Lecture 9-River Dynamics 3

Question 1

Froude number purpose

Answer 1

Will water continue downstream or go back upstream when it hits an obstacle

Question 2

How to solve for mean velocity when water is flowing at critical velocity

Answer 2

Velocity = Fr x sqrt(gY)
Where fr=1 at critical velocity
And g=9.8
Y= depth.

Question 3

Changes in space and time of the profile (4)

Answer 3

Steady flow
Uniform flow
Varied flow
Unsteady flow

Question 4

Uniform flow

Answer 4

Steady and uniform

• velocity is constant in space (reach of interest)
• depth is constant in space

Question 5

Steady flow

Answer 5

• Velocity is constant through time

- depth is constant through time

Question 6

Varied flow

Answer 6

Depth and velocity are not constant in time and space.

Question 7

Unsteady flow

Answer 7

Velocity and depth are not constant through time (flood wave)

Question 8

Significance of uniform flow

Answer 8

• flow is steady if average velocity doesn’t change over time
• acceleration =0, velocity does notchange
• can be laminar
• or turbulent (our focus)

Question 9

Prandtl’s velocity profile

Answer 9

What is the distribution of velocity in turbulent flow?
In turbulent flow, turbulent forces > viscous forces
Eddy viscosity depends on flow characteristics and varies in space within a flow

Question 10

τ =ε ( dv /dy)

Answer 10

Prandtl's velocity profile formula
τ = shear stress
ε = eddy viscosity (not a constant)
v = velocity at a point
y = distance above bed
d = change in

Question 11

ε = ρι2 (dv/dy)

Answer 11

ε = Eddy viscosity
ρ = mass density
ι (squared) = mixing length

Question 12

Eddy viscosity assumptions (2)

Answer 12

1. ι = ky
The mixing length is proportional to distance from the bed
2. τ =τ0 =γ y S0
The shear stress is constant throughout flow and equal to boundary shear stress given by laminar flow.
τ0 = shear stress at the base
γ = weight density
y = depth
S0 = slope at the base

Question 13

v = 2.5 V* ln ( 30y / ks )

Answer 13

Final velocity profile equation
Velocity related to friction V* =(gyS0) to power of 1/2
y =depth
ks = constant for effective roughness length (grain size at the bed)

Question 14

v= 2.5 V* ln(by/y0)

Answer 14

Formula to calculate the mean velocity