1b. introduction

INTRODUCTION (Contd…)
Lecture # 01 (b)

CONTENTS OF TODAY’S LECTURE:
• Physical properties of Fluids
 Density
 Specific Weight
 Specific Volume
FLUID MECHANICS-I  Specific gravity
 Surface tension
CE-224

Engr. Fazal-E-Jalal
Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 1

Distinction between a Solid & Fluid
• Molecules of solid are usually closer together
than those of a fluid.
• The attractive forces between the molecules
of a solid are so large that a solid tends to
retain its shape.
• In case of fluids, the attractive forces between
the molecules are smaller.


Distinction between a Solid & Fluid
• An ideal elastic solid will deform under load
and once load is removed will return to it’s
original state. Plastic solids deform under
action of applied loads and deformation
continues as long as load is applied, providing
the material does not rupture.
The intermolecular cohesive forces in a fluid are not great
enough to hold various elements of fluid together. Hence a
fluid will flow under the action of slightest stress and flow will
continue as the stress is present.

Distinction between a Gas and a Liquid
• A fluid may be either gas or a liquid. Gas
molecules are much farther than those of a
liquid. Hence a gas is very compressible. On
removal of external pressure, it expands
indefinitely.
• A liquid is relatively incompressible. If all
pressure (except that of it’s vapor pressure) is
removed, it does not expand but the cohesion
holds the molecules together.
Therefore a liquid may have FREE SURFACE i.e. a surface from which all
pressure is removed, except that of it’s own vapor.

• A vapor is a gas whose temperature and
pressure are such that it is very near the liquid
phase.
• Thus, steam is considered as a vapor because
it’s state is not normally far from water.
A Gas may be defined as:
“A highly super-heated vapor, that is, it’s
state is far removed from a liquid phase.”
Thus, air is a gas.

• The volume of gas or liquid is greatly affected
by changes in pressure or temperature or
both.
• Whenever significant temperature or phase
changes are involved in dealing with vapors
and gases, the subject is largely dependent on
heat phenomenon (Thermodynamics).
• Thus Fluid mechanics & Thermodynamics are
inter related.


Density and Specific weight
• The density ƿ (rho) or mass density of a fluid is
mass per unit volume while the specific weight ɣ
(gamma)is it’s weight per unit volume. Specific
wt. is the force exerted by gravity on unit weight
of fluid.
• Units of Density: Slugs/ft3 (B.G system) and kg/m3
(S.I system). Also, can be expressed as lb.sec2/ft4
or N.s2/m4
• Units of Specific weight: lb/ft3 (B.G system) and
N/m3 (S.I system).

• Density ƿ is absolute, since it depends on
mass, which is independent of location.
• Specific weight ɣ, on the other hand is not
absolute, since it depends on the value of g,
which varies with location (primarily latitude
& elevation above mean sea level).
• Densities & specific weights of fluids vary with
temperature.


• Density and specific weight of a fluid are
related as:
• Ƿ = ( ɣ / g ) or ɣ = ƿ.g
• Physical quantities are dimensionally
homogeneous, the dimensions of density are:
• In B.G System: Ƿ = ɣ/g = (lb/ft3)/(ft/s2) =
lb.sec2/ft4 = mass/Vol. = slugs/cubic feet
• In S.I System: Ƿ = ɣ/g = (N/m3)/(m/s2) =
N.s2/m4 = mass/Vol. = kg/cubic meter

Specific weights of Liquids
• The specific weight of liquid depends on:
– Temperature (Inversely related)
– Pressure (Directly related)
– g value
– Presence of dissolved air, salts in solutions and
suspended matter. (Increase ɣ to slight amounts)
Unless otherwise specified or implied by a given temperature, the value to
use for water is 62.4 lb/ft3 or 9.81 kN/m3.
Under extreme conditions the specific weight of water is quite different. E.g.
at 260 degree celsius and 6000 psi, the ɣ of water is 51 lb/ft3.
Page# 21(Fluid Mechanics with
Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I engineering applications) 10

Specific Volume
• The volume occupied by a unit mass of fluid.
We commonly apply it to gases.
• ν = 1/ƿ = 1/Density
• Units: In B.G: ft3/slug In S.I: m3/kg
• It is reciprocal of density.


Specific Gravity
• Denoted by “s”, the specific gravity of a liquid is
the dimensionless ratio.
• Sliquid = ƿliquid / ƿ water at standard temperature

• Physiscts use 4 °C (39.2 °F) as the standard but
engineers often use 15.56 °C (60 °F).
• In metric system, the density of water at 4 °C is
1.00 g/cm3 (or 1.00 g/mL3), equivalent to 1000
kg/m3.
• Density of fluid varies with temperature.
Page# 15, 16
(Fluid Mechanics
with engineering
applications)

Practice Problems
• 2.3.1
• 2.3.2 (Fluid
• 2.3.3 Mechanics with
• 2.3.4
• 2.3.5
engineering
• 2.3.6 applications)
• 2.3.7


Surface Tension
• Liquids have cohesion and adhesion, both of
which are forms of molecular attraction.
• Cohesion enables a liquid to resist Tensile
stress & adhesion enables it to adhere to
another body.
It is a liquid property by virtue of which force of
attraction generates, at interface between liquid and
a gas i.e. liquid surface and at the interface between
two immiscible (not mixable) liquids, which exerts a
tension force in the surface.

Surface Tension
• When second fluid is not specified at
interface, it is understood that liquid surface is
in contact with air.
• The surface tension values for liquids slightly
decreases with increasing temperature.
• “Capillarity” is the property of exerting forces
on fluids by fine tube or porous media; it is
due to both cohesion and adhesion.


Surface Tension
• When cohesion is less (than adhesion), the
liquid will wet the solid surface in contact and
rise at the point of contact.
• If cohesion is more, the liquid surface will
depress at the point of contact.
For Instance, Capillarity makes water rise in the glass
tube, while mercury depresses below the true level.
The curved liquid surface that develops in a tube is
called Meniscus.


A cross section in capillary rise in a tube looks
like as shown in the figure.
From Free body considerations, equating the
lifting forces created by surface tension to
gravity force.

Lifting forces = Gravity forces

Meniscus
2 r cos = r2hɣ

D h
h = (2 cos ) / (ɣ.r)
Where;
= Surface tension (sigma) in units of force / L
= Wetting angle
Capillary Rise ɣ = Specific weight of liquid
r = Radius of tube
h = Capillary rise


Surface Tension
• The expression h = (2 cos ) / (ɣ.r) can be used to
compute the approximate capillary rise or
depression in the tube.
• If the tube is clean, = 0 degree for water and
about 140 degrees for mercury.
• The equation overestimates the amount of
capillary rise or depression, particularly for larger
diameter tubes.
• For tube diameters larger than 0.5 inch, capillary
effects are negligible.

Surface Tension
• Surface tension effects are generally negligible
in most engineering situations. However, they
can be important in problems involving
capillary rise.
As in soil water zone, without capillary
most forms of vegetable life would
perish. Similarly, while calculating
pressures and taking reading one shall
keep in mind that reading is correct if
and only surface tension effect is zero.


Surface Tension
• These effects are also important in hydraulic
model studies when the model is small, in the
break up of liquid jets, and in the formation of
drops and bubbles.
• The formation of drops is extremely complex
to analyze but is, for example, of critical
concern in the design of inkjet printers, a
multi-billion-dollar business.
Page# 39 (Fluid Mechanics
with engineering
applications)

Practice Problems
• 2.12.1
• 2.12.2
(Fluid Mechanics
• 2.12.3 with engineering
• 2.12.4 applications)
• 2.12.5


Standard Atmosphere
• First adopted in 1920’s in USA and Europe to
satisfy need for standardization of aircraft
instruments and aircraft performance.
• ICAO (International Civil Aviation
Organization) Standard Atmosphere
– Upto 32 km
• ISO (International Standards Organization)
Standard Atmosphere.
– Upto 50 km


Standard Atmosphere
• U.S Standard Atmosphere: (Last revised in
1976). Incorporates ICAO and ISO standards.
– Upto 86 km (and extends as far as 1000 km for
some quantities)

The standard absolute pressure behave very
differently from temperature, decreasing quite
rapidly and smoothly to almost zero at an altitude
30 km.


Standard Atmosphere
1. Troposphere: 2. Stratosphere:
In the lowest 11.02 km. The
temperature decreases rapidly and
About 9 km thick. The
linearly. temperature remains constant
at -56.5 degree Celsius.

U.S Standard
Atmosphere
3. Mesosphere: 4. Ionosphere:
At an altitude of 50 km. Here T This is the upper part of
increases first slowly and then mesosphere. T decreases
rapidly. here

Vapor Pressure of Liquids
• All liquids tend to evaporate or
vaporize, which they do by projecting
molecules into the space above their surfaces.
• If this is a confined space, the partial pressure
exerted by the molecules increases until the
rate at which the molecules re-enter the liquid
= the rate at which they leave, we call the
vapor pressure as Saturation pressure.


Vapor Pressure of Liquids
• At any given temperature, if the pressure on
the liquid surface falls below the saturation
pressure, a rapid rate of evaporation results,
known as Boiling.
– Thus we can refer to the saturation pressure as
the Boiling pressure for a given temperature, and
it is of practical importance for liquids.
We call the rapid vaporization and recondensation of liquid as it briefly passes
through a region of low absolute pressure cavitation. This phenomenon is often
very damaging and so we must avoid it.


Vapor Pressures of Liquids
• The very low vapor pressure of mercury makes
it particularly suitable for use in Barometers.


1b. introduction

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1b. introduction