Chapter 4: Flowing Fluids

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Chapter 4 Flowing Fluids Pressure Variation
(part 1)

• Qualitative description of flow
• Types of visualizations
• Types of flows (part 1)
• Frames of reference (part 1)
• Eulers equation of motion

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Understanding Flow - Measurements

• To measure / understand flow, we often use a
  number of visualization techniques
• Experiments
• Computations
• Theoretical predictions
• Types (defined in a moment)
• Pathline
• Streakline
• Streamline
• Timeline (less common)

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Flow visualization pathline vs. streakline

• Pathline
• Streakline

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Flow visualization - streamline

• Streamline vectors tangent to the direction of
  flow at every point (not exactly shown here)

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Why do we care??

• Understanding, measuring flow
• Two different distinctions of flow (for now)
• Steady vs. unsteady
• a question of time
• Uniform vs. non-uniform
• a question of space
• Two different frames of reference
• Eulerian
• Lagrangian

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Steady flow uniform vs. non-uniform

• Steady flow at every point in space, the
  velocity is unchanging, independent of time
• Flow could be steady if qin qout
• In the non-uniform flow, the fluid acceleration
  is not equal to zero

qin
qout
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Un-steady flow uniform vs. non-uniform

• unsteady flow the velocity is changing,
  independent of time
• Flow could be unsteady if qin ? qout
• In the non-uniform flow, the fluid acceleration
  is not equal to zero

qin
qout
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Summary
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Some comments about (un) steady (non-) uniform
flows and visualization

• Steady uniform flow
• Streamline, streakline, pathline, are all the
  same, always
• (the visualization example was unsteady
  uniform)
• (the computational example was steady
  non-uniform)
• Steady flow
• Uniform flow

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• Eulerian vs. Lagrangian frame of reference
• Quick summary for now

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Which best represents

• Lagrangian frame of reference?
• Eulerian frame of reference?
• (a) Streamline
• (b) Streakline
• (c) Pathline

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Eulers equation

• Valid for inviscid, incompressible flow only!

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Eulers equation

• Consider the fluid-filled accelerating truck.
• Where is the pressure greatest?
• How can we calculate the pressure of B relative
  to that of A?

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Euler derivation, continued

• Now what about the pressure difference between B
  and C? Which is greater?
• How can we calculate the pressure of C relative
  to that of B? Relative to that of A?

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Euler derivation, continued

• Now, what do we do when g is not perpendicular to
  acceleration direction?