Lecture 7-River Dynamics 1

Question 1

Hydraulics of river flow equation

Answer 1

Q=Av=wdv
Q = discharge
A = area (width x depth)
v = average velocity

Question 2

What determines the flow velocity?

Answer 2

Fluid mechanics (all the forces that are pushing, pulling and acting on water)

Question 3

Why are rivers important to study in a hydrological sense?

Answer 3

They are a combination of everything happening upstream:
-groundwater
-soil water movement
-precipitation
-evaporation
all of this ends up combined in rivers which then moves through water through the catchment
-health of rivers tells us about the health of the system
-also one of the most hazardous components of the system (floods)

Question 4

When does flow occur:

Answer 4

fluid subjected to mechanical potential energy gradient

• gravity (gravitational potential energy)
• hydrostatic pressure (hydrostatic potential energy)

Question 5

mechanical potential energy gradient (break it down)

Answer 5

gradient: difference between two things over a length/time (relative differences)
energy: forces which push/pull
potential: baseline but not always realised (what forces are more/less important)
mechanical: how objects will relate to each other

Question 6

gravity (force)

Answer 6

• 9.81 m s^(-2)
• relative difference: gradient when comparing two points at different heights relative to a datum
• goes from high to low to balance

Question 7

hydrostatic pressure (force)

Answer 7

1. Magnitude:
   - force related to the weight of water and air above
   - Pressure = Pw + Pa
   - Pw = water pressure determined by the weight density of water and the height of water above
   - Pa = air pressure above
   - Hydrostatic pressure is a component of potential energy
   - need to know relative difference when comparing two points
2. Direction:
   - at any point, pressure is equal in all directions (only determined by weight above)

Question 8

other forces retard flow or alter course due to (1):

Answer 8

boundary conditions

Question 9

Force formula

Answer 9

Force = mass x acceleration (operate as a point)

Question 10

Force formula

Answer 10

Force = mass x acceleration (operate as a point)
where:
Acceleration = dV / dt (change of velocity over change of time)

Question 11

Hydrostatic potential energy formula

Answer 11

Epp = 𝛄By
Epp = Potential energy of hydrostatic pressure
where y = vertical distance from the surface

Question 12

Gravitational potential energy formula

Answer 12

Epg = 𝛄Bz
Epg = Potential energy gradient
𝛄 = weight density
B = volume
z = height above datum

Question 13

Potential energy formula

Answer 13

Ep = Epg + Epp

basically add together hydrostatic potential energy + gravitational potential energy

Question 14

Forces in open-channel flows:

Answer 14

• Induce/maintain: act in the direction of flow →
• Resist: act opposite to flow ←
• Turncoat: act with or against flow depending on specific conditions ↔
• Act perpendicular to flow •

Question 15

Forces in open-channel flows:

Answer 15

• Induce/maintain: act in the direction of flow →
• Resist: act opposite to flow ←
• Turncoat: act with or against flow depending on specific conditions ↔
• Act perpendicular to flow •

Question 16

Hydrostatic pressure gradient formula

Answer 16

Fp / M = g⧍Y / X
Y=depth
X = distance between them
(can act in either direction)

Question 17

Frictional forces

Answer 17

-Viscosity

Question 18

Frictional forces

Answer 18

• Viscosity

- Turbulence

Question 19

Viscosity

Answer 19

-friction of a fluid that resists forces tending to cause flow (shear stress resisting motion)
-no-slip condition
-water at the bed has the same velocity as the bed, as we get further up the bed as less influence
-water at the surfacing is moving fastest
-think deck of cards
—————–>
————–>
———–>
——–>
—–>
–>
__________

Question 20

Turbulence

Answer 20

• related to eddy viscosity

- depends on the characteristics of the flow (depth and velocity)

Question 21

Minor forces that happen perpendicular to flow

Answer 21

• surface tension
• centrifugal
• coriolis

Question 22

Surface tension

Answer 22

• pull on water as it tries to keep bonded together

- only significant in very small water volumes

Question 23

Centrifugal

Answer 23

• related to curvature of the path

- when going around a bend, will change speed and trajectory

Question 24

Coriolis

Answer 24

• related to rotation of the earth

- left is S. Hemisphere, right in N. Hemisphere

Question 25

Forces summary and overall equation

Answer 25

-Accelerate motion: gravity, pressure gradient -Resist motion: pressure gradient, viscosity, turbulence -Right angle to motion: surface tension, coriolis, centrifugal These components expressed as a formula: Fg-Fv-Ft+Fp-Fp-Fs-Fr-Fc = M * (dV/dt) Simplified to: Fg - Fv - Ft = M * (dV/dt)

Question 26

Forces summary

Answer 26

- Accelerate motion: gravity, pressure gradient - Resist motion: pressure gradient, viscosity, turbulence - Right angle to motion: surface tension, coriolis, centrifugal

Question 27

Overall forces equation

Answer 27

``` Including all forces expressed as a formula: Fg-Fv-Ft+Fp-Fp-Fs-Fr-Fc = M * (dV/dt) Simplified to: Fg - Fv - Ft = M * (dV/dt) (gravity, viscosity and turbulence) ```

Question 28

Why to classify flow types

Answer 28

- think about which forces are more/less important in different scenarios (ex: surface tension and viscosity have bigger effect on very small flows) - helps how we go about calculating velocity and then discharge down the track

Question 29

Laminar flow zone

Answer 29

consistent velocity through the profile

Question 30

Turbulent flow zone

Answer 30

with a decent body of water there will be mixing between layers, water at the surface moves faster, have laminar flow at the bed

Question 31

Boundary layer and momentum transfer time steps

Answer 31

1. free-stream velocity 2. free-stream enters boundary 3. transition 4. turbulent boundary layer fully developed (loss of momentum due to boundary layer, each state has a different velocity distribution/profile)

Question 32

Free-stream velocity

Answer 32

No vertical gradient (no shear stress, so viscosity is not important) (no base, laminar flow)

Question 33

Free-stream enters boundary

Answer 33

``` No slip property → Water next to boundary → has v=0 → boundary layer development → velocity profile development ```

Question 34

Transition

Answer 34

water starts mixing, different velocities start to develop

Question 35

Turbulent boundary layer fully developed

Answer 35

Water at the surface moves fastest v>0 (faster than previous time steps, water below) laminar flow only at the base (most streams/rivers!)

Question 36

Flow classification, 2 main types:

Answer 36

- laminar vs turbulent | - dependent on the relative forces operating on water body

Question 37

Flow classification 3 steps:

Answer 37

- relative magnitude of gravity, viscous and turbulent forces (difference) - rate of change of mean velocity or mean depth with respect to time (temporal) - rate of change of mean velocity or mean depth in downstream direction (spatial)

Question 38

Reynolds equation

Answer 38

Re = VR / u R = A/P to calculate relative magnitude of forces Re <500: viscous dominates, so flow is laminar Re >500: turbulent forces dominate Re>2000: fully turbulent

Question 39

Froude number

Answer 39

Fr = V/√gY what's more important gravity or turbulence Fr < 1: gravity exceeds flow velocity (wave can travel upstream) subcritical = tranquil Fr > 1: turbulent forces greater, supercritical = rapid Fr = 1: critical

Question 40

Changes in space and time

Answer 40

- steady flow - uniform flow - varied flow - unsteady flow