Course Details by 5KxFLO6


									Properties of Fluids-Basic Concepts

                 Prof. Rohit Goyal
     Professor, Department of Civil Engineering
   Malaviya National Institute of Technology Jaipur

Topics Covered

   Applications of FM
   Definition of Fluid
   Properties of Fluids
       Density
       Viscosity
       Surface Tension
       Compressibility
Fluid Mechanics???

   It is physical science dealing with the
    action of fluids at rest or in motion, and
    with applications and devices in
    engineering using fluids.
   Fluid mechanics can be subdivided
    into two major areas
       fluid statics, deals with fluids at rest
       fluid dynamics, deals with fluids in motion

Applications of Fluid Mechanics

   We experience fluid mechanics in
    every day life
       Blood circulation through body
       Water, sewerage, gas flow through pipes
       Pumps, turbines, hydraulic machines
       Aircraft, ship movements through air,
       Spin and flight of cricket, golf ball etc.
    Definition of Fluid

   Matter can have three physical form
       Solid, liquid and gaseous
       Liquid and gaseous phases are
        combined together to be represented as
        fluids – Why?
           Because these phases have some common
    Definition of Fluid…

   A fluid is defined as a substance which deforms
    continuously under the action of shear stress,
    regardless of it’s magnitude

Definition of Fluid…

   So, in solids, deformation grows and
    with it the resistance to shear stress
    increases. It stops as soon as both
    shear stress and it’s internal resistance
    are equal
   For fluids, deformation continues till
    shear stress is applied and equilibrium
    is never reached
Liquid Vs Gases

   In liquids, molecules are packed closer
       Unlike solid, molecules can change relative
        position amongst themselves
       Still significant force of attraction between
       Incompressible
   In Gases, molecules are further apart
       Very weak force of attraction, fills container
       Compressible
Continuum Concept

   Molecules of fluids are separated in space
    (more so in gases). Molecules may be in
    continuous motion
   Density, pressure, velocity for a point at any
    instant would not make sense if there is a
    void at that point at that instant
   In order to simplify things we do not go to
    molecular level for certain aspects and so
    assume fluid as “continuum”
Continuum Concept…
   This concept fails at extreme states of
    pressure and temperatures
   According to requirement of continuum, we
    must deal with dimensions much larger than
    mean free path of molecules
   Mean free path: Average path before
    colliding with another particle
   Air’s mean free path at earth surface is
    6.25x10-6 cm.

Fluid Properties

   Fluid properties are measures of
    its characteristics
       Density, specific weight, specific
       Viscosity
       Compressibility
       Surface Tension etc.

   Density is defined as the mass in a unit
    volume, usually defined as  (rho)
    = m/V (m is mass in kilograms and V is
    volume in m3)
   Density of water at 4oC is 1000 kg/m3.
   Density at a point is defined as

                m 
      lim       
         V  0  V
                   
   Measurement of Density-Solid

      Density  = 103 g/27 ml = 3.81 g/ml
      or 3.81 g/cc.
                              Volume=27 ml


Mass=103 g
Measurement of Density-Liquid

   Density  = 50 g/50 ml = 1.0 g/ml
   or 1.0 g/cc.
                             Mass=93-43=50 g

                               Volume=50 ml

Measurement of Density-Gases

   Density  = 0.2 g/500 ml = 0.0004 g/ml
   or 0.0004 g/cc.

                                     =0.2 g

                                 Volume=500 ml

Specific Weight

   Specific weight of a fluid is the weight
    per unit volume, usually defined as 
    =  g (where g is acceleration due to
   Specific weight of water = 9.81 kN/m3.
   Specific weight may vary with altitude,
    density usually remains constant
Specific Volume

   Specific Volume is volume occupied by
    unit mass of a fluid
   It is inverse of density ().
   It’s unit would be m3/kg
   It is commonly applied to gases
   Usually denoted by v.

Specific Gravity

   Specific gravity is the density of a
    substance divided by the density of
    another substance that is used as a
   For solids and liquids, water at 4oC
    (39oF) is usually the standard. (In
    Engineering 20oC is used)
   Water has maximum density at 4oC
   The viscosity of a liquid is a measure of how
    much the liquid resists flow, usually denoted
    by .
   Viscosity tends to prevent fluids from flowing
    when subjected to an applied force.
       High-viscosity fluids resist flow;
       low-viscosity fluids flow easily.
   The tenacity with which a moving layer of
    fluid drags adjacent layers of fluid along with
    it determines its viscosity


   Like solids in fluids also there is attraction
    between molecules known as cohesion
   Cohesion causes resistance to flow between
    two layers moving at different speeds
       Faster layer tries to increase velocity of slower
        layer and vice versa
   Also momentum transfer between the layer
    causes mix traffic and so cause resistance
    (mixing length theory)
   The viscosity of water is lower than that of heavy
    oils because oils contain large, convoluted
    molecules that catch on one another.
   The polarity of the molecules in water, however,
    causes them to attract one another, making water
    more viscous than a nonpolar liquid, such as
   Viscosity decreases as temperature increases
    because additional heat energy enables molecules
    to overcome attractions to one another and move
    more freely.
   Except for very high pressures viscosity usually
    does not vary with pressure
Definition of Viscosity

   Viscosity is defined by Newton's law of
   Newton formulated that shear stress is
    proportional to the rate of deformation
    in fluids (rate of shear strain)
       Shear stress ()  deformation rate (v/y)
   Constant of proportionality is defined as
    viscosity ().
  Deformation of Fluid

     v    is known as viscosity. Also known as
                                                 23

     y   dynamic viscosity or absolute viscosity
Newtonian Fluids

   Not all fluids obey Newton’s law of viscosity
   Those fluids which follows it are known as
    Newtonian fluids
   Other are non-Newtonian fluids (like paints,
    printing ink, tar slurry etc.).
   Non-Newtonian fluids are studied under
    rheology, a science of deformation and flow.

Classification of Fluids

Unit of Viscosity

   Unit of Viscosity () is N.s/m2. In terms of
    mass it would be kg/m.s.
   Another unit is Poise (after French scientist
    Poiseuille) is also used to express viscosity
   1 poise (P) = 1 g/(cm.s)
   1 N.s/m2=10 P
   Viscosity of water at 20oC is 1 centipoise.

Kinematic viscosity

   We often encounter the term /
   So a term kinematic viscosity, referred as 
    (nu) is defined as ratio of dynamic viscosity
    and density.
    = /.
   Unit of  is m2/s. It is also expressed in
    terms of strokes (English mathematician)
   1 stroke = 1 cm2/s.

   Viscosity
    of some

Surface Tension

   A small drop of liquid becomes spherical,
    the smallest surface possible
   The molecules at the surface are pulled in
    by the cohesive force between themselves
    and molecules inside the droplet.
   The liquid keeps its droplet shape because
    there are no liquid molecules outside the
    surface to balance this inward pull.

Surface Tension in Water

Surface Tension

   Liquid behaves as if there free surface is
    stretched like membrane under tension
   This is because molecules on surface are
    pulled only from three sides by like
    molecules (cohesion) as compared to rest of
    them being pulled from all four directions
   Tensile strength computed per unit length is
    termed as surface tension, usually denoted
    by  (Sigma).
Capillary action

   Like cohesion (attraction between like
    molecules) attraction between unlike
    molecules is called adhesion
   Cohesion and adhesion give rise to capillary
    rise when a small tube is inserted into a
   Degree of adhesion is represented by
    contact angle as shown next, water < 90o
    and mercury > 900
Capillary Rise/Depression

Capillary Rise/Depression

   Capillary rise in a small clean circular
    glass tube can be calculated by
    balancing the weight of liquid which
    has risen to height say h to the surface
    tension force, so
   h = 4  cos() /  g d
   Or by observing h we can find value of
    surface tension ()
   All fluid undergo changes in volume under
   Changes may be negligible for liquids up to certain
   Compressibility is defined as
       C = -(V/V)/ p
       Negative sign because V is negative for positive p
   Bulk modulus of elasticity (K) is reciprocal of
    compressibility, so (K=1/C)
   Compressibility must usually be accounted for in
    phenomena such as water hammer/pressure waves
Vapor Pressure
   Vapor Pressure is pressure created by the vapor, or
    gas, of a substance that forms above a liquid or
    solid of the same substance.
   All liquids, and even some solids, vaporize
   The term vapor pressure usually refers to
    equilibrium vapor pressure, or the pressure at which
    the rate that particles (atoms or molecules) leave
    the substance to form vapor equals the rate that
    particles reenter the substance from the vapor.


   In some flow systems, liquid pressure
    at certain points may become less
    than vapor pressure of that liquid,
    causing vaporization.
   Vapor in form of bubble then travels of
    zone of higher pressure and collapses
    into liquid leading to cavitation.

Ideal Fluid
   Euler first recognized that dynamical laws for fluids
    can only be expressed in a relatively simple form if
    the fluid is assumed incompressible and ideal, that
    is, if the effects of friction or viscosity can be
   Because, however, this is never the case for real
    fluids in motion, the results of such an analysis can
    only serve as an estimate for those flows where
    viscous effects are small.

Flow Properties

   Apart from fluid properties, there are
    certain flow properties of interest in
    fluid mechanics
       Pressure
       Velocity
       Discharge
       Type and state of flow
       Pathline, streamline and streakline

   Pressure is the force per unit area
    exerted by a liquid or gas on a body or
    surface, with the force acting at right
    angles to the surface uniformly in all
                                  F 
   Pressure at a point p  A 0
                             lim        
                                 A 
   Unit of pressure is kN/m2

   Velocity of a particle is the time rate of
    change of its distance.
   Velocity is vector quantity which has
    both magnitude and direction (Speed
    is scalar)
   Velocity may vary with space and time
    and so v= v(x, y, z, t)
   Velocity may be absolute or relative

   Quantity of flow crossing a section per
    unit time is called the rate of flow or
   Section is usually physical section but
    may also be imaginary section as a
    concept (example discharge between
    two streamlines).
   Unit for discharge is m3/sec.
Discharge computation

   If we have velocity diagram for flow
    through a say, pipe

                   Velocity Diagram
   Q   v dA
   Average velocity is a useful concept
    which allows us to write simply Q = AV
Type of Flow

   Type of flow could be
   Steady or Unsteady
       Steady, when properties such as
        pressure and velocity does not change
        with time
   Uniform and Non-uniform
       When properties does not change with
State of flow
   Fluid motion and resistance to motion
    may be governed by many different types
    of forces such as
       Inertia force
       Gravity force
       Viscous force
   Based on relative importance of forces
    state of flow may be defined as laminar
    or turbulent, sub or super critical etc.
Pathline, streamline & streakline

   In order to describe flow patterns we
    sometime make use of imaginary lines such
   Pathline: This is a path traversed by a single
    particle over an interval of time.
   Streamline: It is a imaginary line joining points
    along the velocity vector at any instant. By
    definition there cannot be any flow
    perpendicular to direction of flow
   Streakline: It is a line joining particles which
    have passed a fixed point in flow field.

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