b. Determine the dimensions and units of physical quantities

c. Identify the key fluid properties used in the analysis of fluid behavior

d. Use the concepts of viscosity, vapor pressure and surface tension

e. Recognize the various types of fluid flow problems encountered in our daily life

Introduction to Fluid Mechanics

What is Fluid?

Anything which can flow.

What is Mechanics?

Physical science that deals with both stationary and

moving bodies under the influence of forces

Statics

Bodies at Rest

Dynamics

Bodies in Motion

Introduction to Fluid Mechanics What is Fluid Mechanics?

Science that deals with fluid at rest (fluid statics) or in motion (fluid dynamics) and interaction of fluids with solids or fluid at the boundary.

Classification of Fluid Mechanics

Hydrodynamics

(study of motion of fluid especially incompressible i.e. water, gases at low speeds)

Hydraulics

(Flow of liquids in pipes and open channels)

Gas dynamics

(Flows of liquids that undergo density changes i.e. flow of gases through nozzles at high speed)

Aerodynamics

(Flow of gases especially air over bodies such as aircraft, automobiles etc)

Meteorology

(Science deals with atmosphere)

Oceanography

(Deals with ocean science and its applications)

Hydrology

(Study of waters of earth on and below the surface of planet)

What is Fluid

Substance exists in three different phases

Solid

Liquid

Gas

Plasma (at very high temperature)

Substance in the liquid or gas phase is referred as FLUID.

Thus we can say that, all matter exists in two forms FLUID and SOLID.

Difference between Solid and Fluid

Solid is “hard” while fluid is “soft”

Ability to resist applied shear stress that tends

to change its shape

Solid Liquid

It can resist applied shear stress by deforming It deform continuously under the action of

shear stress, no matter how small it is

Stress is proportional to strain Stress is proportional to strain rate

When a constant shear force is applied, a

solid eventually stops deforming at some

fixed strain angle

Fluid never stops deforming and approaches a

constant rate of strain. Fluid at rest has zero

shear stress known as hydrostatic stress

condition.

Difference between Solid, Liquid and Gas

* Intermolecular bonds are strongest in solids and weakest in gases.

* Molecules in solids are closely packed together, whereas in gases they are separated by relatively large

distances .

* The molecules in a solid are arranged in a pattern that is repeated throughout due to small distances

between molecules in a solid, the attractive forces of molecules on each other are large and keep the

molecules at fixed positions.

* The molecular spacing in the liquid phase is not much different from that of the solid phase, except the

molecules are no longer at fixed positions relative to each other and they can rotate and translate

freely.

* In a liquid, the intermolecular forces are weaker relative to solids, but still strong compared with gases.

The distances between molecules generally increase slightly as a solid turns liquid.

Difference between Liquid and Gas

Liquid: Molecules move relative to each other

Total volume remain fixed due to strong cohesive forces

Takes the shape of container and forms a free surface

Gas: Molecules are widely spaced due to weak cohesive forces

Expands and fill the entire space available

Cannot form a free surface

Rheology

Matter that acts as solid but with the

application of shear stress for the extended

period of time it behaves as fluid

Asphalt, toothpaste, slurry etc

Comparison of Solid, Liquid and Gas Attribute Solid Liquid Gas

Visualization

Macroscopic

description

Solids hold their shape-no

need of container

Liquids take the shape of

container and can stay in open

container by forming a free

surface

Gases expand to fill the closed

container

Mobility of

molecules

Little mobility due to strong

intermolecular forces

Flow easily even there are

strong intermolecular forces-

weaker than solids

Molecules move around freely with

little interaction expect during

collision

Density High-steel has 7700kg/m3 Medium-water has 1000kg/m3 Low-air has 1.2kg/m3 at sea level

Molecular

spacing

Small-molecules are close

together

Small- molecules are close

together

Large-molecules are far apart

Effect of shear

stress

Produces deformation Produces flow Produces flow

Viscosity N/A High-decrease with increase of

“T”

Low-increase as “T” increases

compressibility Difficult to compress-steel

has bulk modulus 160*109 Pa

Difficult to compress-water

has bulk modulus 2.2*109 Pa

Easy to compress-Gas has bulk

modulus at room temperature

2.2*105 Pa

Applications of Fluid Mechanics

Human Body (Heart is pumping blood to all parts of

body through veins and arteries etc.)

Piping system for water, natural gas and sewage in houses, cities etc.

Heating and air conditioning system

Automobile (fuel from the fuel tank to cylinder etc.)

Design and analysis of aircrafts, ships, submarines, wind turbines etc.

Design of buildings, bridges and even billboards

Natural phenomenon (rain cycle, winds, ocean waves, rise of ground water to tops of trees etc.)

What kinds of forces act on Fluid particles? Each fluid particle experience surface force (pressure, friction) that

are generated by contact with other particles or solid body and

body force (gravity, electromagnetic) throughout the particle.

For example, 1. diving board, 2. body moves thru fluid, so we can say

that stresses in fluid are mostly generated thru motion rather than by

deflection.

Stress: Force per unit area

The normal component of the force acting on a surface per unit area

is “normal stress”. The tangential component of the force acting on

the surface per unit area is “tangential stress”

Surface of fluid particle is in contact with

other fluid particle and so a contact force is

generated b/w the particles.

The No-Slip Condition (cont.) Fluid flow is confined by solid surface

Flow of liquid in a solid pipe or over a solid non-porous surface.

Fluid in direct contact with solid surface sticks to it, hence there is no slip known as “No slip condition”

No Temperature Jump Condition Similar to no slip condition but in heat transfer

When two bodies at different temperatures are brought into contact, heat transfer occurs until both bodies assume the same temperature at the points of contact. Therefore, a fluid and a solid surface have the same temperature at the points of contact. This is known as the no-temperature-jump condition

Classification of Fluid Flow

Viscous Vs Inviscid Regions of Flow

Frictional force develops b/w two layers

Flows in which the frictional effects are significant known

as Viscous Flow.

Classification of Fluid Flow (Cont.) Internal Vs External Flow

Flow of an unbounded fluid over a surface i.e. plate is known as

external flow

Flow in a confined space such as flow through pipes knows as internal flow.

Flow in a duct which is partially filled with liquid and there is free surface known as open-channel flow.

Classification of Fluid Flow (Cont.)

Compressible Vs Incompressible Flow

If the density of fluid remained nearly constant through the

flow known as incompressible flow

Liquids are usually incompressible while gases are compressible

For example; a Pressure of 210atm required to change the density of water by just 1percent at 1atm while for gases pressure of 0.001atm is required.

Classification of Fluid Flow (Cont.) Laminar Vs Turbulent Flow

Highly ordered flow is known as

laminar flow e.g. flow of high viscosity fluid such as oil at low velocity

Disordered or chaotic flow is known as turbulent flow e.g. flow of low viscosity fluid such as air at high velocity

Flow that alternated between being laminar and turbulent known as transitional flow


Forced Vs Natural Flow

In forced flow, external source is required such as fan,

pump in order to flow the fluid in pipe or over a surface.

In natural flow, fluid motion is through natural means e.g.

rise of warmer fluid or fall of cooler fluid.

“Thermo siphoning effect”


Steady Vs Unsteady Flow

No change of properties such as velocity, temperature etc.

at a point with time is steady flow and the opposite is unsteady flow.

Heat exchangers, turbines, compressors etc operate for a long period of time and thus classified as steady flow devices.


One, two and three Dimensional Flow

A flow is said to be one-, two-, or three-dimensional if the flow velocity varies in

one, two, or three primary dimensions, respectively

System and Control Volume System, Boundary and Surrounding

Quantity of matter or region in space selected for study is system

Mass or region outside the system is surroundings

Real or imaginary surface separates the system from surroundings is boundary. It can be fixed or moveable and has zero thickness or volume.

System and Control Volume

Open, Close and Isolated System

Mass, energy can enter or leave the system

No mass can enter or leave the system, but

energy in the form of heat can enter

No Mass, energy can enter or leave the system


Closed System (control mass)

system


Open System (control volume)

Properties of System

Intensive and Extensive properties Any characteristics of a system such as Pressure, velocity,

temperature is property

Properties that are independent of mass of system are intensive

Properties whose values depend on mass or size of system are

extensive

Example:- A tank of liquid having a total mass of 36 kg rests on a support in the

equipment bay of the Space Shuttle. Determine the force (in newtons) that the

tank exerts on the support shortly after lift off when the shuttle is accelerating

upward as shown in Fig. at 15 ft / s2.

a= (15 ft/s2)(0.3048 m/ft)

Fluid as “Continuum”

The properties of a fluid arise from its molecular

structure, engineering problems are usually concerned

with the bulk behavior of fluids. The number of molecules

involved is immense.

Quantities such as velocity and pressure can then be

considered to be constant at any point, and changes due

to molecular motion may be ignored.

Fluid as “Continuum” (Cont.)

We are all familiar with fluids—the most common being air and

water—and we experience them as being “smooth,” i.e., as

being a continuous medium. Unless we use specialized

equipment, we are not aware of the underlying molecular

nature of fluids.

This molecular structure is one in which the mass is not

continuously distributed in space, but is concentrated in

molecules that are separated by relatively large regions of

empty space.


A region of space “filled” by a stationary fluid (e.g., air,

treated as a single gas) looks like a continuous medium, but

if we zoom in on a very small cube of it, we can see that we

mostly have empty space, with gas molecules scattered

around, moving at high speed (indicated by the gas

temperature).


Consider how we determine the density at a point. Density is defined as mass per

unit volume. The mass δm will be given by the instantaneous number of molecules in

δV (and the mass of each molecule), so the average density in volume δV is given by

density = δm /δV .

We say “average” because the number of molecules in δV , and hence the density,

fluctuates. For example, if the gas was air at standard temperature and pressure (STP)

and the volume was a sphere of diameter 0.01 μm, there might be 15 molecules in δV,

but an instant later there might be 17 (three might enter while one leaves). Hence the

density at “point” C randomly fluctuates in time.

In this figure, each vertical dashed line represents a specific chosen volume, δV, and

each data point represents the measured density at an instant. For very small volumes,

the density varies greatly, but above a certain volume, δV/, the density becomes

stable—the volume now encloses a huge number of molecules.

For example, if δV =0.001 mm3 (about the size of a grain of sand), there will on

average be 2.5*1013 molecules present.


As a consequence of the continuum assumption, each

fluid property is assumed to have a definite value at every

point in space. Thus fluid properties such as density,

temperature, velocity, and so on are considered to be

continuous functions of position and time.

Rarefied Gas Theory

Dimensions, Dimensional Homogeneity,

and Units

Any physical quantity can be characterized by dimensions.

The magnitudes assigned to the dimensions are called units.

Some basic dimensions such as mass m, length L, time t, and

temperature T are selected as primary or fundamental

dimensions.

Others such as velocity V, energy E, and volume V are expressed

in terms of the primary dimensions and are called secondary

dimensions, or derived dimensions.

Dimensions, Dimensional Homogeneity,

and Units (Cont.)

Dimensional Homogeneity

The dimensions of the left side of all theoretically derived

equations must be the same as those on the right side

Equation: V = Vo + at

Dimension: LT-1= LT-1+ LT-1

Since the dimensions on the left equal to that on the right, the

equation above is Dimensionally Homogeneous

Restricted Homogenous Equation

Equations that are restricted to particular system of units

For example, equation of freely falling body traveling the distance

“d” is;

d=4.90t2

The well known equation is;

d=gt2/2

g= 32.2 ft/s2

g=9.8 m/s2

Example:- (Restricted and general

Homogenous Equation)

Analysis of Behavior of Fluid

Different fluids have different behavior. For example, gases are light

and easily compressible while liquids are rather heavy and

incompressible.

Syrup flows slowly from a container while water flows rapidly

when poured from a container.

To quantify these differences, certain fluid properties are used.

Measurement of Fluid Mass and Weight

Density

Mass per unit volume

It varies from fluid to fluid

For Liquids, variation in temperature and pressure have a little effect

on density. At 20°C, for example, the density of water changes from

998 kg/m3 at 1 atm to 1003 kg/m3 at 100 atm, a change of just 0.5

percent.

At 1 atm, for example, the density of water changes from 998 kg/m3

at 20°C to 975 kg/m3 at 75°C, a change of 2.3 percent.

For Gases, the density strongly influenced by variation in temperature

and pressure.

Specific Volume

The reciprocal of density or volume per unit mass. This is uncommon in

fluid mechanics but commonly used in thermodynamics.


Specific Weight

Weight per unit volume

𝛾 = 𝜌𝑔

Density is used to characterize the mass of fluid while specific

weight is used to characterize the weight of fluid system.

For example, water has specific weight of 9.80 kN/m3 at 15oC.


Specific Gravity (Relative Density)

Ratio of density of fluid to the specific density of water at some

temperature. The specified temperature is taken as 4oC as the

density is 1000kg/m3 at this “T”

SG=𝜌

𝜌𝐻20 @ 4𝑜𝐶

For example, SG of “Hg” at 20oC is 13.55 so its density will be;

(13.55)(1000) = 13600kg/m3

Thus, density, specific weight and specific gravity are all

interrelated.

Ideal Gas Law

Gases are highly compressible as compared to liquid

Changes in density directly related to changes in temperature and pressure

𝜌 ≡𝑃

𝑅𝑇

P = Absolute pressure

T = Absolute Temperature

R = gas constant

Pabs = Pg + Patm

Pg is pressure relative to the atmospheric pressure.

Patm = 101 kPa

Example:- The compressed air tank shown in Fig. has a volume of 0.024m3. The

temperature is 20oC and the atmospheric pressure is 101.3 kPa.

FIND When the tank is filled with air at a gage pressure of 345 kPa,

determine the density of the air and the weight of air in the tank.

Viscosity

Fluidity of the fluid known as viscosity.

Density, specific weight are insufficient to

properly characterize the behavior of

fluid. For example, oil and water have

approximately same value of density but

their behavior is different when flowing.

Example:-

Example:-

The dynamic viscosity of water at 20°C is 1.00 × 10-3 N.s/m2, and the viscosity at

40°C is 6.53 × 10-4 N.s/m2.

estimate the viscosity at 30°C.

Example:-

A board 1 m by 1 m that weighs 25 N slides down an inclined ramp (slope = 20°)

with a velocity of 2.0 cm/s. The board is separated from the ramp by a thin film of

oil with a viscosity of 0.05 N.s/m2.

Neglecting edge effects, calculate the space between the board and the ramp.

Viscous Resistance

Viscous Resistance of Bearings

Lubrication of Bearing

1. Highly viscous oil leads to greater resistance so greater

power loss

2. Light oil may not be able to maintain the required film

between the metal surfaces results into wear and tear of

both surfaces

3. Viscosity of oil changes with temperature

Viscous Resistance (Cont.)

Power required to overcome the viscous resistance in following cases;

a. Viscous Resistance of Oiled Bearings

b.Viscous Resistance of Foot-step Bearings

c. Viscous Resistance of Collar Bearings

Compressibility of Fluids

Bulk Modulus

Volume or density of fluid changes with the change in pressure or temperature. Fluid expands as they are heated and contract as they are cooled.

The question is how compressible is the fluid is?

The property commonly used to characterize the compressibility of fluid is the “Bulk Modulus” just as Young’s modulus of elasticity in solids.

Equation:-

Example:-

Compressibility of Fluids (Cont.)

Compression and Expansion of Gases

Gases are compressible and when they are

compressed or expanded, the relationship

b/w density and pressure depends on the

nature of the process.

Isothermal Process:-

Isentropic Process:-

Equation:-

Example:-

Example:-

A 0.03m3 cubic foot of air at an absolute pressure of

101.3kPa is compressed isentropically to (0.015) m3

by the tire pump.

What is the final pressure?


Speed of Sound

A loud speaker diaphragm causes a

localized disturbances as it vibrates and the

small change in pressure created by the

motion of the diaphragm is propagated thru

air with finite velocity. The velocity at which

the small disturbances propagates is called

the acoustic velocity or speed of sound.

Equation:-

Example:-

Example:- A jet aircraft flies at a speed of 885 km/h at an altitude of

10,500 m, where the temperature is -54 oC and the specific

heat ratio is k =1.4.

Determine the ratio of the speed of the aircraft, V, to that of

the speed of sound, c, at the specified altitude.

Compressibility of Fluids (Cont.) Vapor Pressure

Evaporation

Liquid molecules at the surface have sufficient momentum to overcome the intermolecular cohesive forces and escape into the atmosphere. Vapor Pressure

Pressure exerted by saturated vapor on the liquid surface Boiling

Formation of vapor bubbles within the fluid mass is initiated when the absolute pressure in the fluid reaches the vapor pressure Cavitation

If the pressure developed in the flowing fluid is lowered than vapor pressure, boiling will occur. These produced vapor bubbles in flowing fluid are swept into the region of high pressure where they suddenly collapse with sufficient intensity to cause structural damage. The formation and collapse of vapor bubbles in a flowing fluid is known as cavitation

Compressibility of Fluids (Cont.) Cavitation (cont.) Possibility of the liquid pressure in liquid-flow systems dropping below the

vapor pressure at some locations, and the resulting unplanned vaporization.

For example, water at 10°C may vaporize and form bubbles at locations (such

as the tip regions of impellers or suction sides of pumps) where the pressure

drops below 1.23 kPa. The vapor bubbles (called cavitation bubbles since

they form “cavities” in the liquid) collapse as they are swept away from the

low-pressure regions, generating highly destructive, extremely high-pressure

waves. This phenomenon, which is a common cause for drop in performance

and even the erosion of impeller blades, is called cavitation, and it is an

important consideration in the design of hydraulic turbines and pumps. Water

hammer is caused by acoustic waves propagating and reflecting in a confined

liquid, for example, when a valve is closed abruptly. The resulting noise can be

similar to “hammering” on the pipes, hence the term


Surface Tension

It is the intensity of the molecular attraction per unit

length along any line in the surface

Depends on Temperature (𝜎 ↓as T↑)

Fluid/surface it is in contact with


Surface Tension

Noting that surface tension acts along the circumference

and the pressure acts on the area, horizontal force

balances for the droplet and the bubble give

Example:- Pressures are sometimes determined by measuring the

height of a column of liquid in a vertical tube.

What diameter of clean glass tubing is required so that the

rise of water at 20oC in a tube due to capillary action (as

opposed to pressure in the tube) is less than h =1.0 mm?


Capillary Effect

The rise or fall of a liquid in a small-diameter tube

inserted into the liquid. Such narrow tubes are called

capillaries.

1. Rise of kerosene oil through a cotton wick

2. Rise of water to the top of tall trees


Capillary Effect

Wetting fluid

Non-wetting fluid


Capillary Effect

Capillary rise

This relation is also valid for non-wetting liquids (such

as mercury in glass) and gives the capillary drop. In this

case, ∅ > 90° and thus cos ∅ < 0, which makes h

negative. Therefore, a negative value of capillary rise

corresponds to a capillary drop


Capillary Effect

Capillary rise is inversely proportional to the radius of the

tube. Therefore, the thinner the tube is, the greater the rise

(or fall) of the liquid in the tube. In practice, the capillary

effect is usually negligible in tubes whose diameter is

greater than 1 cm. When pressure measurements are made

using manometers and barometers, it is important to use

sufficiently large tubes to minimize the capillary effect.

The capillary rise is also inversely proportional to the

density of the liquid. Therefore, lighter liquids experience

greater capillary rises.

Example:-

A shaft 100mm diameter rotates at 60

rpm in a 200mm long bearing. If the

surfaces are uniformly separated by a

distance of 0.5mm and linear velocity

distribution in the lubricating oil having

dynamic viscosity 4 centipoises, find the

power absorbed in the bearing.

Example:-

A vertical shaft of 150mm diameter runs

inside a bearing at 300rpm. If the space

b/w the lower end of the shaft and the

bearing is 1mm filled with a oil of viscosity

60 poises, determine the necessary power

absorbed in overcoming the viscous

resistance.

Example:-

The external and internal radii of a collar

bearing are 100mm and 75mm

respectively. The space b/w the collar

surface and bearing is 2.5mm and is filled

with an oil. If the power lost in

overcoming the viscous resistance is

23.6W when the shaft is running at 250

rpm, find the viscosity of the oil.

Example:- The viscosity of some fluids changes when a strong electric field is applied on them. This

phenomenon is known as the electrorheological (ER) effect, and fluids that exhibit such

behavior are known as ER fluids. The Bingham plastic model for shear stress, which is

expressed as t = ty + µ(du/dy) is widely used to describe ER fluid behavior because of its

simplicity. One of the most promising applications of ER fluids is the ER clutch. A typical

multidisk ER clutch consists of several equally spaced steel disks of inner radius R1 and

outer radius R2, N of them attached to the input shaft. The gap h between the parallel

disks is filled with a viscous fluid. (a) Find a relationship for the torque generated by the

clutch when the output shaft is stationary and (b) calculate the torque for an ER clutch

with N=11 for R1=50 mm, R2=200 mm, and n=2400 rpm if the fluid is SAE 10 with µ=0.1

Pa.s, ty=2.5 kPa, and h=1.2 mm.

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