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Properties of Fluids for Fluid Mechanics

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Properties of Fluids for Fluid Mechanics P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi Continuum Hypothesis In this course, ... – PowerPoint PPT presentation

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Title: Properties of Fluids for Fluid Mechanics


1
Properties of Fluids for Fluid Mechanics
  • P M V Subbarao
  • Associate Professor
  • Mechanical Engineering Department
  • IIT Delhi

Basic Steps to Design.
2
Continuum Hypothesis
  • In this course, the assumption is made that the
    fluid behaves as a continuum, i.e., the number of
    molecules within the smallest region of interest
    (a point) are sufficient that all fluid
    properties are point functions (single valued at
    a point).
  • For example
  • Consider definition of density ? of a fluid
  • dV limiting volume below which molecular
    variations may be important and above which
    macroscopic variations may be important.

3
Static Fluid
For a static fluid
Shear Stress should be zero.
For A generalized Three dimensional fluid
Element, Many forms of shear stress is possible.
4
One dimensional Fluid Element
Y
uU
u0
X
?
5
Fluid Statics
  • Pressure For a static fluid, the only stress is
    the normal stress since by definition a fluid
    subjected to a shear stress must deform and
    undergo motion.

Y
X
Z
  • What is the significance of Diagonal Elements?
  • Vectorial significance Normal stresses.
  • Physical Significance ?
  • For the general case, the stress on a fluid
    element or at a point is a tensor

6
Stress Tensor
7
First Law of Pascal
Proof ?
8
Simple Non-trivial Shape of A Fluid Element
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Fluid Statics for Power Generation
  • P M V Subbarao
  • Associate Professor
  • Mechanical Engineering Department
  • IIT Delhi

Steps for Design of Flow Devices.
17
Pressure Variation with Elevation
  • For a static fluid, pressure varies only with
    elevation within the fluid.
  • This can be shown by consideration of equilibrium
    of forces on a fluid element
  • Basic Differential Equation
  • Newton's law (momentum principle) applied to a
    static fluid
  • SF ma 0 for a static fluid
  • i.e., SFx SFy SFz 0

1st order Taylor series estimate for pressure
variation over dz
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19
  • For a static fluid, the pressure only varies with
    elevation z and is constant in horizontal xy
    planes.
  • The basic equation for pressure variation with
    elevation can be integrated depending on
  • whether ? constant i.e., the fluid is
    incompressible (liquid or low-speed gas)
  • or ? ?(z), or compressible (high-speed gas)
    since g is constant.

20
Pressure Variation for a Uniform-Density Fluid
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23
Draft Required to Establish Air Flow
Flue as out
Air in
24
Natural Draft
Zref
pA pref Dp
Hchimney
Tgas
Tatm
B
A
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Zref,,pref
pA pref Dp
Hchimney
Tgas
Tatm
B
A
27
Pressure variations in Troposphere
Linear increase towards earth surface
Tref pref are known at Zref.
a Adiabatic Lapse rate 6.5 K/km
28
Reference condition At Zref TTref p pref
29
Pressure at A
Pressure variation inside chimney differs from
atmospheric pressure. The variation of chimney
pressure depends on temperature variation
along Chimney. Temperature variation along
chimney depends on rate of cooling of hot gas Due
to natural convection. Using principles of Heat
transfer, one can calculate, Tgas(Z). If this is
also linear T Tref,gas agas(Zref-Z). Lapse
rate of gas, agas is obtained from heat transfer
analysis.
30
Natural Draft
  • Natural Draft across the furnace,
  • Dpnat pA pB
  • The difference in pressure will drive the
    exhaust.
  • Natural draft establishes the furnace breathing
    by
  • Continuous exhalation of flue gas
  • Continuous inhalation of fresh air.
  • The amount of flow is limited by the strength of
    the draft.

31
Pressure Measurement
32
Pressure Measurement
Pressure is an important variable in fluid
mechanics and many instruments have been devised
for its measurement. Many devices are based on
hydrostatics such as barometers and manometers,
i.e., determine pressure through measurement of a
column (or columns) of a liquid using the
pressure variation with elevation equation for an
incompressible fluid.
33
PRESSURE
  • Force exerted on a unit area Measured in kPa
  • Atmospheric pressure at sea level is 1 atm, 76.0
    mm Hg, 101 kPa
  • In outer space the pressure is essentially zero.
    The pressure in a vacuum is called absolute zero.
  • All pressures referenced with respect to this
    zero pressure are termed absolute pressures.

34
  • Many pressure-measuring devices measure not
    absolute pressure but only difference in
    pressure. This type of pressure reading is called
    gage pressure.
  • Whenever atmospheric pressure is used as a
    reference, the possibility exists that the
    pressure thus measured can be either positive or
    negative.
  • Negative gage pressure are also termed as vacuum
    pressures.

35
Manometers
Enlarged Leg
Inverted U Tube
U Tube
Two Fluid
Inclined Tube
36
Absolute, Gauge Vacuum Pressures
System Pressure
Gauge Pressure
Absolute Pressure
Atmospheric Pressure
Absolute zero pressure
37
Absolute, Gauge Vacuum Pressures
Atmospheric Pressure
Vacuum Pressure
System Pressure
Absolute Pressure
Absolute zero pressure
38
An important Property of A Fluid
39
Shear stress(t) Tangential force on per unit
area of contact between solid fluid
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43
Elasticity (Compressibility)
  • Increasing/decreasing pressure corresponds to
    contraction/expansion of a fluid.
  • The amount of deformation is called elasticity.

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Surface Tension
  • Two non-mixing fluids (e.g., a liquid and a gas)
    will form an interface.
  • The molecules below the interface act on each
    other with forces equal in all directions,
    whereas the molecules near the surface act on
    each other with increased forces due to the
    absence of neighbors.
  • That is, the interface acts like a stretched
    membrane, e.g.

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Vapour Pressure
  • When the pressure of a liquid falls below the
    vapor pressure it evaporates, i.e., changes to a
    gas.
  • If the pressure drop is due to temperature
    effects alone, the process is called boiling.
  • If the pressure drop is due to fluid velocity,
    the process is called cavitation.
  • Cavitation is common in regions of high velocity,
    i.e., low p such as on turbine blades and marine
    propellers.

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