AE 1350
Lecture Notes #5
WE HAVE LOOKED AT..
• Why should we study properties of
atmosphere?
• Ideal Gas Law: p = rRT
• Variation of Temperature with Altitude
• Variation of Pressure with Altitude
• Variation of Density with Altitude
• Tables of Standard Atmosphere
TOPICS TO BE COVERED
• Incompressible flow
• Streamlines and stream tubes
• Conservation of Mass (Continuity)
Incompressible Flow
• Air is a compressible fluid.
• Its density WILL change if temperature changes,
or if some external force is applied.
– Example: A child squeezing a balloon
• A flow is said to be incompressible if there are no
changes in density attributable to (or caused by)
the velocity or speed of the flow.
• Theory and observations in wind tunnels suggest
that most flows may be treated as incompressible
(I.e. constant density) until the Mach number is
sufficiently high (>0.4 or so.)
What has flow speed got to do with
compressibility?
Fluid particles send out signals in the form of acoustic
waves to the surrounding fluid, indicating their motion.
If there is sufficient time for the sound waves to travel before the
fluid particle arrives, the fluid particles downstream will “hear”
the message and clear out.
Otherwise, there will be a crush (compression), or even a stampede
(shock wave).
Shocks form when the acoustic waves
generated by the air particles
in front of the body
can not outrun the body.
Shocks
Streamlines in Steady Flow
Inviscid (ideal) flow
Viscous flow
•Streamlines describe the path the
fluid particles will take.
•At any point on the streamline,
the flow velocity is tangential to
the streamline.
•Viscosity alters the shape of streamlines
around bluff bodies.
•Scientists inject smoke particles into
streamlines to make them visible to
the naked eye.
Streamlines over a Cylinder
(Low Reynolds Number of 10)
Reynolds
Number
where D  Cylinder

r VD

dia.
Streamlines over a Cylinder
(High Reynolds Number of 2000)
Reynolds
Number
where D  Cylinder

r VD

dia.
Streamlines over an Airfoil
at
High Angles of Attack
Flow
Separation
Continuity
• Consider a stream tube, i.e. a collection of
streamlines that form a tube-like shape.
• Within this tube mass can not be created or
destroyed.
• The mass that enters the stream tube from the left
(e.g. at the rate of 1 kg/sec) must leave on the right
at the same rate (1 kg/sec).
Continuity
Rate at which mass enters=r1A1V1
Area A1
Density r1
Velocity V1
Rate at which mass leaves=r2A2V2
Area A2
Density r2
Velocity V2
Continuity
In compressible flow through a “tube”
rAV= constant
In incompressible flow, r does not change. Thus,
AV = constant
Continuity (Continued..)
AV = constant
If Area between streamlines
is high, the velocity is low
and vice versa.
Low Velocity
High Velocity
Continuity (Continued..)
High Velocity
AV = constant
If Area between streamlines
is high, the velocity is low
and vice versa.
In regions where the
streamlines squeeze together,
velocity is high.
Low Velocity
Venturi Tube is a Device
for
Measuring Flow Rate
we will study later.
Low velocity
High velocity