Lecture 7-River Dynamics 1 Flashcards
Hydraulics of river flow equation
Q=Av=wdv
Q = discharge
A = area (width x depth)
v = average velocity
What determines the flow velocity?
Fluid mechanics (all the forces that are pushing, pulling and acting on water)
Why are rivers important to study in a hydrological sense?
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)
When does flow occur:
fluid subjected to mechanical potential energy gradient
- gravity (gravitational potential energy)
- hydrostatic pressure (hydrostatic potential energy)
mechanical potential energy gradient (break it down)
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
gravity (force)
- 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
hydrostatic pressure (force)
- 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 - Direction:
- at any point, pressure is equal in all directions (only determined by weight above)
other forces retard flow or alter course due to (1):
boundary conditions
Force formula
Force = mass x acceleration (operate as a point)
Force formula
Force = mass x acceleration (operate as a point)
where:
Acceleration = dV / dt (change of velocity over change of time)
Hydrostatic potential energy formula
Epp = πBy
Epp = Potential energy of hydrostatic pressure
where y = vertical distance from the surface
Gravitational potential energy formula
Epg = πBz Epg = Potential energy gradient π = weight density B = volume z = height above datum
Potential energy formula
Ep = Epg + Epp
basically add together hydrostatic potential energy + gravitational potential energy
Forces in open-channel flows:
- Induce/maintain: act in the direction of flow β
- Resist: act opposite to flow β
- Turncoat: act with or against flow depending on specific conditions β
- Act perpendicular to flow β’
Forces in open-channel flows:
- Induce/maintain: act in the direction of flow β
- Resist: act opposite to flow β
- Turncoat: act with or against flow depending on specific conditions β
- Act perpendicular to flow β’
Hydrostatic pressure gradient formula
Fp / M = gβ§Y / X
Y=depth
X = distance between them
(can act in either direction)
Frictional forces
-Viscosity
Frictional forces
- Viscosity
- Turbulence
Viscosity
-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
ββββββ>
βββββ>
ββββ>
βββ>
ββ>
β>
__________
Turbulence
- related to eddy viscosity
- depends on the characteristics of the flow (depth and velocity)
Minor forces that happen perpendicular to flow
- surface tension
- centrifugal
- coriolis
Surface tension
- pull on water as it tries to keep bonded together
- only significant in very small water volumes
Centrifugal
- related to curvature of the path
- when going around a bend, will change speed and trajectory
Coriolis
- related to rotation of the earth
- left is S. Hemisphere, right in N. Hemisphere
Forces summary and overall equation
-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)
Forces summary
- Accelerate motion: gravity, pressure gradient
- Resist motion: pressure gradient, viscosity, turbulence
- Right angle to motion: surface tension, coriolis, centrifugal
Overall forces equation
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)
Why to classify flow types
- 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
Laminar flow zone
consistent velocity through the profile
Turbulent flow zone
with a decent body of water there will be mixing between layers, water at the surface moves faster, have laminar flow at the bed
Boundary layer and momentum transfer time steps
- free-stream velocity
- free-stream enters boundary
- transition
- turbulent boundary layer fully developed
(loss of momentum due to boundary layer, each state has a different velocity distribution/profile)
Free-stream velocity
No vertical gradient (no shear stress, so viscosity is not important)
(no base, laminar flow)
Free-stream enters boundary
No slip property β Water next to boundary β has v=0 β boundary layer development β velocity profile development
Transition
water starts mixing, different velocities start to develop
Turbulent boundary layer fully developed
Water at the surface moves fastest v>0 (faster than previous time steps, water below) laminar flow only at the base
(most streams/rivers!)
Flow classification, 2 main types:
- laminar vs turbulent
- dependent on the relative forces operating on water body
Flow classification 3 steps:
- 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)
Reynolds equation
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
Froude number
Fr = V/βgY
whatβs 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
Changes in space and time
- steady flow
- uniform flow
- varied flow
- unsteady flow
