AE 1350 Lecture Notes

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AE 1350Lecture Notes 5
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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

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TOPICS TO BE COVERED

• Incompressible flow
• Streamlines and stream tubes
• Conservation of Mass (Continuity)

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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 (gt0.4 or so.)

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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).
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Shocks form when the acoustic waves generated by
the air particles in front of the body can not
outrun the body.
Shocks
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Streamlines in Steady Flow

• Streamlines describe the path the fluid
  particles will take.
• At any point on the streamline, the flow
  velocity is tangential tothe streamline.
• Viscosity alters the shape of streamlinesaround
  bluff bodies.
• Scientists inject smoke particles into
  streamlines to make them visible tothe naked
  eye.

Inviscid (ideal) flow
Viscous flow
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Streamlines over a Cylinder(Low Reynolds Number
of 10)
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Streamlines over a Cylinder(High Reynolds Number
of 2000)
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Streamlines over an AirfoilatHigh Angles of
Attack
Flow Separation
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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).

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Continuity
Rate at which mass leavesr2A2V2
Rate at which mass entersr1A1V1
Area A1 Density r1 Velocity V1
Area A2 Density r2 Velocity V2
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Continuity
In compressible flow through a tube rAV
constant
In incompressible flow, r does not change.
Thus, AV constant
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Continuity (Continued..)
AV constant If Area between streamlines is
high, the velocity is low and vice versa.
Low Velocity
High Velocity
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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
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Venturi Tube is a DeviceforMeasuring Flow
Ratewe will study later.
High velocity
Low velocity