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

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?