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FluidMechanics

Experiments in

Sarbjit Singh

Second Edition

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Experiments in Fluid Mechanics

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EXPERIMENTS INFLUID MECHANICS

SARBJIT SINGHAssociate Professor

Department of Civil EngineeringThapar University, Patiala

New Delhi-1100012012

SECOND EDITION

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EXPERIMENTS IN FLUID MECHANICS, Second EditionSarbjit Singh

© 2012 by PHI Learning Private Limited, New Delhi. All rights reserved. No part of this bookmay be reproduced in any form, by mimeograph or any other means, without permission inwriting from the publisher.

ISBN-978-81-203-4511-9

The export rights of this book are vested solely with the publisher.

Fourth Printing (Second Edition) . . . . . . . . . January 2012

Published by Asoke K. Ghosh, PHI Learning Private Limited, M-97, Connaught Circus,New Delhi-110001 and Printed by Mudrak, 30-A, Patparganj, Delhi-110091.

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Contents

������� ����������� ����������Fluid Mechanics: An Introduction ............................................................................................. 3

1.1 Fluid and Fluid Mechanics ........................................................................................... 31.2 Units and Dimensions .................................................................................................. 31.3 Some Physical Properties of Fluids .............................................................................. 31.4 Types of Fluids ............................................................................................................. 51.5 Fluid Pressure at a Point ............................................................................................... 51.6 Pascal’s Law ................................................................................................................. 51.7 Basic Equation of Pressure Variation in a Fluid at Rest ............................................. 51.8 Atmospheric, Absolute and Gauge Pressures .............................................................. 61.9 Measurement of Pressure by Manometers ................................................................... 6

1.9.1 Simple Manometers ......................................................................................... 71.9.2 Differential Manometers ................................................................................. 8

1.10 Hydrostatic Forces on Submerged Surfaces .............................................................. 101.11 Buoyancy and Floatation............................................................................................ 111.12 Stability of Submerged and Floating Bodies ............................................................. 111.13 Basic Principles of Fluid Flow and Control Volume ................................................. 121.14 Continuity Equation in Cartesian Coordinates .......................................................... 131.15 Types of Fluid Flows .................................................................................................. 131.16 Streamline and Stream Tube....................................................................................... 151.17 Potential Function ....................................................................................................... 151.18 Stream Function .......................................................................................................... 15

Preface viiPreface to the First Edition ix

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1.19 Flow Net ...................................................................................................................... 151.20 Bernoulli’s Theorem ................................................................................................... 161.21 Impulse Momentum Equation .................................................................................... 171.22 Kinetic Energy and Momentum Correction Factors .................................................. 181.23 Free and Forced Vortex Motions ............................................................................... 191.24 Flow Through Pipes .................................................................................................... 191.25 Types of Resistances and Losses of Energy in Pipes ................................................ 191.26 Flow Measuring Devices ............................................................................................ 221.27 Hydraulic Machines ................................................................................................... 281.28 Flow in Channels ........................................................................................................ 281.29 Methods of Measurement of Discharge in Laboratory .............................................. 291.30 Calibration of a Flow Measuring Device ................................................................... 291.31 Major Laboratory Equipments ................................................................................... 30

�������� �����������Experiment 1 Flow Through a Variable Duct Area—Bernoulli’s Experiment ................. 35

Experiment 2 Calibration of Venturimeter ........................................................................ 41

Experiment 3 Calibration of Orificemeter ......................................................................... 47

Experiment 4 Determination of Friction Factor for Pipes of Different Materials ............ 53

Experiment 5 Determination of Loss Coefficients for Pipe Fittings ................................. 59

Experiment 6 Verification of Momentum Equation .......................................................... 65

Experiment 7 Calibration of V-notch ................................................................................. 71

Experiment 8 Determination of Hydrostatic Force on aVertically Submerged Surface ..................................................................... 75

Experiment 9 Determination of Hydraulic Coefficients of Orifice ................................... 81

Experiment 10 Determination of Coefficient of Discharge of CircularOrifice Using Variable Head Method .......................................................... 87

Experiment 11 Determination of Metacentric Height .......................................................... 91

Experiment 12 Drawing of Flow Net: Hele-Shaw Method and ElectricalAnalogy Method .......................................................................................... 97

Experiment 13 Calibration of Rotameter ........................................................................... 103

Experiment 14 Transition of Flow—Reynolds Experiment ............................................... 107

Experiment 15 Free Vortex Flow ....................................................................................... 113

Experiment 16 Forced Vortex Flow ................................................................................... 119

Experiment 17 Centrifugal Pump Test Rig ........................................................................ 125

Experiment 18 Flow in a Pipe Bend ................................................................................... 131

Appendix A ................................................................................................................................ 137

Appendix B ................................................................................................................................ 143

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Preface

The book titled Experiments in Fluid Mechanics published in the year 2009 has now beenbifurcated into two books titled as below:

1. Experiments in Fluid Mechanics (It retains the same title as in the year 2009.)2. Experiments in Hydraulic Engineering

The original book published in 2009 contained 30 experiments both from the domains ofFluid Mechanics and Hydraulic Engineering. The experiments in Fluid Mechanics are prescribedfor several undergraduate branches of engineering such as civil, mechanical, production,aerospace, chemical, biotechnology, electrical (wherever prescribed), and instrumentation andcontrol (wherever prescribed). On the other hand, the experiments in Hydraulic Engineering areprescribed only for the undergraduate students of civil engineering. The bifurcation of theoriginal edition (2009) into two books has therefore been guided by the rationale explained here.

This new book, titled Experiments in Fluid Mechanics, Second Edition, now contains 18experiments selected from the prescribed curriculum of Fluid Mechanics of various universitiesand institutes. As before, these experiments are designed to be performed by the undergraduatestudents of several engineering branches who all study Fluid Mechanics as a prescribed course.In the new book, the main objectives and the format of the original edition remain the same.

The book is divided into two parts. Part I allows the students to review the fundamental theorybefore stepping into the laboratory environment. Part II provides the step-wise details of eachexperiment which include objective, brief theory of the experiment, experimental setup,procedure, observations and calculations, graphs to be plotted, and a concluding discussion ofthe experiment. The book also contains two appendices. Appendix A gives various questionsbased on each experiment to test the student’s understanding of the learned material.Appendix B gives data on physical properties of water, air and some commonly used fluids in thelaboratory, and also lists other standard data to be used in various experiments.

Suggestions and criticism for the improvement of the text will be gratefully acknowledgedand incorporated.

Sarbjit Singh

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Preface to the First Edition

This book has been written to guide the undergraduate students of various branches of engineeringin conducting laboratory experiments in Basic Fluid Mechanics as well as in Advanced FluidMechanics. The book is an outcome of the author’s experience of teaching these subjects for morethan 15 years, and developing the fluid mechanics laboratory for conducting experiments.

Thirty experiments have been selected from the syllabi of courses on Basic Fluid Mechanicsand Advanced Fluid Mechanics. The first fifteen experiments are designed to be performed bythe students of several branches of engineering studying fluid mechanics as a common course(Civil, Mechanical, Electrical, Instrumention and Control, and Chemical Engineering). Theremaining fifteen experiments are meant to be performed by the students of Civil Engineeringand Mechanical Engineering, who study another advanced course on Fluid Mechanics.

The book is organized into two parts. Part I presents the basic related theory of all theexperiments to be performed. Part II gives the step-wise details of various experiments whichinclude objective, theory, experimental set-up, procedure, observations and calculations, graphsto be plotted, and a concluding discussion of the experiment. A rough observation sheet is attachedto each experiment to record observations during the course of the experiment. This observationsheet should be signed by the teacher after completion of the experiment. The normal/log-loggraph sheets are attached with the experiments, wherever required. Appendix A gives severalquestions based on each experiment. Appendix B gives data on physical properties of water, airand some commonly used fluids in the lab, and also lists some other useful data related to theexperiments.

Suggestions and criticism for the improvement of the text will be gratefully acknowledged.

Sarbjit Singh

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A fluid may be defined as a substance which is capable offlowing. A fluid at rest does not offer any resistance to theshear stress, i.e. it deforms continuously as long as shearstress is applied. It has no definite shape of its own, butconforms to the shape of the containing vessel.

Fluid mechanics is that branch of science which dealswith the study of fluids at rest as well as in motion. Itincludes the study of all liquids and gases but is generallyconfined to the study of liquids and those gases only forwhich the effects due to compressibility may be neglected.

In general, the study of fluid mechanics may be dividedinto three categories, viz. fluid statics, fluid kinematics, andfluid dynamics. Fluid statics is the study of fluids at rest.Fluid kinematics is the study of fluids in motion withoutconsidering the forces responsible for the fluid motion.Fluid dynamics is the study of fluids in motion with forcescausing flow being considered.

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A dimension is a name used to describe the measurablecharacteristics of an object in terms of mass, length, time,temperature, etc. A unit is an accepted standard formeasuring the dimension. The various dimensions used influid mechanics are expressed in four fundamental

Fluid Mechanics: An Introduction

dimensions, viz. mass, length, time, and temperature.Temperature is used only for compressible fluid flows.These fundamental dimensions can be measured in any oneof the systems of units, viz. CGS, MKS and SI. SI (SystemInternational) system of units is used nowadays. Thefundamental units of fundamental dimensions in SI systemare shown in Table 1.1. Besides these fundamental units,there are a number of other derived units which areexpressed in terms of fundamental units.

Table 1.1

Fundamental dimensions Fundamental units

Mass (M) kilogram (kg)

Length (L) metre (m)

Time (T) second (s)

Temperature kelvin (K) or oCelsius (oC)

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Mass density: Mass density of a fluid is the masswhich it possesses per unit volume at a standardtemperature and pressure (STP). It is denoted by the symbol� (rho) and is also known as specific mass. Therefore, massdensity,

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m� =

∀ (1.1)

where m is the mass of fluid having volume �.

The unit of mass density in SI system iskg/m3 and its value at standard temperature and atmosphericpressure (STP) for water at 4oC is 1000 kg/m3 and for airat 20oC is 1.24 kg/m3.

Specific weight: Specific weight of a fluid is its weightper unit volume at STP and is denoted by � (gamma).Specific weight is also known as weight density or unitweight. Therefore, specific weight

W� =

∀ (1.2)

where W is the weight of fluid having volume �.

SI unit of specific weight is N/m3 and its value for waterat STP is 9810 N/m3.The specific weight of a fluid changesfrom one place to another depending upon the changes inthe gravitational acceleration, g. The mass density andspecific weight are related to each other as

� = �g (1.3)

Specific gravity: Specific gravity of a fluid is the ratio ofspecific weight (or mass density) of the fluid (�s) to thespecific weight (or mass density) of a standard fluid. Forliquids, the standard fluid is taken as water at 4°C, and, forgases, the standard fluid is air or hydrogen at somespecified temperature and pressure. Specific gravity is alsoknown as relative density and may be denoted by G or S.Thus,

s

wG

�

�� (1.4)

By knowing the specific gravity of any fluid, its specificweight can be calculated.

Specific volume: Specific volume is the volume per unitweight of fluid. Thus, it is the reciprocal of specific weight.The term ‘specific volume’ is most commonly used in thestudy of compressible fluids.

Viscosity: Viscosity is primarily due to cohesion andmolecular momentum exchange between the fluid layers. Itis defined as “the property of a fluid by virtue of which thefluid offers resistance to the movement of one layer of fluidover an adjacent layer and, as the fluid flows, this effectappears as shear stress acting between the moving layers offluid”. The fast moving upper layer exerts a shear stress onthe lower slow moving layer in the positive direction offlow. Similarly, the lower layer exerts a shear stress on theupper moving fast layer in the negative direction of flow.

According to Newton, shear stress (�) acting betweenthe fluid layers is proportional to spatial change of velocitynormal to flow, i.e. shear stress,

�dudy

∝

or

� �dudy

= (1.5)

where � (Greek ‘mu’) is a constant of proportionality andis called coefficient of viscosity or dynamic viscosity orsimply viscosity of the fluid. The term (du/dy) is calledvelocity gradient at right angle to the direction of flow.

Equation (1.5) is known as Newton’s law of viscosity.The units of � in different systems are shown in

Table 1.2.

Table 1.2

System Units of �

SI Ns/m2 = Pa � sMKS kg(f) � s/m2

CGS dyn � s/cm2

The unit dyn�s/cm2 is also called poise (P) and 1P = 1/10Pa�s. A poise is a relatively large unit, hence the unitcentipoise (cP) is generally used and 1 cP = 0.01 P.Viscosity of water and air at 20oC and at standardatmospheric pressure are 1.0 cP and 0.0181 cP respectively.

Kinematic viscosity: Kinematic viscosity is the ratio ofdynamic viscosity (�) to the mass density (�) and is denotedby the symbol � (Greek ‘nu’).

��

�= (1.6)

In SI units, � is expressed as m2/s. In CGS system, it isexpressed as cm2/s. The unit cm2/s is also termed stoke and1 stoke = 1 cm2/s = 10–4 m2/s. Also, 1 centistoke = 0.01 stoke.

Surface tension and capillarity: Liquids havecharacteristic properties of cohesion and adhesion. Surfacetension is due to cohesion, whereas capillarity is due toboth cohesion and adhesion.

Surface tension is the property of a liquid by virtue ofwhich the free surface of liquid behaves like a thinstretched membrane. It is a force required to maintain unitlength of free surface in equilibrium and may be denoted by� (Greek ‘sigma’). In SI units, surface tension is expressedas N/m. Surface tension values are generally quoted forliquids when they are in contact with air, e.g. � for air–

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water interface (at 20 oC) is equal to 0.0736 N/m and, forair–mercury interface, it is equal to 0.4944 N/m.

Capillarity is the phenomenon of rise or fall of liquidsurface relative to the adjacent general level of liquid. It isalso known as meniscus effect. The rise of liquid surface isknown as capillary rise and the fall of liquid surface ascapillary depression. Capillary rise will take place whenadhesion is more than cohesion and fall will occur whencohesion is more than adhesion. It has been observed thatfor tubes of diameters greater than 5 mm, the capillary riseor fall is negligible. Hence, in order to avoid a correctionfor capillarity effects, diameter of tubes used in manometersfor measuring pressure should be more than 5 mm.

Compressibility: Compressibility of a fluid is expressedas reciprocal of bulk modulus of elasticity. In case ofliquids, effects of compressibility are neglected, howeverin some special cases such as rapid closure of a valve (as inwater hammer phenomenon), where changes of pressureare either very large or sudden, it is necessary to considerthe effects of compressibility.

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Fluids are classified into two types, viz. ideal fluids and realfluids. Ideal fluids are those fluids which have no viscosity,surface tension and compressibility. These fluids areimaginary and do not exist in nature. No resistance isencountered to these fluids, as they move. The concept ofideal fluids is used to simplify the mathematical analysis offluid flow problems. Real fluids possess viscosity, surfacetension and compressibility and these fluids are actuallyavailable. As such, certain resistance is always encounteredto these fluids when they move. Water and air, though realfluids, have very low viscosity and, therefore, they aretreated as ideal fluids for all practical purposes without anyappreciable error.

Real fluids are further of two types, i.e. Newtonian andnon-Newtonian fluids. Newtonian fluids are those fluidswhich obey Newton’s law of viscosity, i.e. for Newtonianfluids there is a linear relationship between shear stress andvelocity gradient, e.g. water, air, etc.

Non-Newtonian fluids are those fluids which do notobey Newton’s law of viscosity. The viscous behaviour ofnon-Newtonian fluids may be given by the power lawequation of the type,

�

ndu

kdy

⎛ ⎞= ⎜ ⎟⎝ ⎠(1.7)

where k is called consistency index and n is called flowbehaviour index.

Examples: Milk, blood, liquid cement, concentratedsolution of sugar, etc.

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When a fluid is contained in a container, it exerts a force atall points of the container. The force so exerted per unitarea is called fluid pressure or intensity of pressure (p), i.e.

Fp

A= (1.8)

where F is the pressure force and A is the area on which thefluid pressure acts.

The fluid pressure on a surface always acts normal tothe surface. This is because of the fact that a fluid at restcannot sustain shear stress.

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According to the Pascal’s law, the intensity of pressure atany point in a fluid at rest is same in all directions. Thisimplies that when a certain pressure is applied at any point,it is equally transmitted in all directions.

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According to this equation, there is no variation of pressurein the longitudinal direction (x-direction) and transversedirection (z-direction) and the pressure varies only alongthe vertical direction (y-direction). Mathematically,

0px

∂ =∂

, �p

gy

∂ = −∂

and 0pz

∂ =∂

(1.9)

Negative sign in the equation signifies that pressuredecreases with increase in y, i.e. elevation.

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1. Equation (1.9) can be written as

�dp

gdy

= − (1.10)

Equation (1.10) can be integrated to find thedifference in pressure between two points (say 1and 2) in a fluid placed in a container. Thus, we get

� �

1 21 2

p py y

g g⎛ ⎞ ⎛ ⎞+ = +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

(1.11)

where p1 is the fluid pressure at point 1, y1 is theelevation of point 1 from some assumed datum

Experiments In Fluid Mechanics

Publisher : PHI Learning ISBN : 9788120345119 Author : Sarbjit Singh

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