Mechanics of Fluids 2 Marks (ALL-Units)

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    MECHANICS OF FLUIDS

    Two Marks Questions & Answers

    UNIT I : DEFINITIONS AND FLUID PROPERTIES

    1. Define density or mass density.Density of a fluid is defined as the ratio of the mass of a fluid to its volume.

    Density, = mass/volume (Kg/m3)water = 1000 Kg/m3

    2. Define specific weight or weight density.Specific weight or weight density of a fluid is defined as the ratio between the weight of a

    fluid to its volume.Specific weight, = weight/volume (N/m3) =

    gwater = 9810 N/m3

    3. Define specific volume.Specific volume of a fluid is defined as the volume of fluid occupied by an unit wt or unit

    mass of a fluid.Specific volume vs = volume/ wt = 1/ = 1/g ----- for liquidsSpecific volume vs = volume/ mass = 1/ ----- for gases

    4. Define dynamic viscosity.Viscosity is defined as the property of fluid which offers resistance to the movement of

    one layer of fluid over another adjacent layer of the fluid.

    du = ---------dy

    - dynamic viscosity or viscosity or coefficient of viscosity (N-s/m2)

    1 N-s/m2 = 1 Pa-s = 10 Poise

    5. Define Kinematic viscosity.It is defined as the ratio between the dynamic viscosity and density of fluid.

    = / (m2/s)

    1 m2/s = 10000 Stokes (or) 1 stoke = 10-4 m2/s

    6. Types of fluids.Ideal fluid, Real fluid, Newtonian fluid, Non-Newtonian fluid, Ideal Plastic fluid.

    7. Define Compressibility.It is defined as the ratio of volumetric strain to compressive stress.

    Compressibility, = (d Vol/ Vol) / dp (m2/N)

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    8. Define Surface Tension.Surface tension is defined as the tensile force acting on the surface of the liquid in

    contact with a gas or on the surface between two immiscible liquids such that the contactsurface behaves like a membrane under tension.

    Surface Tension, = Force/Length (N/m)

    water = 0.0725 N/m Mercury = 0.52 N/m

    9. Surface tension on liquid droplet, = pd/4Surface tension on a hollow bubble, = pd/8Surface tension on a liquid jet, = pd/2

    - surface tension (N/m) d- diameter (m)p - pressure inside (N/m2)

    ptotal = pinside + patm patm = 101.325 x 103 N/m2

    10. Define Capillarity.

    Capillarity is defined as a phenomenon of rise or fall of a liquid surface in a small tuberelative to the adjacent general level of liquid when the tube is held vertically in the liquid.The rise of liquid surface is known as capillary rise while the fall of liquid surface is known ascapillary depression.

    Capillary Rise or fall, h = (4 cos) / gd

    = 0 for glass tube and water = 130 for glass tube and mercury

    11. Define Vapour Pressure.When vaporization takes place, the molecules start accumulating over the free liquid

    surface exerting pressure on the liquid surface. This pressure is known as Vapour pressure of

    the liquid.

    12. Define Control Volume.A control volume may be defined as an identified volume fixed in space. The boundaries

    around the control volume are referred to as control surfaces. An open system is alsoreferred to as a control volume.

    13. Types of fluid.Ideal fluid - ideal fluids are that fluid which has no viscosity, surface tension and they are

    incompressible. They are imaginary fluids. It is used to simplify the mathematical analysis ofliquids in motion.

    Real fluid - the real fluids are those fluids which posses the properties such as viscosity,

    surface tension and compressibility. These fluids are actually available in nature.Newtonian fluid - a real fluid in which the shear stress is directly proportional to the rate

    of shear strain is known as Newtonian Fluid. Such type has a constant coefficient ofviscosity. There is a linear relation between shear stress and rate of shear strain.

    Non-Newtonian fluid - a real fluid in which the shear stress is not proportional to the rateof shear strain is known as Non-Newtonian fluid. There is non-linear relation between shearstress and rate of shear strain.

    Ideal Plastic - a fluid in which shear stress is more than the yield value and shear stress isdirectly proportional to the rate of shear strain and known as Ideal Plastic Fluid.

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    14. Define cavitation.If any flow system the pressure at any point in the liquid approaches to vapour pressurebubbles of vapour are formed. When they exposed to high pressure region they collapse.The pressure developed by collapsing bubbles erodes the material and cavities are formed.This phenomenon is known as Cavitation.

    15. Define system.A system is defined as a chosen lump of fluid in space, which is considered for the

    analysis of a given problem. It is also referred as fluid element. This is generally infinitelysmall but could be bigger depending up on the problem under consideration.

    Types of system:Open system - in which mass & momentum can enter & leave the system throughboundaries. It is used in fluid mechanics.Closed system - used in thermodynamics.Isolated system.

    16. What is mean by continuum?

    The analysis of all fluid flow problems assures that the fluid is in a state of continuumand all the properties of the fluid are considered to be continuous function of spacevariables. Concept of continuum assumes continuous distribution of mass within the matterunder the consideration of a fluid with no gaps or voids in it.

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    UNIT II : FLUID STATICS & KINEMATICS

    Pressure Measurement

    1. Define Fluid Pressure.The normal force excreted by a fluid per unit area of the surface is called fluid

    pressure. It always acts perpendicular to the surface in contact.

    2. State Hydrostatic law.The rate of increase of pressure in a vertical direction is equal to specific weight

    of the fluid at that point.

    p/z =

    p = gH --- for Incompressible fluid flow

    3. State Pascals LawThe pressure (pressure intensity) at any point in a fluid at rest has the same

    magnitude in all directions. In other words when a certain pressure is applied at anypoint in a fluid at rest the pressure is equally transmitted in all directions.

    px = py = pz

    4. List the machines which use Pascals Law.(a) Hydraulic Jack(b) Hydraulic Crane(c) Hydraulic Lift(d) Hydraulic Riveter, etc

    5. List the various types of pressure(a) Atmospheric Pressure(b) Absolute Pressure(c) Gauge Pressure(d) Vacuum Pressure (or) Suction Pressure

    Draw the diagrammatic representation of types of pressure

    B

    +ive Gauge Pressure at - BAbsolute pressure at - B

    Atmospheric Pressure

    Vacuum Pressure at - AOr

    A-ive Gauge Pressure at - A

    Absolute pressure at - A

    Absolute Zero

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    Write the relationship among various types of pressures.

    Absolute Pressure = Atmospheric Pressure + Gauge Pressure

    pabs. = patm + pgauge

    Absolute Pressure = Atmospheric Pressure - Vacuum Pressurepabs. = patm - pvacuum

    6. Define manometer.The manometers are defined as the devices used for measuring the pressure at

    a point in a fluid, by balancing the column of fluid by the same (OR) another column ofthe fluid.

    7. Write the classifications of manometer.

    The manometers are classified into(a) Simple Manometer - piezometer, U-tube manometer, vertical single column

    manometer, inclined single column manometer,

    (b) Differential Manometer - two piezometer manometer, U-tube differentialmanometer, Inverted U-tube differential manometer, Micro Manometer.

    8. Define simple manometer.Simple manometers are those which measure pressure at a point in a fluid

    contained in a pipe (OR) in a vessel. It consists of glass tube having one of its endsconnected to the gauge point where the pressure is to be measured and the otherremains open to atmosphere.

    9. Define differential manometer.Differential manometers are the devices used for measuring the difference of

    pressure between two points in a pipe (OR) in a 2 different pipes. A differential

    manometer consists of a U-tube containing a heavy liquid, whose two ends areconnected to the points where difference of pressure is to be measured.

    10. Define Mechanical GaugeMechanical gauges are the pressure measuring devices which deflects under the

    action of the applied pressure and this mechanical movement of pointer moves against agraduated circumferential scale.

    Types:Bourdon Tube Pressure Gauge Diaphragm Pressure GaugeBellows Pressure Gauge Dead Weight Pressure Gauge

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    Hydrostatic Force1. Define total pressure.

    Total pressure is the force exerted by a static fluid on a surface either plane or curved,when the fluid comes in contact with the surface. It acts in the direction normal to thesurface.

    2. Define Centre of pressure and write expression for the same different cases.

    The Centre of Pressure is defined as the point of application of total pressure on thesurface. The centre of pressure lies below centre of gravity, as well as depth of centre ofpressure is independent of fluid properties.

    hcp = h --- for Horizontal Planehcp = h --- for Horizontal Planehcp = h --- for Horizontal Planehcp = h --- for Horizontal Plane

    Buoyancy

    1. What is mean by Buoyancy?The tendency for an immersed body to be lifted up in the fluid due to an upward

    force opposite to the action of gravity is known as Buoyancy.

    2. State Archimedes Principle.

    3. Define Meta Centre & Meta Centric Height.

    4. List the various types of equilibrium and define each one.(a) Stable Equilibrium:(b) Unstable Equilibrium:(c) Neutral Equilibrium:

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    Kinematics of fluid flow

    1. Mention two general method used to describe the motion of a fluid.a. Lagrangian Method: In this method any individual fluid particle is selected which

    is considered throughout its course of motion and the observation is made aboutthe behaviour of this particle during its course of motion.

    b. Eulerian Method: In this method any point in the space occupied by the fluid is

    selected and the observation is made of whatever changes of velocity, density,and pressure which take place at that point. Out of these two methods, theEulerian Method is commonly adopted in fluid mechanics.

    2. List the types of fluid flow.a. Steady and unsteady flowb. Uniform and non-uniform flowc. Laminar and Turbulent flowd. Compressible and incompressible flowe. Rotational and ir-rotational flowf. One, Two and Three dimensional flow

    3. Define Steady and Unsteady flow.

    Steady flowFluid flow is said to be steady if at any point in the flowing fluid variouscharacteristics such as velocity, density, pressure,etc do not change with time.

    1. V/t = 0 p/t = 0 /t = 0

    Unsteady flowFluid flow is said to be unsteady if at any point flowing fluid any one or allcharacteristics which describe the behaviour of the fluid in motion change withtime.

    2. V/t 0 p/t 0 /t 0

    4. Define Uniform and Non-uniform flow.

    Uniform flowWhen the velocity of flow of fluid does not change both in direction andmagnitude from point to point in the flowing fluid for any given instant of time, theflow is said to be uniform.

    1. V/s = 0 p/s = 0 /s = 0

    Non-uniform flowIf the velocity of flow of fluid changes from point to point in the flowing fluid at anyinstant, the flow is said to be non-uniform flow.

    2. V/s 0 p/s 0 /s 0

    5. Compare Laminar and Turbulent flow.

    Laminar and Turbulent flowA flow is said to be laminar if Reynolds number is less than 2000 for pipe flow.

    Laminar flow is possible only at low velocities and high viscous fluids. In laminartype of flow, fluid particles move in laminas or layers gliding smoothly over theadjacent layer.

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    Turbulent flowIn Turbulent flow, the flow is possible at both velocities and low viscous fluid. Theflow is said to be turbulent if Reynolds number is greater than 4000 for pipe flow. InTurbulent type of flow fluid, particles move in a zig - zag manner.

    6. Define Compressible and incompressible flow

    Compressible flowThe compressible flow is that type of flow in which the density of the fluidchanges from point to point i.e. the density is not constant for the fluid. It isexpressed in kg/sec.

    constant

    7. Incompressible flowThe incompressible flow is that type of flow in which the density is constant for

    the fluid flow. Liquids are generally incompressible. It is expressed in m3/s. = constant

    8. Define Rotational and Ir-rotational flow.

    Rotational flowRotational flow is that type of flow in which the fluid particles while flowing alongstream lines and also rotate about their own axis.

    Ir-rotational flowIf the fluid particles are flowing along stream lines and do not rotate about their

    own axis that type of flow is called as ir-rotational flow

    9. Define One, Two and Three dimensional flow.

    One dimensional flowThe flow parameter such as velocity is a function of time and one space co-ordinate only. u = f (x), v = 0 & w = 0.

    Two dimensional flowThe velocity is a function of time and two rectangular space co-ordinates.

    u = f1(x,y), v = f2(x,y) & w =0.

    Three dimensional flowThe velocity is a function of time and three mutually perpendicular directions.

    u = f1(x,y,z), v = f2(x,y,z) & w = f3(x,y,z).

    10. Mention the range of Reynolds number for laminar and turbulent flow in a pipe.If the Reynold,s number is less than 2000, the flow is laminar. But if theReynolds number is greater than 4000, the flow is turbulent flow.

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    11. Write the continuity equation.

    The equation based on the principle of conservation of mass is called continuityequation.

    u/x + v/y + w/z = 0 ----- three dimensional flow

    u/x + v/y = 0 ----- two dimensional flow

    Q = a1v1 = a2v2 ----- one dimensional flow

    12. List the various types of fluid flow pattern.

    Stream Line - A stream line is an imaginary line drawn through a fluid in such a way that thetangent to it gives the direction of velocity of fluid at that point.

    Stream Tube - A stream tube is the tube imagined to be formed by a group of stream

    lines passing through a small closed curve which may or may not be circular.

    Path Line - A path line may defined as the line traced by a single fluid particle as itmoves over a period of time. Thus, a path line will show the direction of velocity of thesame particle at successive instants of time.

    Streak Line - A stream line is defined as the line that is traced by a fluid passingthrough fixed point in a fluid flow.

    13. Define rate of flow (OR) discharge.

    The rate of flow of fluid is the quantity of fluid passing through a section in unit time.

    For liquids, the rate of flow is equal to the volume of fluid passing through a section in

    unit time and hence it is termed as volume flow rate.Volume/time = area x velocity (m3/s)

    For gases, the rate of flow is equal to the mass of fluid passing through a section in unittime and hence it is termed as mass flow rate.

    Mass/time = density x area x velocity (kg/s)

    14. Define velocity and acceleration of fluid particle.The velocity at any point is the ratio between the displacement of a fluid element

    along its path. It is a vector quantity and expressed in three dimensions.

    V = ui + vj + wk

    Resultant Velocity, V = u2+v2+w2

    The acceleration is defined as the time rate of change of velocity.

    a = axi + ayj + azk

    Resultant Acceleration, a = ax2+ay2+az2

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    15. Define Convective & Local acceleration

    Total Acceleration = Convective acceleration + Local acceleration

    Convective Acceleration [v(v/s)] : It is the rate of change of velocity w.r.t. space. It isdue to non-uniformity of the flow. For uniform flow the convective acceleration is zerov(v/s)=0 i.e. velocity is constant.

    Local Acceleration [(v/t)] : It is the rate of change of velocity w.r.t. time. It is due toun-steadyness of the flow. For steady flow, the local acceleration is zero [v/t = 0].

    16. Write acceleration in three dimensional coordinate

    ax= u u/x + v u/y + w u/z + u/t

    ay = u v/x + v v/y + w v/z + v/t

    az= u w/x + v w/y + w w/z + w/t

    Resultant Acceleration, a = ax2+ay2+az2

    For Steady flow, u/t = 0 ; v/t = 0 ; w/t = 0, therefore

    ax= u u/x + v u/y + w u/z

    ay = u v/x + v v/y + w v/z

    az= u w/x + v w/y + w w/z

    Resultant Acceleration, a = ax2+ay2+az2

    17. Define Velocity PotentialVelocity potential() is a scalar function of space and time such that its -ive

    derivatives w.r.t. any direction gives fluid velocity in that direction.

    u = - /x v = - /y w = - /z

    2/x2+ 2/y2+ 2/z = 0 --- Laplace Equation for continuity.

    The Velocity potential exist only for ir-rotational flow.

    18. Define Stream FunctionThe stream function is defined as a scalar function of space and time such that its

    partial derivatives w.r.t. any direction gives the velocity component at right angles (in theanti-clock direction) to that direction.

    u = - /y v = /x

    Stream function exists only if continuity equation is satisfied.

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    19. Write the Relationship between velocity potential and stream function.

    /x = /y & /y = - /x

    20. Write the condition for flow to be ir-rotational

    x= (1/2) (w/y - v/z)

    y= (1/2) (u/z - w/x)

    z= (1/2) (v/x - u/y)

    For Ir-rotational flow,

    x = 0 (OR) w/y = v/z

    y = 0 (OR) u/z = w/x

    z = 0 (OR) v/x = u/y

    21. Define flow net and mention its use.

    A grid obtained by drawing a series of stream lines and equi-potential lines isknown as Flow Net.

    Use: To determine the groundwater discharge to the well To determine the seepage discharge through earth dam, bunds,etc. To determine the seepage or uplift discharge below hydraulic structures.

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    UNIT III : FLUID DYNAMICS

    Dynamics

    1. Define Dynamics of Fluid Flow

    Whenever forces are considered in the analysis of fluid flow then it is called Dynamics ofFluid flow.

    2. List the various types of forcesGravitational Force, Fg Pressure Force, FpViscous Force, Fv Turbulent Force, FtSurface Tension Force, Fs Compressibility Force, Fc

    According to Newtons law of motion,Net force, F = sum of all forces = Fg + Fp + Fp + Fi + Fs + Fc

    According to EulerNet force, F = Fg + Fp

    3. Write the Eulers Equationp + vv + z = 0

    4. Write the Bernoullis equation applied between two sections

    p1/g + v21/2g + Z1 = p2/g + v

    22/2g + Z2

    p/g = pressure headv2/2g = kinetic headZ = datum head

    5. State the assumptions used in deriving Bernoullis equationFlow is steady; Flow is laminar; Flow is irrotational;Flow is incompressible; Fluid is ideal.

    6. Write the Bernoullis equation applied between two sections with losses.

    p1/g + v21/2g + Z1 = p2/g + v

    22/2g + Z2 + hloss

    7. List the instruments works on the basis ofBernoullis equation.

    Venturi meter; Orifice meter; Pitot tube.

    8. Write the discharge equation for Venturi meter.

    QT = a1 a2(2gh) / (a12 - a22) Qa =

    Cd QT

    Where, a1 - area at inlet (m2)

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    Viscous Flow

    1. What is Hagen poiseuilles formula?

    (P1-P2) / g = hf= 32 L / gD2

    The expression is known as Hagen poiseuille formula.Where P1-P2/ g = Loss of pressure head,

    = Coefficient of viscosity,L = Length of pipe

    2. Write the expression for shear stress?Shear stress = - (p/x) (r/2)

    max = - (p/x) (R/2)3. Give the formula for velocity distribution: -

    = Average velocity,

    D = Diameter of pipe,

    The formula for velocity distribution is given as u= - ( ) (p/x) (R2-r2)

    Where R = Radius of the pipe, r = Radius of the fluid element

    4. Give the equation for average velocity : -

    The equation for average velocity is given as =- (1/8) (p/x) R2

    Where R = Radius of the pipe

    5. Write the relation between Umax and ?

    Umax / = { - ( ) (p/x) R2 }/ { - (p/x) R2 }Umax / = 2

    6. Give the expression for the coefficient of friction in viscous flow?

    Coefficient of friction between pipe and fluid in viscous flow f =16/ ReWhere, f = Re = Reynolds number

    7. What are the factors to be determined when viscous fluid flows through the circularpipe?The factors to be determined are:

    i. Velocity distribution across the section.ii. Ratio of maximum velocity to the average velocity.iii. Shear stress distribution.iv. Drop of pressure for a given length.

    8. Define kinetic energy correction factor?Kinetic energy factor is defined as the ratio of the kinetic energy of the flow per sec

    based on actual velocity across a section to the kinetic energy of the flow per sec based on

    average velocity across the same section. It is denoted by ().K. E factor () = K.E per sec based on actual velocity / K.E per sec based on Averagevelocity

    9. Define momentum correction factor ():It is defined as the ratio of momentum of the flow per sec based on actual velocity to the

    momentum of the flow per sec based on average velocity across the section.= Momentum per sec based on actual velocity/Momentum Per sec based on average

    velocity

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    Turbulent Flow

    1. State Darcy-Weisbach equation OR What is the expression for head loss due to friction?

    hf= 4flv2 / 2gdwhere, hf= Head loss due to friction (m), L = Length of the pipe (m),

    d = Diameter of the pipe (m), V = Velocity of flow (m/sec)f = Coefficient of friction 4f = friction factor

    Momentum Equation

    1. Define Impulse Momentum Equation (or) Momentum Equation.The total force acting on fluid is equal to rate of change of momentum.According to Newtons second law of motion, F = ma

    F dt = d(mv)

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    UNIT IV : BOUNDARY LAYER AND FLOW THROUGH PIPES

    Boundary Layer

    1. Define Boundary layer.When a real fluid flow passed a solid boundary, fluid layer is adhered to the solidboundary. Due to adhesion fluid undergoes retardation thereby developing asmall region in the immediate vicinity of the boundary. This region is known asboundary layer.

    2. What is mean by boundary layer growth?At subsequent points downstream of the leading edge, the boundary layer regionincreases because the retarded fluid is further retarded. This is referred asgrowth of boundary layer.

    3. Classification of boundary layer.(i) Laminar boundary layer, (ii) Transition zone, (iii) Turbulent boundary layer.

    4. Define Laminar boundary layer.Near the leading edge of the surface of the plate the thickness of boundary layeris small and flow is laminar. This layer of fluid is said to be laminar boundary

    layer.The length of the plate from the leading edge, upto which laminar boundary layerexists is called as laminar zone. In this zone the velocity profile is parabolic.

    5. Define transition zone.After laminar zone, the laminar boundary layer becomes unstable and the fluidmotion transformed to turbulent boundary layer. This short length over which thechanges taking place is called as transition zone.

    6. Define Turbulent boundary.

    Further downstream of transition zone, the boundary layer is turbulent andcontinuous to grow in thickness. This layer of boundary is called turbulentboundary layer.

    7. Define Laminar sub LayerIn the turbulent boundary layer zone, adjacent to the solid surface of the plate thevelocity variation is influenced by viscous effects. Due to very small thickness,the velocity distribution is almost linear. This region is known as laminar sublayer.

    8. Define Boundary layer Thickness.It is defined as the distance from the solid boundary measured in y-direction to

    the point, where the velocity of fluid is approximately equal to 0.99 times the freestream velocity (U) of the fluid. It is denoted by .

    9. List the various types of boundary layer thickness.Displacement thickness(), Momentum thickness(), Energy thickness()

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    10. Define displacement thickness.The displacement thickness () is defined as the distance by which the boundaryshould be displaced to compensate for the reduction in flow rate on account ofboundary layer formation.

    = * 1 - (u/U) ] dy

    11. Define momentum thickness.

    The momentum thickness () is defined as the distance by which the boundaryshould be displaced to compensate for the reduction in momentum of the flowingfluid on account of boundary layer formation.

    = * (u/U) - (u/U)2 ] dy

    12. Define energy thickness

    The energy thickness (**) is defined as the distance by which the boundaryshould be displaced to compensate for the reduction in kinetic energy of theflowing fluid on account of boundary layer formation.

    = * (u/U) - (u/U)3 ] dy

    Flow through Pipe

    1. What is meant by energy loss in a pipe?When the fluid flows through a pipe, it looses some energy or head due tofrictional resistance and other reasons. It is called energy loss. The losses areclassified as; Major losses and Minor losses

    2. Explain the major losses in a pipe.The major energy losses in a pipe is mainly due to the frictional resistancecaused by the shear force between the fluid particles and boundary walls of thepipe and also due to viscosity of the fluid.

    3. Explain minor losses in a pipe.

    The loss of energy or head due to change of velocity of the flowing fluid inmagnitude or direction is called minor losses. It includes: sudden expansion of thepipe, sudden contraction of the pipe, bend in a pipe, pipe fittings andobstruction in the pipe, etc.

    4. State Darcy-Weisbach equation OR What is the expression for head loss due to friction?

    hf= 4flv2 / 2gdwhere, hf= Head loss due to friction (m), L = Length of the pipe (m),

    d = Diameter of the pipe (m), V = Velocity of flow (m/sec)f = Coefficient of friction

    5. What are the factors influencing the frictional loss in pipe flow?Frictional resistance for the turbulent flow is,

    o Proportional to vn where v varies from 1.5 to 2.0. oProportional to the density of fluid.o Proportional to the area of surface in contact. oIndependent of pressure.o Depend on the nature of the surface in contact.

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    6. Write the expression for loss of head due to sudden enlargement of the pipe.

    hexp = (V1-V2)2 /2gWhere, hexp = Loss of head due to sudden enlargement of pipe.

    V1 = Velocity of flow at pipe 1; V2 = Velocity of flow at pipe 2.

    7. Write the expression for loss of head due to sudden contraction.

    hcon =0.5 V2/2ghcon = Loss of head due to sudden contraction. V = Velocity at outlet of pipe.

    8. Write the expression for loss of head at the entrance of the pipe.hi =0.5V2/2g

    hi = Loss of head at entrance of pipe. V = Velocity of liquid at inlet of the pipe.

    9. Write the expression for loss of head at exit of the pipe.ho = V2/2g

    where, ho = Loss of head at exit of the pipe.V = Velocity of liquid at inlet and outlet of the pipe.

    10. Give an expression for loss of head due to an obstruction in pipeLoss of head due to an obstruction = V2 / 2g ( A/ Cc (A-a ) -1 )2

    Where, A = area of pipe, a = Max area of obstruction,V = Velocity of liquid in pipe A-a = Area of flow of liquid at section 1-1

    11. What is compound pipe or pipes in series?When the pipes of different length and different diameters are connected end toend, then the pipes are called as compound pipes or pipes in series.

    12. What is mean by parallel pipe and write the governing equations.When the pipe divides into two or more branches and again join togetherdownstream to form a single pipe then it is called as pipes in parallel. The

    governing equations are:1. Q1 = Q2 + Q3 hf1 = hf2

    13. Define equivalent pipe and write the equation to obtain equivalent pipe diameter.The single pipe replacing the compound pipe with same diameter without change indischarge and head loss is known as equivalent pipe.

    1. L = L1 + L2 + L3

    2. (L/d5) = (L1/d15) + (L2/d25) + (L3/d35)

    14. What is meant by Moodys chart and what are the uses of Moodys chart?The basic chart plotted against Darcy-Weisbach friction factor against Reynolds

    Number (Re) for the variety of relative roughness and flow regimes. The relativeroughness is the ratio of the mean height of roughness of the pipe and itsdiameter (/D).

    Moodys diagram is accurate to about 15% for design calculations and used for alarge number of applications. It can be used for non-circular conduits and also foropen channels.

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    15. Define the terms a) Hydraulic gradient line [HGL] b) Total Energy line [TEL]Hydraulic gradient line: It is defined as the line which gives the sum of pressurehead and datum head of a flowing fluid in a pipe with respect the referenceline.

    HGL = Sum of Pressure Head and Datum head

    Total energy line: Total energy line is defined as the line which gives the sum of

    pressure head, datum head and kinetic head of a flowing fluid in a pipe withrespect to some reference line.

    TEL = Sum of Pressure Head, Datum head and Velocity head

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    UNIT V : SIMILITUDE AND MODEL STUDY

    Dimensional Analysis

    1. Define dimensional analysis.Dimensional analysis is a mathematical technique which makes use of the study of

    dimensions as an aid to solution of several engineering problems. It plays an important role inresearch work.

    2. Write the uses of dimension analysis? It helps in testing the dimensional homogeneity of any equation of fluid motion. It helps in deriving equations expressed in terms of non-dimensional parameters.

    It helps in planning model tests and presenting experimental results in a systematicmanner.

    3. List the primary and derived quantities.

    Primary or Fundamental quantities: The various physical quantities used to describea given phenomenon can be described by a set of quantities which are independent of eachother. These quantities are known as fundamental quantities or primary quantities. Mass(M), Length (L), Time (T) and Temperature () are the fundamental quantities.

    Secondary or Derived quantities: All other quantities such as area, volume, velocity,acceleration, energy, power, etc are termed as derived quantities or secondary quantitiesbecause they can be expressed by primary quantities.

    4. Write the dimensions for the followings.Dynamic viscosity () - ML-1T-2, Force (F) - MLT-2,Mass density () - ML-3, Power (P) -ML2T-3

    5. Define dimensional homogeneity.An equation is said to be dimensionally homogeneous if the dimensions of the terms on its

    LHS are same as the dimensions of the terms on its RHS.

    6. Mention the methods available for dimensional analysis.Rayleigh method, Buckinghum method

    7. State Buckinghams theorem.It states that if there are n variables (both independent & dependent variables) in a

    physical phenomenon and if these variables contain m functional dimensions and arerelated by a dimensionally homogeneous equation, then the variables are arranged into n-mdimensionless terms. Each term is called term.

    8. List the repeating variables used in Buckingham theorem.Geometrical Properties - l, d, H, h, etc,Flow Properties - v, a, g, N, , Q, etc,Fluid Properties - , , , , , etc.

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    9. Write the dimensions for the followings.

    Quantities Symbol Unit Dimension

    Area A m2 L2

    Volume V m3 L3

    Angle Deg. Or Rad M0L0T0

    Velocity v m/s LT-1

    Angular Velocity Rad/s T-1

    Speed N rpm T-1

    Acceleration a m/s2 LT-2

    Gravitational Acceleration g m/s2 LT-2

    Discharge Q m3/s L3T-1

    Discharge per meter run q m2/s L2T-1

    Mass Density Kg/m3 ML3

    Sp. Weight or Unit Weight N/m3 ML-2T-2

    Dynamic Viscosity N-s/m2 ML-1T-1

    Kinematic viscosity m2/s L2T-1

    Force or Weight or Drag force F or W N MLT-2

    Pressure or Pressure intensity p N/m2 or Pa ML-1T-2

    Modulus of Elasticity E N/m2

    or Pa ML-1

    T-2

    Bulk Modulus K N/m2 or Pa ML-1T-2

    Workdone or Energy W or E N-m ML2T-2

    Torque T N-m ML2T-2

    Power P N-m/s or J/s or Watt ML2T-3

    Efficiency No Unit M0L0T0

    term No Unit M0L0T0

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    Model Analysis

    1. Define model and prototype.The small scale replica of an actual structure or the machine is known as its

    Model, while the actual structure or machine is called as its Prototype. Mostly models aremuch smaller than the corresponding prototype.

    2. Write the advantages of model analysis.o Model test are quite economical and convenient.o Alterations can be continued until most suitable design is obtained. oModification of prototype based on the model results.o The information about the performance of prototype can be obtained well in

    advance.

    3. List the types of similarities or similitude used in model anlaysis.Geometric similarities, Kinematic similarities, Dynamic similarities

    4. Define geometric similaritiesIt exists between the model and prototype if the ratio of corresponding lengths,

    dimensions in the model and the prototype are equal. Such a ratio is known as ScaleRatio.

    5. Define kinematic similaritiesIt exists between the model and prototype if the paths of the homogeneous

    moving particles are geometrically similar and if the ratio of the flow properties is equal.

    6. Define dynamic similaritiesIt exits between model and the prototype which are geometrically and kinematicallysimilar and if the ratio of all forces acting on the model and prototype are equal.

    7. Mention the various forces considered in fluid flow.

    Inertia force Fi= Av2 Viscous force Fv= vL

    Gravity force Fg= ALg Pressure force Fp = pA2

    Surface Tension force Fs= L Elasticity force Fe = KA

    8. Define model law or similarity law.The condition for existence of completely dynamic similarity between a model

    and its prototype are denoted by equation obtained from dimensionless numbers. Thelaws on which the models are designed for dynamic similarity are called Model laws orLaws of Similarity.

    9. List the various model laws applied in model analysis.

    Reynolds Model Law, Froudes Model Law,Eulers Model Law, Weber Model Law, Mach Model Law

    10. State Reynolds model lawFor the flow, where in addition to inertia force the viscous force is the only other

    predominant force, the similarity of flow in the model and its prototype can beestablished, if the Renolds number is same for both the systems. This is known asReynolds model law. Re(p) = Re(m)

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    11. State Froudes model lawWhen the forces of gravity can be considered to be the only predominant force

    which controls the motion in addition to the force of inertia, the dynamic similarities of theflow in any two such systems can be established, if the Froude number for both thesystem is the same. This is known as Froude Model Law. Fr(p) = Fr (m)

    12. State Eulers model law

    In a fluid system where supplied pressures are the controlling forces in additionto inertia forces and other forces are either entirely absent or in-significant the Eulersnumber for both the model & prototype which known as Euler Model Law.Eu (p)=Eu(m)

    13. State Webers model lawWhen surface tension effect predominates in addition to inertia force then the

    dynamic similarity is obtained by equating the Webers number for both model and itsprototype, which is called as Weber Model Law. We(p) = We(m)

    14. State Machs model lawIf in any phenomenon only the forces resulting from elastic compression are

    significant in addition to inertia forces and all other forces may be neglected, then the

    dynamic similarity between model and its prototype may be achieved by equating theMachs number for both the systems. This is known Mach Model Law. Ma(p) = Ma (m)

    15. Classify the hydraulic models.The hydraulic models are classified as: Undistorted model & Distorted model

    16. Define undistorted modelAn undistorted model is that which is geometrically similar to its prototype, i.e. the

    scale ratio for corresponding linear dimensions of the model and its prototype are same.

    17. Define distorted modelDistorted models are those in which one or more terms of the model are not

    identical with their counterparts in the prototype.

    18. Define Scale effectAn effect in fluid flow that results from changing the scale, but not the shape, of a

    body around which the flow passes.

    19. List the advantages of distorted model.

    o The results in steeper water surface slopes and magnification of wave heights inmodel can be obtained by providing true vertical structure with accuracy.

    o The model size can be reduced to lower down the cast.o Sufficient tractate force can be developed to produce bed movement with a small

    model.

    20. List the disadvantages of distorted model.o The pressures may not be reproduced in magnitude & direction.o Proper longitudinal bed slope may not be maintained.o Difficult to transfer the velocity to prototype.