FLUID

Fluid Mechanics-I 1

FLUID MECHANICS-I

• Recommended Books: “Fluid Mechanics with Engineering

Applications” 10th EditionBy: E. John Finnemore & Joseph B.

Franzini “Fluid Mechanics with Engineering

Applications” SI Metric editionBy: Robert L. Daugherty, Joseph B.

Franzini & E. John Finnemore “Fundamentals of Fluid Mechanics”By: Musen Young

** Useful links:• http://www.civil.canterbury.ac.nz/

pubs/FM4CE.pdf

Engr. AURANGZEB 00923459026940

Prepared by: Engr. Fazal-E-Jalal

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COURSE CONTENTS

1. Introduction2. Fluid Statics3. Forces on Immersed bodies4. Fluid Kinematics5. Hydrodynamics6. Flow measurement7. Steady Flow through pipes8. Uniform flow in open channels9. Dimensional Analysis and Similitude

Before Mid Term

After Mid Term


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1.INTRODUCTION

LECTURE# 01


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Contents

• Scope of Fluid Mechanics 1. Applications 2. Branches of Fluid mechanics 3. Advancement with advent of computers• Dimensions and Units 1. British Gravitational System 2. System International 3. Scope of above mentioned systems Prepared by: Engr. Fazal-E-Jalal

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Scope of Fluid Mechanics

• Fluid Mechanics is involved in:1. Movement of clouds in atmosphere2. Flight of birds through air3. Flow of water in streams4. Breaking of waves at seashore• F.M include “gases” and “liquids”, with air

and water as most prevalent.


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• Some other aspects that include F.M are: Flow in pipelines and channels Movements of air and blood in body Air resistance or Drag Wind loading on buildings Motion of projectiles, jets, shock waves Lubrication


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Combustion Irrigation Sedimentation Meteorology Oceanography


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• A knowledge of Fluid mechanics is required to properly design:

a) Water supply systemsb) Wastewater Treatment facilitiesc) Dam Spillwaysd) Valves, Windmills, Turbines, Pumpse) Flow meters, Heating & Air-conditioning system f) Hydraulic shock absorbers and brakes


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g) Automatic transmissionsh) Aircrafts, Ships, Submarinesi) Windmills, Turbines, Pumps etc.

It is clear that every body’s life is affected by Fluid mechanics in variety of ways. All engineers should have at least a basic knowledge of fluid phenomenon.


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Fluid Mechanics

Interaction of forcesA substance which is capable of flowing

More about Fluids….

They have no definite shape of their own but

conforms to the shape of containing vessel

A fluid may be in liquid or gaseous form.

Ideal fluids are those that have no viscosity and

surface tension and they are compressible. In

practice such fluids don’t exist.

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Fluid Mechanics is the science of mechanics of liquids and gases, and is based on the same fundamental principles that are employed in the mechanics of solids.

The mechanics of fluids is more complicated subject than mechanics of solids, however, because with solids one deals with separate and tangible elements, while with fluids there are no separate elements to be distinguished.



FLUID MECHANICS

1. Fluid Statics

2. Kinematics3. Fluid Dynamics



Fluid Statics is the study of mechanics of fluids at REST.

Fluid Dynamics deals with velocities & accelerations and

forces exerted by or upon fluids in

MOTION.

Kinematics deals with velocities and

streamlines without considering FORCES or

ENERGY.




• HYDRODYNAMICS: In mathematics, it is a subject that deals with an imaginary ideal fluid that is completely frictionless.

• When dealing with liquids, this subject is called HYDRAULICS.

• Ideal fluids + Real fluids = Fluid MechanicsIdeal: HydrodynamicsReal: Liquids (Hydraulics) and gases



Dimensions and Units

• To properly define a physical property or a fluid phenomenon, one must express the property or phenomenon in terms of some sets of units.

For example, the diameter of a pipe might be 160 mm and the average flow velocity 8 m/s. A different sets of units might have been used, such as diameter of 0.16 m and velocity of 800 cm/s.




• Modern Fluid Mechanics: The basic principles of hydrodynamics are combined with experimental data.With advent of computer, during last couple of decades the entirely new field of COMPUTATIONAL FLUID DYNAMICS has been developed.Various numerical methods such as Finite differences, Finite elements, Boundary elements and Analytical elements are now used to solve problems in Fluid mechanics.




• We will be dealing with two systems of units:1. English Units (British Gravitational i.e. BG System or

US Customary System or FPS System)2. Metric Units (Systeme Internationale d’ Unites i.e.

S.I System)

Because English units have been used in the technical literature for so many years and as S.I system, nowadays, is been used by almost every country all over the world; it is essential for engineer to be familiar with both the systems.




• In fluid mechanics, the basic dimensions are:1. Length (L)2. Mass (M)3. Time (T)4. Force (F)5. Temperature (Ѳ)

First three are the basic units e.g. In F = ma , “a” i.e. acceleration is expressed by its basic dimensions as LT-2



Dimension BG System SI UnitLength (L) Foot (ft) Meter (m)

Mass (M) Slug ( = lb.sec2/ft) Kilogram (kg)

Time (T) Second (sec) Second (sec)

Force (F) Pound (lb) Newton (N) (= kg.m/s2)

Temperature (Ѳ)

Absolute Rankine (°R) Kelvin (K)

Ordinary Fahrenheit ( °F) Celsius ( °C)

In the two systems of units that we will be dealing, the commonly used units for the basic five dimensions are:




• S.I system employs L,M and T and derives F from MLT-2.

• Force in S.I is defined as NEWTON. Newton is defined as “ The force required to accelerate one kilogram of mass at rate of one meter per second” 1 Newton = (1 kg) (1 m/s2)

• On the other hand, the British Gravitational system employs L,F and T and derive Mass as F/a = FL-1T2




• Mass in BG system is defined as SLUG. Slug can be defined as “ Mass that accelerates at one foot per second when acted upon by a force of one pound”

• 1 Slug = (1 lb) (1 ft/sec2) = 1 lb.sec2/ft• 1 lb = (1 slug)(1 ft/sec2)

We see that the definition of mass in BG system depends on definition of pound, which is “ The force of gravity acting on a platinum standard whose mass is 0.45359243 kg.”Weight is defined as “ The gravitational force F between two bodies of masses m1 and m2, given by Newton’s law of Gravitation.” F = G.(m1m2)/r2Prepared by: Engr. Fazal-E-Jalal



• Where, “G” is Universal constant of Gravitation and “r” is distance between the centers of two masses.

• If “m” is mass of object on earth and “ M” is mass of earth, then “r” is radius of earth, so that;

• F = m.(GM)/r2

• Weight of object is; W = m.g where g = GM/r2




• Clearly, “g” varies slightly with altitude and latitude on earth, since the earth is not truly spherical, while in space and in other planets it is much different.

• Also, the earth’s rotation by centrifugal action reduces the apparent weight of an object by at most 0.35 % at the equator.

• Because the force depends on value of “g”, which in turn varies with location.




• BG system based on Length, Force and Time is referred as Gravitational system.

• S.I system based on Length, Mass and Time is Absolute system because it is independent of the gravitational acceleration “g”.

A partial list of derived quantities encountered in Fluid mechanics and their commonly used dimensions in terms of L,M,T & F is:



Quantity Commonly used dimensions

BG Unit SI Unit

Acceleration (a) LT-2 Ft/sec2 m/s2

Area (A) L2 Ft2 m2

Density ML-3 Slug/ft3 Kg/m3

Energy, Work or Heat FL Ft.lb N.m = J

Flow rate (Q) L3T-1 Ft3/sec (cfs) M3/sec

Frequency T-1 Cycles/sec (sec-1) Hz (Hertz, s-1)

Kinematic Viscosity(ν)

L2T-1 Ft2/sec M2/sec

Power FLT-1 Ft.lb/sec N.m/sec = W

Pressure(p) FL-2 Lb/in2 N/m2 = Pa

Specific weight (ɣ) FL-3 Lb/ft3 N/m3

Velocity (V) LT-1 Ft/sec m/s

Viscosity (μ) FTL-2 Lb.sec/ft2 N.s/m2

Volume L3 ft3 m3




• Radians don’t have dimensions, because they are defined as the arc length divided by radius.

• On earth’s surface, variation in “g” is very small and by international agreement, the standard gravitational acceleration at sea level is 32.1740 ft/sec2 or 9.80665 m/sec2 (for problem solving we usually use 32.2 ft/s2 or 9.81 m/s2)




• For unit mass (I slug or 1 kg) on the earth’s surface, we note that:

• In BG Units; W = mg = (1 slug)(32.2 ft/s2) = 32.2 N

• In S.I Units; W = mg = (1 Kg)(9.81 m/s2) = 9.81 N




• Other systems of units are:1. English Engineering System (lb-f and lb-m)2. Absolute Metric System (CGS System)3. MKS Metric System (Kg-f and Kg-m)• Both EE & MKS system are “Inconsistent

systems” whereas BG & S.I systems are “Consistent systems”.

CGS system is both consistent and non gravitational, it is little used for engineering applications because its unit of force dyne is so small; 1 Dyne = (1g)(1 cm/s2) = 10-5 Newtons.




• Non standard or Traditional abbreviations used by engineers sometimes e.g. fps, gpm, cusec etc.

• Acres, Tons, and Slugs are not abbreviated.• When units are named after people, they are

capitalized. E.g. newton (N), joule (J), pascal (Pa) etc.

• The abbreviation capital L for liter is a special case. (to avoid confusion with 1)




• We will use kg for kilogram mass and lb for pound force. The abbreviation lb for pound is taken from Latin word “libra”.

• The units second, minute hour, day and year are correctly abbreviated as s, min, h, d and y in the S.I system, and although in BG system they should be abbreviated as sec, min, hr, day and yr.




• Kelvin (K) is also abbreviated without a degree.

• UK & US Gallons. UK ( = 4.55 Liters) US (= 3.78 Liters). If not specified, assume the US gallon.

• When dealing with very large or small numbers, series of prefixes is adopted in S.I units. e.g. mega, milli, kilo etc.




• Often we need to convert quantities from BG units into S.I units, and vice versa. Conversion factors may be used.

In SI units, LENGTHS are commonly expressed in millimeters, centimeters, meters or kilometers, depending on the distance being measured.AREAS are usually expressed in square cm, square meters or hectares (ha), depending on the area being measured. 1 hectare = 10,000 m2 = 2.5 Acres




• 1 N = 0.225 lb• Units for stress in S.I are N/m2 i.e. Pascal (Pa)• 1 Pa = 0.021 lb/ft2 = .00015 psi• Units of Energy is Joule. 1 joule = 1 N.m• Unit of power is Watt (W). W = J/s = N.m/s

When we have to work with less usual units, like centipoise (for viscosity) or ergs (for energy), It is best to convert them into S.I or BG units as soon as possible.


FLUID

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