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By N.E.M Business Solutions
Fluids
Contents
Properties
The difference
between Fluids and other Substances.
Matter is primarily
found in three forms: solids, liquids and gases. Gases and liquids together
are called fluids. The molecules of a solid are usually mutually closer 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. This is not the case for a
fluid, where the attractive forces between the molecules are smaller. There
are plastic solids, which flow under the proper circumstances, and even
metals may flow under high pressures. On the other hand there are certain
viscous fluids liquids that do not flow readily and is easy to confuse them
with plastic solids. The distinction is that any fluid, no matter how
viscous will yield in time to the slightest stress. But a solid, no matter
how plastic, requires a certain magnitude of stress to be exerted before it
will flow. Also when the shape of a solid is altered by external forces, the
tangential stresses between adjacent particles tend to restore the body to
its original configuration. With a fluid, these tangential stresses depend
on the velocity of deformation and vanish as the velocity approaches zero.
When motion ceases, the tangential stresses disappear and the fluid does not
regain its original shape.
Properties of
fluids:
- Density, Specific weight, specific
volume and specific gravity: The density of a fluid is its mass
per unit volume, while the specific weight is the weight per unit
volume. They are related as g = r g. The specific volume n is the
volume occupied by a unit mass of fluid. Specific volume is the
reciprocal of density. n = 1/ r. Specific gravity s of
a liquid is the ratio of its density to the density of water at a
standard temperature. Engineers use 600F as this temperature.
Specific gravity of a gas is the ratio of its density to the
density of hydrogen or air at some specified temperature and pressure.
- Compressible and incompressible
fluids: Fluids may be either of a constant or variable density. There is
nothing like an incompressible fluid, but the term is applied to those
fluids whose density changes negligibly with pressure. Liquids are
ordinarily considered incompressible fluids, but sound travels through
them demonstrating that they are elastic.
- Compressibility: This is defined as
the change in volume due to change in pressure. It is inversely
proportional to its volume modulus of elasticity, also known as bulk
modulus. The bulk modulus is analogous to the modulus of elasticity
of solids; however for fluids it is defined on a volume basis.
- Vapour pressure of liquids: As all
liquids tends to evaporate or vaporize, which they do by projecting
molecules into the space above their surfaces. The pressure exerted by
the molecules increases till some of the molecules start re-entering the
liquid. This pressure is called the vapour pressure.
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Viscosity
Viscosity: The viscosity
of a fluid is a measure of its resistance to shear or angular deformation.
In other words, viscosity of a fluid is that property which determines the
amount of resistance to a shearing force. It is due primarily to interaction
between fluid molecules. The friction forces in fluid flow result from
cohesion and momentum interchange between molecules in the fluid. This
decides that as temperature increases the viscosities of all liquids
decrease and those of all gases increase. Viscosity of a fluid can be
expressed in two ways:
- Kinematic viscosity
- Dynamic viscosity
Viscosities of liquids
decrease with temperature increases but are unaffected by pressure changes.
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Fluid flow in a pipe
The fluid flow in a pipe is governed by
the following equation:
dp + r vdv + dZ = 0
where P is the pressure, r is the density and Z is the head of the fluid.
Integrating the equation,
P + (1/2)r v2 + Z = C
C is any arbitrary constant.
This can also be written as
P1 + (1/2) r v12
+ Z1 = P2 + (1/2) r v22 + Z2
where the subscripts 1 and 2 denote any two positions.
This equation is called Euler's equation and it implies that at different
points in the pipe the energy of the fluid is constant. This equation does
not take the frictional losses in the pipe into account.
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Static Pressure,
Dynamic Pressure and Total Pressure
Static pressure is that
which would be measured by an instrument moving with the flow. However, it
is rather difficult to make this measurement in a practical situation.
Stagnation pressure is obtained when the flowing fluid is decelerated to
zero speed by a friction less process. This is also called the total
pressure and
P0 = P +
(1/2) r v2
Where P0 = stagnation pressure or total pressure
P = static pressure
r = density of the fluid
v = velocity of flow.
The term (1/2) r v2 has the dimensions of pressure and is called
the dynamic pressure of the fluid.
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Head Loss
Head loss is defined as the loss of
energy per unit mass of the fluid. It represents the irreversible conversion
of mechanical energy to an unwanted thermal energy and loss of this energy
via heat transfer. Head loss can be regarded as a sum of ‘major losses’,
which are due to frictional effects in fully developed flow in constant area
tubes and minor losses due to entrances, fittings, area changes and so on.
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Fluid Hammer
When a valve in a pipe
with a flowing fluid is suddenly closed, a fluid hammer pressure wave is set
up. The very high pressures generated by such waves can damage the pipe. The
maximum pressure generated by the fluid hammer ph is a function
of the fluid density r , initial flow speed u0 and the velocity
of the pressure wave set up in the pipe cp.
ph = f (r ,
u0, cp ).
The fluid hammer
causes pressure fluctuations in the fluid in the pipe because of which the
pipe expands and contracts. This is a critical problem in case of power
plants, where the flow of water must be varied rapidly in proportion
to the load changes on the turbine. Incidentally, the pressure wave is
always set up as a result of abrupt decrease in velocity.
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Reynolds Number
The Reynolds number is a dimension less
constant which determines the type of flow in a pipe. It represents the
ratio of inertial forces to the viscous forces.
For circular pipes flowing full,
Reynolds number
Re = (VDr /m ) = (VD/n )
where V = mean velocity of fluid
D = diameter of the pipe
n = kinematic viscosity f the fluid
r = mass density of the fluid
m = absolute viscosity of the fluid.
For non circular cross sections, the ratio of the cross sectional area to
the wetted perimeter is used as the Reynolds number.
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Laminar &
Turbulent Flow
In laminar flow
fluid particles move along straight, parallel paths in layers or laminae.
The magnitudes of velocities of adjacent laminae are not the same. Shear
stress and rate of angular deformation govern this type of flow. The
viscosity of the fluid is dominant and thus suppresses any tendency to
turbulent conditions. The Reynolds number determined for this type of flow
is less than 2000. At a given cross section the velocity distribution
follows a parabolic law of variation for a laminar flow. The maximum
velocity at the centre of the pipe is twice the average velocity.
In turbulent flow the particles of the fluid move in a haphazard fashion in
all directions. It is impossible to trace the motion of an individual
particle. There is more uniform distribution of velocity. The Reynolds
number determined for a turbulent flow is greater than 2000.
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Critical Velocity
The critical velocity of practical
interest to engineers is the velocity below which all turbulence is damped
out is damped out by the viscosity of the fluid. The Reynolds number for
upper limit of laminar flow is about 2000.
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