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Chapter 4: Flowing Fluids & Pressure Variation (part 1)

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) Euler’s equation of motion. Understanding Flow - Measurements.

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Chapter 4: Flowing Fluids & Pressure Variation (part 1)

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  1. 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) Euler’s equation of motion

  2. 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)

  3. Flow visualization – pathline vs. streakline • Pathline • Streakline

  4. Flow visualization - streamline • Streamline – vectors tangent to the direction of flow at every point (not exactly shown here)

  5. 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

  6. 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

  7. 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

  8. Summary

  9. 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:

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

  11. Which best represents • Lagrangian frame of reference? • Eulerian frame of reference? • (a) Streamline • (b) Streakline • (c) Pathline

  12. Euler’s equation • Valid for inviscid, incompressible flow only!

  13. Euler’s 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?

  14. 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?

  15. Euler derivation, continued • Now, what do we do when g is not perpendicular to acceleration direction?

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