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Force on the face All '" fI. Spocific Volume 2 1. Then pressu re in the right limb above Y-Y. UllfJmNl'r re l lillg. From eq uation 1. Int roduction 7. Jet Propulsion

You Save: Buy This product. Snapshot About the book. Table of Contents: Properties of Fluids 2. Pressure and Its Measurement 3. Hydrostatic Forces on Surfaces 4. Buoyancy and Floatation 5.

Kinematics of Flow and Ideal Flow 6. Dynamics of Fluid Flow 7. Orifices and Mouthpieces 8.

Notches and Weirs 9. Viscous Flow Turbulent Flow Flow Through Pipes Dimensional and Model Analysis Boundary Layer Flow Forces on Sub-merged Bodies Compressible Flow Flow in Open Channels Impact of Jets and Jet Propulsion Hydraulic Machines - Turbines Centrifugal Pumps Reciprocating Pumps Mechanical Engineering Objective Type.

Engineering Heat And Mass Transfer. Objective Mechanical Engineering. Mechanical Engineering Test Preparation: Part 1. Industrial Automation and Robotics.

U n iform F low 5. Uniform Potential Flow P afaliel toy-Axis 5. Sou rce Flow Sink Flow Solved Problems 5.

Free-Vortex Flow 5. Source and Sink Pair Solved Problems 5. Doublet Solved Problem 5. Chapter 6. Dynam ics or Fluid Flow 6. Int rodu ction 6. Equ a tion s of Motion 6. Euler's Eq uation of Motion 6. Bernoulli's Equation from Euler's Equation 6. As s um ptions Solved Problems 6.

P ractica l Applications of Bernoulli's Equation 6. Vc nlurimctcr Soh, 'od Problems 6. Pilot-tube Solved Problems 6,,28 6. The Momentum Equation Solved Problems 6. Moment of Momen tum Equation Solved Problems 6. Free Liquid J ets Solved Problems 6. Orifices and Mouthpi eces ;'14 7. Int roduction 7. Classifications ofO rifiees 7. Flow Through an Orifice Hydraulic Co-efficients 31' 7.

Determination of Co-efficient or Discharge C d ' 7. Determination of Co-efficient or Velocity C. Flow Through Large Orifices 7.

Classification of Mouthpieces 7. Notches an d We ir s 8. Cl a ssification of Notches and Weirs 8. For Rectangular Weir Or Notch 8. Velocity of Approach Solved Problems 8. Cipolletti Weir or Notch Solved Problems 8. Discharge Over a Broad-C rested Weir Discharge Over an Ogee Weir 8.

Viscous Flow 9. Introduction 9. Kinetic Energy Corn dion and Mom! Power Absorbed in Viscous Flow 9. M lthods of Dt t.. Capillary Tube Method 9. Falling Sph.. Rotating Cylinder Method 9. Turbulent Flow Introduction Reynold s Experiment Frictional Loss in Pipe Flow Expression for Co-effici..

Reynold s Expression for Tu rbulent Shear Stress Velocity Distribution in Turbulent Flow in Pipes Hydrodynamically Smooth and Rough Boundaries Velocity Dis.

Flow Through Pipell Loss of Energy in Pipes Minor Energy H ead Losses Loss of Head Due to Sudden Enlargement Loss of Head at the Entrance of a Pipe Loss of Head at the Exit of Pipe Loss of Head Due to an Obstruction in a Pipe Loss of Head Du e to Bend in P ipe Hydraulic Gradient and Total Energy Line Hydraulic Gradi en t Lin e Flow Through Syphon Solved Problems Equivalent Pipe Solved Problem Power Transmission Through Pipes Condition for Maximum Transmission of Power Flow Through Nozzles Power Transmitted Through Nozzle Diameter of Nozzle for Maximum Transmission of Pow..

Water Hammer in Pipes Gradual Closure of Valve Sudden Closure or Valve and Pipe is Rigid Sudden Closure of Valve and P ipe is Elastic Pipe Network Hardy Cross Method Solved Problem Dime n s ional and Mo d e l Ana lysis Secondary or Derived Quantities Solved Problem Dimensio nal Homogeneity Methods of Dimensional Analys is Rayleigh's Method Solved Problems Buckingham's 1!

Method of Selecting Repeating Variables Procedure for oolving Problems by Buckingham's 1! Model Analysis Similitude-Types of Similarities Types of Fort. Dimensionless Numbers Reynold's Number R. Froude's Number F, Euler's Number E " Weber's Number IV, Turbulent Boundary Layer Distorted Mod els Model Laws or Similarity Laws Reynold's Model Law Solved Problems Analysis of Turbulent Boundary Layer lS. Classification of Model s Weber Model Law Boundary Layer Flow La minar Boundary Layer Separation of Boundary Layer Energy Thickness lin Solved P roblems Mome ntu m T hickness 9 Definitions Eu ler's Model Law Mach Model Law Solved Problem Location of Sepa ration Point Solved Problem Stream-lined Body Equation of Sta te Drag Fonce Acting on a Rotating Cylinde r Pressure Drag and Friction Drag ElI"pansion and Compression of Perfect Gas Forces on Sub-merged Bodies Magnus E ffect Solved Problems Expression for Drag and Li ft Development of Lift on an Airfoil Compressible Flow Bluff Body Drag on II Cylinder Lift Steady-state of a Flying Object Solved Problems Drag Thermodynamic Relation s Veloeity of Sound in Terms of Bulk Modulus Expression for Stagnati.

Vdoci ty of Sound fo r Adiabatic Process Zone of Action Mach Number Solved Problems Momentum Equations Continuity Equation Mach Angle Basic Equations of Compressible Flow Value of II or!! Zone or Silence Solved Problems Bernoulli's Equation Solved Problems Area Velocity Relation ship for Compressible Flow Stagnation Properties Velocity of Sound for Isothe rmal Process Expression for Stagnation Pressure p.

Expression for Stagnation Density p. Steady Flow and Unsteady Flow Alternate Depths Critical Flow Non-Uniform Flow through Open Channels Most Economi cal Section of Channels Specific Energy and Specific Energy Curve Hydraulic Jump or Standing Wave Exprf'ssion for Depth of Hydraulic Jump Critical Velocity Ve Classification Qf flow in Channels Cri t ical Depth he Jet Propulsion of Ships Solved P roblems Length of Hydraulic Jump Solved Problems Back Water Curve and Affux Force Exerted by a Jet of Water on a Series.

Gradually Varied Flow G. Jet Propulsion Definitions Solved Problems Pelton Wheel or Turbine Unit Quantities Radial Flow Reaction Turbines Characteristic Curves of Hydraulic Turb ines Unit Discharge IS. Hy d r a u li c Mlic hin es--Turbines Unit Powe r Types of Draft Tubes Draft-Tube IS. Velocity Triangles and Work Don". General Layout of a Hydroe lectric Power Plant Axial Fl w Readion Tu rbine Specific Speed IS.

Definitions of Heads and Efficiencies of a Turbine Uni t Speed Turbines Derivati n of the Specific Speed IS. Francis Tu rbine Classification of Hydraulic T urbines Use of Unit Quantities N. Degree of Reaction IS.

Draft-Tube Theory IS. Constant Efficiency Curves Priming of a Centrifugal Pump Hydraulic Machines Subjected to Cavitation Multistage Centrifugal Pumps for High Heads Operating Characteristic Curves Effects of Cavitation Main Characteristic Curves Centrifugal Pumps Cavitation in Centrifugal Pump Solved Problem Cavitation in Turbines Cavitation Main Parts of a Reciprocating Pump Main Parts ofa Centrifugal P ump Specific Speed of a Centrifugal Pump N.

Maximum Suction Lift o r Suction Height Constant Efficiency Curves or Musche! Curves or Iso-Efficiency Curves Multistage Centrifugal Pumps Governing ofl'urbines Highlights Exercise Chapler Slip of Reciprocating Pump Leverage of the Hydraulic Press Capacity of Hydraulic Accumulator Solved Problems Differential Hydraulic Accumulator Indicator Diagram Actual Heavy Hydraulic Press Solv. Work Done by Redprocating Pump The Hydraulic Accumulator The Hydraulic Press The Hydraulic intensifier Solved Problems Negative Slip of the Reciprocating Pump F l uid System 1.

Mechanical Advantage Classification of Reciprocating Pumps Solved Problems The Hydrauli c Ram Solved Problems 2 1. Air Vessels Solved Problems The Hydraulic Lift Direct Acting Hydraulic Lift Suspended Hydraulic Lift Solved Problems The Air Lift Pump The Hyd raulic Torque Converter 10'" The Fluid or Hydraulic Coupling The Hydraulic Crane Solved Proble ms The density of liquids ma y be cOrlsidercd as COrlSlant while that of gases changes with th e variation o f pressure and temperature.

Specific weig ht or weight density of a fluid is the ratio between the weight of a fluid to its volume. Thus this branch of scienl'C deals WiTh the stat ic. It is denoted by the symbol p rho. DensiTy or mass densi ty of a fluid is defincd as the ratio of the mass of a fluid TO its volume.

Thus weight per unit volume of a fluid is called weight density and it is denoted by the symbo l w. The unit of mass density in SI urlit is kg per cubic metre. The study of fluids at rest is called fluid statics.. The study of fluids in Illotion. Th us mass per unit vo lum e of a Iluid is called density. Thus mathematically.

Specific gravity is defined as the rali o of th e weight densit y or de nsity of a fluid to the weight de nsit y o r den sity uf a standard fluid. Mathem aticall y. It is commonly applied 10 gases. Mathemat ically. For exa mple.. For liquids. Specific volu ille of a fluid is defi ned as the volume of a fluid occupied by a unit mass or volum e per unit mass of a fluid is callcd specific vo lu11Ie..

Specific gravity is nlso called relntivc dens it y. It is c. Problem 1. When twO laye rs of a fluid.. OO[ IV ". This shear stress is propo rtional to the rate of c han ge of ve- locit y with respec t to y. Gi ven: Th e uni ts of viscosity is obtained by putt ing the dimcnsions o f the quantities in cq uation 1. Mathe maticall y. Area ". POiSC c m' em ' 1 Th us for solving numerical prob lems.

OJ poise or 1. In CGS units.. The 1: P rtf' '" Centipoise Length 1. Somclimcs a unit of v. Alt rrnllil' Mdhod. P '" Poise 1 The visco..

It SImes that1h" she ar sIres. P " Constants for the liquid ror water. In liquids. Bul in case of gas. S Types of Fluids With the increase in tempera ture. Ideal plastic fluid. Equation 1. All lhe nuids. Equation I. P'" 0. A fluid. Non -New tonian fluid. A real fluid. Ideal Plastic Fluid.. Ihe cohesive forces decreases wilh the resuh o f decreasing viscosity.

Ideal nuid.. I Fo r liquid s. R"nl Fluid. Non -Newtonian Fluid. Temperature affects the viscosity. The relation between viscosity and temperatu re for liquid. Real fluid. The viscosity of liquids dcneasc s with Ihe increase of tcmpcrmurc while Ihe viscosity of gases inncascs with the increase of tempermure. This is duc to reason that Ihe viscous forces in a fluid arc duc to cohesive forces and molecular momentum lransfcr. Newtonian fluid. Problem Take dYllamic I'iscosify offtllid IS 8.

Id"al Fluid. The fluids may be classified into the following five types: Fillillile fora mill po. Using lhe equalion X 10 poise '" tl.

Iatp of sic. The w. III'ss of oil fillll is J. Area uf the plate. Shear force. S x to 1 III Speed of shaft. Speed of plate relative 10 anOlhcr plale. I Ns Solullon. Area of plate. Eacll shit' of II. Dista nce between plates. Shear stress is given by equ ati on I" lly" 1. I' oil ill poiSi'. Component of weight IV.

IIPP"f pllllr. Eac h s id e of a square pla te.. Area 0. Solutio n. Area A 0. Velocity grad ien t. I" mill kin"". Ma ss densit y. Density of wate r Problem 1.

I' 4 Viscosity. Usi ng th e relation v:: Kinematic viscosi ty v:: G iven: III Thic kn ess of oil fi lm. Speed o f shaft. Wall 60 '" I I Ii..

I'" 1. If ' 10 In m Problem 1. F '" Shcar stress x Area '" x1tDxL". Gi ve n: Shear Str 'sses till Shear stress is g iven by. Veloc ity grad ient. T heir va lues are dctc nnincd from boundary cond ition s as: Let speed of sleeve is "2 when force. If " torqut' of J2. Solu t ion.

Speed of sleeve. Viscosity of g lyce rine. Let th e viscusit y. Wh en the thin plate is in the middle of the tw o plane surfaces 1Re fer to Fig. Distan ce Iwtw".

I-l x. Thl' Spllcr b. CaSt' II. Ihrough Ihe gap. ISN 0. When the thin plalc is at 11 distanceofQ. IOx 10 x. Ulem 2. Width of gap " 2. Jl" 2. I Lei Ihe lltil1 plate is al a distance 0. When plale is in the m iddle of the gap.

Ihe shear force on Ihe Tight side of the metallic plale. Bul gas. If Ihe c hange in de nsity occu rs a1 co nstanl temp erature. The gas constant..!!. T he rel ati onship be twee n press ure absolut e. K For air.. One kilogram mole is defined as the product of One kilogrlllll mass oflhe gas and its molecular weight. IlImi"8 i.

Weight den s ity. Dnfr- Find i prl'. A ssuml'. For temperature. Using equation 1. K which is defined as Ih". For Iso thermal Proces! LeI 'V" Volume of a g as cnclo.. Increase uf pn: Pina l press ure " Nlc m 2. Final vol ume.

K is given by cqu31io n 1. Il '" Constant Differentiating. Usi ng equat ion 1. II" liqllid durNlus by O. Solu llon. All the molecules on the free surface experience a downward force. The I1wgnitudc of this force per uni t icngth of Ih. It is denoted by Greek Idlef 0 calkd sigma. The molecule C. Th us the resultant force actirlg on the molecule A is zero. C of a liquid in a mass of liquid. Let the droplet is cut into two halves.. Thus the free surfa.

Thus a net result.: The phenomenon of surface tension is explained by Fig.. On the enlire surface oflhe droplel. In M KS units. But the molecule IJ. Consider 11 small spherical droplet of a liquid of radi us. Su rface tensioll. A llOliow bubble like a soap bubble in air has 1WO surfaces in co ntact wilh air. COil sider a liquid jet of diameter "tf and lenglh 'L' as shown in Fig. I' in exc ess of outside pressure is.

Lli e.

Solut ion. Thus two surfaces arc subjected to surface lensioll. III suc h cao. Capillarity is defined as a phenomenon of rise or fall of a liquid surface in a small! The rise of liquid surface is known as capi lla ry rise while the fall o f the liquid surface is known as capillary depression. Under a state ofeq uilihrium. E IJress ion fur Cljllillary Risc.

But the force at he surface of the liquid in Ihe tube is due to surface Tensioll. Its val ue depends upon the specific weight of the liquid.

Consider a glass lube of small diameter 'd' opened at ooth ends and is inserted in a liquid. The liquid wi ll rise in the tube aoove the level of the liquid. Surface tension. IF '" pg h. P '" pgll 4 4 Equal ing the IWO.. Take surfllce lellsiollS 0'" 0. Theil in equilibrium.

SCl"Ond force is due to hydrostatic fo rce acting upward and is equal 10 inlensity of pressure al a deplh '11' x Area 1. Iflhe g lass lube is dipped in mercury. Ail S.. The negalive sign ind icmcs the capill: Capi lI ary rise.

Tllia' drllsity of. J m II x 05 x Tangc mi a l veloc ity of shan. Tile IIIirk1l1'S. IOOOx 9. J III: The bubbles of these vapouT5 arc carr ied by the flowing liquid into th e region of high pressure where they collapse. When vaporization lakes place. These vapour molecules ge t accumulated in Ihe space between th e free liquid s urface and top of the vessel. When Ih e v. Ihe boil in g of the liqu id wi ll stan.

If Ihe pressure is reduced to such an exten t that it bccotnes equal to or less than the vapour pressure. Ihe molecules escapes from Ihe free surface of Ihe liquid. If The pressure at any point in this flowing liqu id becomes equal to or less Ihan the vapour pressu re. The vaporization whkl!

The metallic surfaces. These accumula ted vapou rs exen a pressure on Ihe liquid su rface. Consider a liquid say waler whic h is confined in a c losed vesse l.

IS kW. Thus a liquid may boil even at onlinary lcnlperature. Watts or. The pressure developed by the collapsing bubbles is so high that the material from The adjoining boundaries geTS eroded and c aviTi es are formed on them. If the pressur" above th e liquid surface is reduced by so me means.

This phenomenon is kno wn as ". It is also cqualto. To convert the unil of viscosity from poise to MKS units.

Differentiate between: Specific volume is the reciprocal of mass density. What is the difference between dynamic viscosity and kinematic viscosity? State their units of mcasuremcnlS. Define the following fluid propenie.

Pa '" Pascal. The shear stress is proponiOllal 10 the velocity gradient "" 4. For isolhcmlal process. For a perfect gas.. Give their dimensions. The "elocity distribution for flow oVer a flat plate i. The cleamnec is Explain the len".

Newtonian and Non-Newtonian fluids. One litre of crude oil weigh' 9. Assume dynamic viscosity as 8 poise. Why does the viscosity of a gas increases with the increase in temperature while that of a liquid decreases with increase in temperature? EXplain the phenomenon of capillarity. Define compressibility. Define surface tension. Whal do you understand by tenns: I lsothennal process.

The weight of thc square is 3'n. No8pur Unil'ersity [Ans. W hat. Obtain an expression for capillary rise of a liquid. An oil film of thickness 1. I kgls-m dynamic viscosity in poise. Deflne and explain Newton 's law of viscosity. Two plates arc placed at a distance of 0. Detennine the fluid viscosity between the plates in the poise. Enunciale Newton's law of. Find the dynamic viscosity of the oil. Explain the importance of viscosity in n uid motion.

Calcu late ilS specific weight. The lower plate is fixed while the upper plate having surface area 1. State the Newton's law of viscosity and Kjve examples of its application. A plate 0. Explain thc importance of compressibility in fluid flow. The weight of a gas is given as In 'luestion If the velocity distribution of a fluid over a plate is gi.. The diametcr of shaft is 0. Calculate lhe shear StreSS al1he poin!.. Molccular weight of nitrogen is Calculale the "clocity gradic and shear stress at distances of O.

Find Ihe surface Icnsion in a SD. In a stream of glycerine in 1Iion. The thickness of the oil fihn is 1. IXlO rn' or 8. DClcmlinc 1he viscosily of a liquid having kincmalic ". IAn s. Ihe shear stress is 0. An oil of viscosity 5 poise is used for lubrication belween a shaft and slecve.

The air is cornpres. The pressure inside a droplet of waler is 10 be 0. The pressure oUlside the droplel of water of diameter 0. The surface lension of watcr in contact with air at 20"C is gh'cn as 0. Calculale the power losl in Ihe oil for a sk'"CYe lenglh of nnn.