1. Fluid properties 1

2. How does 𝑞 𝑠 vary with 𝑞 𝑤 (or 𝑢)?
Under what circumstances may particles be detached (eroded) from rest?
How are particles transported?
What causes particles to be released from transport?

3. How does 𝑞 𝑠 vary with 𝑞 𝑤 (or 𝑢)?
Under what circumstances may particles be detached (eroded) from rest?
How are particles transported?
What causes particles to be released from transport?
1. Incipient motion problem. Depends on both particle and fluid properties, flow depth and fluid velocity.

4. Viscosity
A key physical distinction among fluid transporting agents. 𝜏 𝑥𝑦 =𝜇 𝑑 𝑢 𝑥 𝑑𝑧 𝜇 = dynamic (molecular) viscosity
What are the implications of viscosity differences between air and water?

5. Shear stress and momentum flux
Modify Newton’s description of viscosity: 𝜏 𝑥𝑦 = 𝜇 𝜌 𝑑 𝜌 𝑢 𝑥 𝑑𝑧 𝜌 𝑢 𝑥 has dimensions of mass times velocity per unit volume [M L]/[T L3], or momentum per unit volume 𝜇/𝜌=𝜈, kinematic viscosity

6. Other sources of momentum flux
Fluid motion not always parallel to the boundary! Eddies also increase momentum flux, may be considered a source of viscosity 𝜏 𝑥𝑦 = 𝜇+𝜂 𝑑 𝑢 𝑥 𝑑𝑧 𝜂 = eddy viscosity

7. Turbulence
When does fluid flow become turbulent?

8. Turbulence Reynolds number: 𝑅𝑒= 𝜌𝑢𝑑 𝜇 = 𝑢𝑑 𝜈
Interpretation: ratio of inertial to viscous forces; OR, ratio of eddy viscosity to dynamic viscosity

9. For water…

10. LR2 proposal: Evaluation and comment to USACE of the
“Iowa Mitigation Method” for streams.