Open Channel Flows Introduction Part 2 Flashcards
How is regime defined?
Regime defined by Froude number Fr → most important in channel flow
What is Froude number?
Fr = ratio of flow speed and the shallow-water wave velocity
How can Froud number be calculated?
F_r = U/√gh
What does a super-critical flow mean?
Fr> 1, does not affect flow upstream
What does a critical flow mean?
Fr=1
What does sub-critical flow mean?
Fr<1, may affect flow upstream
When does a hydrualic jump form?
Forms between super and sub-critical flow
When is a flow laminar?
When Re«Re critical
How can the Reynolds number be calculated?
Re = UR/v
What are all open channel flows classified as?
Turbulent
What does steady flow mean?
No variation in time, no change in source discharge
What does unsteady flow mean?
- Variations over time
- A flow in which quantity of liquid flowing per second is not constant
What is a uniform flow?
- No spatial variations
- No along-channel variations in water depth, slope, discharge, etc.
What is a non-uniform flow?
Variations in one or more of the variables e.g., depth, slope, discharge
What are slow varying flows?
Gradual variations; pressure is usually hydrostatic and streamlines are straight
What are rapidly varying flows?
Rapid variations; pressure is generally not hydrostatic and streamlines are curved
What is the force balance like in uniform flow?
Equilibrated
How can width be determined?
dA/dh
When is pressure P hydrostatic?
Pressure p is hydrostatic (linear increase with depth) if streamlines are approximately straight and parallel (uniform/slowly varying flows).
What is the pressure head at the channel bed?
P = ⍴gh
What is the pressure head at the channel bed?
h = P/⍴g
What are the underlying assumptions?
i) uniform/slowly varying flow,
ii) incompressible fluid
iii) steady flow
iv) Friction negligible
What new behaviors can the flow encounter?
- Waves (due to wind, ships, etc.).
- Travelling shocks (e.g. surge waves due to sudden closing of sluice gates).
- Hydraulic jump.
What is the piezometric head equal to?
Piezometric head is equal to the free surface under hydrostatic conditions
What’s the equation for steady uniform flow?
F_1-F_2+F_g-F_f=0
How is the gravity body force calculated?
ρgALs
How is the wall friction force calculated?
𝜏_wPL
Gravity balances…?
Fricition
How can wall shear stress be calculated?
ρgRs
How is the friction related to the velocity in turbulent flows?
For any turbulent flow, the friction (wall shear stress) varies approximately as the square of the mean velocity
How can Chezy coefficient be derived?
- Assume flow is steady and uniform
- Momentum equation
- Friction forces balance with g forces
What is the radius of a a channel if it is really wide?
h
