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Geography 201: Hydrology > Lecture 7-River Dynamics 1 > Flashcards

Lecture 7-River Dynamics 1 Flashcards

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1
Q

Hydraulics of river flow equation

A

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

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2
Q

What determines the flow velocity?

A

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

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3
Q

Why are rivers important to study in a hydrological sense?

A

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)

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4
Q

When does flow occur:

A

fluid subjected to mechanical potential energy gradient

  • gravity (gravitational potential energy)
  • hydrostatic pressure (hydrostatic potential energy)
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5
Q

mechanical potential energy gradient (break it down)

A

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

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6
Q

gravity (force)

A
  • 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
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7
Q

hydrostatic pressure (force)

A
  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)
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8
Q

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

A

boundary conditions

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9
Q

Force formula

A

Force = mass x acceleration (operate as a point)

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10
Q

Force formula

A

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

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11
Q

Hydrostatic potential energy formula

A

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

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12
Q

Gravitational potential energy formula

A 
Epg = 𝛄Bz
Epg = Potential energy gradient
𝛄 = weight density
B = volume
z = height above datum
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13
Q

Potential energy formula

A

Ep = Epg + Epp

basically add together hydrostatic potential energy + gravitational potential energy

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14
Q

Forces in open-channel flows:

A
  • Induce/maintain: act in the direction of flow β†’
  • Resist: act opposite to flow ←
  • Turncoat: act with or against flow depending on specific conditions ↔
  • Act perpendicular to flow β€’
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15
Q

Forces in open-channel flows:

A
  • Induce/maintain: act in the direction of flow β†’
  • Resist: act opposite to flow ←
  • Turncoat: act with or against flow depending on specific conditions ↔
  • Act perpendicular to flow β€’
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16
Q

Hydrostatic pressure gradient formula

A

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

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17
Q

Frictional forces

A

-Viscosity

18
Q

Frictional forces

A
  • Viscosity

- Turbulence

19
Q

Viscosity

A

-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
—————–>
————–>
———–>
——–>
—–>
–>
__________

20
Q

Turbulence

A
  • related to eddy viscosity

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

21
Q

Minor forces that happen perpendicular to flow

A
  • surface tension
  • centrifugal
  • coriolis
22
Q

Surface tension

A
  • pull on water as it tries to keep bonded together

- only significant in very small water volumes

23
Q

Centrifugal

A
  • related to curvature of the path

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

24
Q

Coriolis

A
  • related to rotation of the earth

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

25
Q

Forces summary and overall equation

A

-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)

26
Q

Forces summary

A
  • Accelerate motion: gravity, pressure gradient
  • Resist motion: pressure gradient, viscosity, turbulence
  • Right angle to motion: surface tension, coriolis, centrifugal
27
Q

Overall forces equation

A 
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)
28
Q

Why to classify flow types

A
  • 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
29
Q

Laminar flow zone

A

consistent velocity through the profile

30
Q

Turbulent flow zone

A

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

31
Q

Boundary layer and momentum transfer time steps

A
  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)
32
Q

Free-stream velocity

A

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

33
Q

Free-stream enters boundary

A 
No slip property β†’
Water next to boundary β†’
has v=0 β†’
boundary layer development β†’
velocity profile development
34
Q

Transition

A

water starts mixing, different velocities start to develop

35
Q

Turbulent boundary layer fully developed

A

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

36
Q

Flow classification, 2 main types:

A
  • laminar vs turbulent

- dependent on the relative forces operating on water body

37
Q

Flow classification 3 steps:

A
  • 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)
38
Q

Reynolds equation

A

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

39
Q

Froude number

A

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

40
Q

Changes in space and time

A
  • steady flow
  • uniform flow
  • varied flow
  • unsteady flow

Geography 201: Hydrology (8 decks)

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