Hydrology

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Hydrology

• Open channel
• Flow
• Acad. Year 2003-2004
• FLTBW

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Rivers in Dijle CA
Voer Bertem 41 km2
Discharge m³/s
Dijle St. Joris W 645 km2
10-19 April 2001
Days
3
Major event
Dijle Sint Joris Weert (640 km²)
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(m³/s)
Flow in rivers
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Voer Heverlee ( 51 km²)
(m³/s)
4
Rivier is not a simple channel
open water surface
Uniform flow rare, only in artificial
canals Backwater varying profile curves etc ...
real rivers
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Bernouilli energy equation
y hab bot dsurf to stream
Energy -loss
Total potential
V12/2g
V2/2g
Open water surface
p1/g?d
H1
y
any streamline
H2
z1
Rivier bottom
z
Reference height
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Bernouilli equation at any streamline

• If no friction (ideal fluid with no viscosity)
• However viscosity and no-slip boundary
• Energy is lost ( hL ) along the longitudinal
  slope however H in any vertical is constant

Bernouilli equation see FTV physics course
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Hydraulic radius in hydrology hydraulics

• Definition in heat and mass transfer (FTV, Datta
  etc) hydraulic diameter dh
• Definition in hydraulics hydraulic radius Rh R

hydraulic radius ? geometric radius
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Uniform versus nonuniform flow
Sf
Uniform parallel watersurface bottom and energy
So
Non-uniform not parallel
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Bernouilli energy equation

• Energy of the streamline on the river bottom per
  unit of weight discharge
• Pressure D expressed in waterdepth (D P/?g)
• Height of bottom z
• Average velocity V in a cross-section
• Beware open canals (wet cross-section is not
  constant like in a filled pipe)
• Head losses hL friction and local
• In a vertical the potential remains constant (sum
  of pressure and elevation constant)

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Uniform flow in channel
Slope of total energy-line (Sf) and longitudinal
slope of the bottom (S0) become equal (parallel)
Darcy-Weisbach (see FTV)
Requires constant cross-section and slope
energy losses by friction
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Reynolds number laminar of turbulent

• Water ?10-6 m²/s normally turbulent
• 4 R is characteristic length (diameter pipe)
• R A/P hydraulic radius (!!!!!!!)
• Sheet flow over smooth surface could be laminar
  (rather exceptional)

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Uniform open chanal-flow

• Uniform (eenparig) constant cross-section
  watersurface, bottom- and energy line are
  parallel
• gt friction loss in equilibrium with channel
  slope
• Manning formula (turbulent)

Relation discharge-waterheight is uniform
Rather rare in natural rivers
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Uniform flowin rectangular section
A
P wet perimeter
Ahw P2hw in hydraulics RA/P different as FTV
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Mannings n
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Artifical channels with uniform flow
Well defined cross-section and longitudinal slope
Concrete Channel
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Velocity distribution in a channel
Air resistance (low)
Wet perimeter (higher friction)
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Channel cross-sections
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Specific energy

• energy relative to channel bottom

2 !!!
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Critical depth minimum specific energy for a
given Q

• specific qs Q/B with B top width
• E y Q2/2gA2 where Q/A qs/y
• Take dE/dy (1 qs2/gy3) 0 (find minimum)
  
• For a rectangular channel bottom width B,
• 1. Emin 3/2Yc for critical depth y yc
• yc/2 Vc2/2g
• yc (Q2/gb2)1/3

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Critical, sub- super-critical flow
In general for any channel, B top width (Q2/g)
(A3/B) at y yc Finally Fr V/(gy)1/2
Froude No. Fr 1 for critical flow Fr lt 1 for
subcritical flow Fr gt 1 for supercritical flow
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Mild and steep slope

• If uniform flow ( calculate by Mannings equation
  ) has Fr gt 1
• gt steep slope with supercritical flow
• If uniform flow has Fr lt 1
• gt mild slope and subcritical flow
• Transition goes via critical flow
• Fr 1
• Control sections often use critical flow
  conditions (see discharge measurement)

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Change in slope and overfall
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hydraulic jump UCL
critical flow
sub-critical flow
super-critical flow
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Voer Heverlee
subcritical
ultrasonic level
critical
supercritical
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Example of shallow river
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Change in bed elevation (e.g. dip)
?
waterlevel
riverbed
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Change in bed elevation (e.g. dip)
waterlevel
water
riverbed
reference level
Example with Q2 Frgt1 Frlt1
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Important consequences

• A pit in a river for
• subcritical flow has lower velocities and will
  have more sediment trapping
• supercritical flow has higher velocities and will
  erode

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Rivier is not a simple channel
Uniform flow mostly in artificial canals (
irrigation) Backwater widening bends etc are
common in natural rivers
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Examples non-uniform
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Non uniform is part of the fun rafting
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From super- to subcriticalHydraulic jump

• Concept of specific force (not explained here)
• the momentum (specific force) before and after
  the jump is the same
• energy loss in the jump (local head losses) can
  be used for energy dissipation

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hydraulic jump UCL
super-critical flow
sub-critical flow
Jump from super to sub-critical
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Variations in velocity

• Vertical profile
• cross section

Bend
straight river
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Meandering river
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Spiral flow
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