MEE 340
Fluid Mechanics - Introduction Part 2
Eric Monsu Lee, Ph.D.
College of Engineering and Engineering Technology
Northern Illinois University
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Intensive and Extensive Properties
Intensive properties are independent of the mass of the
system. For example, pressure, temperature, and density.
Extensive properties depends on the size of the system. For
example, mass, volume, and total momentum.
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Why Studying these Properties? I
Helps in System Characterization:
Intensive properties (like pressure, temperature, and density)
describe the state of the fluid at a point, regardless of system
size.
Extensive properties (like mass and volume) help define the
scale or quantity of the system.
Supports Dimensional Analysis
Knowing which properties are intensive or extensive is crucial
for Buckingham Pi theorem, which is widely used in fluid
mechanics to derive dimensionless numbers (e.g., Reynolds
number, Mach number, and Froude number).
Essential for Control Volume Analysis
In control volume problems, distinguishing between intensive
and extensive properties helps in applying conservation laws
(mass, momentum, energy) correctly.
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Why Studying these Properties? II
Critical for Thermodynamic Calculations
Many fluid systems involve energy exchange. Intensive
properties are used to calculate specific energy, enthalpy, and
entropy, which are vital in analyzing pumps, turbines, and
compressors.
Improves Conceptual Understanding
It helps understand how fluids behave under different
conditions. For example, why pressure remains constant
across a small volume but mass does not.
Supports Engineering Design
Engineers use intensive properties to design systems that
operate under specific conditions (e.g., pressure and
temperature), while extensive properties help size components
(e.g., tanks, pipes).
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Examples of Intensive/Extensive Properties
Density
Specific volume
Specific energy
Specific weight
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Continuum Idealization I
Fluids are treated as continuous media, meaning properties like
pressure, temperature, and velocity are defined at infinitesimally
small points, even though fluids are made of discrete molecules
with finite size (dp ).
Fluid properties vary smoothly.
No gaps or voids exist between molecules.
The fluid behaves as if it’s made of a continuous substance.
Mean Free Path (λ) and Molecular Motion
The mean free path is the average distance a molecule travels
before colliding with another molecule.
In gases like air, molecules move freely between collisions.
The mean free path depends on temperature, pressure, and
molecular size.
Click
here
for a video visualizing the mean free path.
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Continuum Idealization II
dp λ
(1)
Rarefied gases
Increasing altitude (H) and reducing pressure (P)
λ increase invalidate the idealization
For example,
dO2 = 10−10 meter
λO2 at 1 atm and 20◦ C ∼ 10−8 meter
The molecular diameter has to be larger than the mean free
path for the continuum idealization claim to be valid.
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Cavitation I
Liquid pressure drops to vapor pressure.
Liquid water bursts to vapor state.
Cavitation bubbles collapse when they move to higher pressure
regions, where they collapse to liquid states, causing noise.
In a propeller or pump, low pressure occurs when velocity is
the greatest at the tips of the blades (V = r ω)
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Cavitation II
Formation of vapor phase in liquid as a result of reduced
pressures at constant ambient temperature.
Boiling in a liquid due to pressure reduction instead of heat
addition. (e.g., water boils at relatively lower temperature at
higher altitude.)
A liquid is said to "cavitate" when vapor bubbles form and
grow as a result of pressure reduction.
Cause pump performance to deteriorate
Create noise and vibration
Lead to mechanical damage
Pump failure
Click
here
for a video about cavitation.
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