LECTURE 5
Properties Of Fluids-Cont.
By Dr. Mohamed Fekry
2 nd Sem.1434
PROPERTIES OF FLUIDS
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Density (r) and Specific Volume (v)
Specific Gravity (SG)
Specific Weight (g)
Density of ideal gas
Coefficient of Compressibility (k)
Coefficient of Volume Expansion (b)
Viscosity (m)
Surface Tension (s)&
Capillary Effect (h)
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- When two solid bodies in contact move
relative to each other, a friction
force develops at the contact surface in
the direction opposite to motion.
- The situation is similar when a fluid
moves relative to a solid or when two
fluids move relative to each other.
- It appears that there is a property that
represents the internal resistance of a
fluid to motion or the “fluidity,” and that
property is the viscosity. The force a
flowing fluid exerts on a body in the flow
direction is called the drag force, and the
magnitude of this force depends, in part,
on viscosity.
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Viscosity (m)
Viscosity measures a fluids ability to
resist shear stress
Real Experiment:
One moving shaft inside another
hollow shaft filled with oil.
In the case the thickness of oil film is
equal to:
L = Ri − Rs
Results:
Mention the relationships of the following parameters.
F = applied force
A = contact area
L = thickness of the fluid layer
V = the velocity of the moving plate
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Hypothetical Experiment:
Where:
v = Velocity of the moving plate (varies linearly from 0 at the
stationary surface to maximum at the contact surface between
the moving plate and oil).
A = Contact area between the moving plate and oil.
F = Applied force to the moving plate.
L = Thickness of oil layer
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L & A = constants
F&v
v & A = constants
F&L
L & v = constants
F&A
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Where μ is the proportional constant.
By observation:
F = μA v/L
Where F is the external applied force.
Summation of forces: Σ F x = 0
Driving forces – Resisting forces = 0
F − FR = 0
↔
F = FR = τ A
F\A = μ v/L
τ = μ v/L
Assumptions:
• Small gap thickness
• v is not too large
v/L = Δv/ΔL = Slope of the velocity distribution (assuming linear
distribution)
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The ideal fluid, with no viscosity (μ = 0), falls on the horizontal axis,
while the true elastic solid plots along the vertical axis. A plastic that
sustains a certain amount of stress before suffering a plastic flow
corresponds to a straight line intersecting the vertical axis at the yield
stress.
There are certain non-Newtonian fluids in which μ varies with
the rate of deformation. These are relatively uncommon in
engineering usage.
Typical non-Newtonian fluids include paints, printer’s ink, gels,
sludge and slurries, and certain plastics.
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Consider a fluid layer of thickness within a small gap
between two concentric cylinders, such as the thin layer of
oil in a journal bearing. The gap between the cylinders can
be modeled as two parallel flat plates separated by
a fluid. Noting that torque is T=FR (force times the moment
arm, which is the radius R of the inner cylinder in this
case), the tangential velocity is V =ωR (angular velocity
times the radius), and taking the wetted surface area of the
inner cylinder to be A=(2πRL) by disregarding the shear
stress acting on the two ends of the inner cylinder, torque
can be expressed as
F  A  m A
V
l
where L is the length of the cylinder and n is the number of revolutions per
unit time, which is usually expressed in rpm (revolutions per minute). Note
that the angular distance traveled during one rotation is 2π rad, and thus the
relation between the angular velocity in rad/min and the rpm is ω = 2πn .
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Therefore, two concentric cylinders can be used as a viscometer,
a device that measures viscosity.
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