Engineering Low-Head Dams for Function and Safety

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Engineering Low-Head Dams for Function and Safety

• Fritz R. Fiedler
• Department of Civil Engineering
• University of Idaho

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What is a Low-Head Dam?

• A dam that is typically less than 15 feet tall
• Used to pond water behind them but not control
  flow
• Head a term that refers to elevation, which can
  be related to fluid pressure and energy

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Why are they dangerous?

• Low-head dams cause water to recirculate, thus
  trapping buoyant objects

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Flow in rectangular channels

• Side view
• Front view

Variables y flow depth (L) w channel width
(L) A flow area yw (L2) V flow velocity
(L/T) Q discharge VA (L3/T) q Q/w
(L2/T) Example y 2 ft w 1.5 ft A 3 ft2 V
3 ft/s Q 9 ft3/s q 6 ft2/s
Q
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States of flow in open channels

• For a given Q, flow in open channels can be
  subcritical, supercritical, or critical
• Subcritical disturbances on water surface will
  travel upstream (flow velocity less than wave
  velocity) high y, low V
• Supercritical disturbances will not travel
  upstream (flow velocity greater than wave
  velocity) low y, high V
• Critical flow velocity equals wave velocity

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Hydraulic Jump
Hydraulic Jump
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1
Q V1A1 V1y1w
Q V2A2 V2y2w
Image source http//www.engineering.usu.edu/class
es/cee/3500/openchannel.htm
Note Q is constant, so V1y1 V2y2 (if w
constant also)
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Froude Number

• Ratio of inertia forces to gravity forces
• F V / (gy)0.5
• G gravitational acceleration
• Subcritical flow F lt 1 (gravity forces larger)
• Supercritical flow F gt 1 (inertia forces larger)
• Critical flow F 1

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Froude Number
Hydraulic Jump
2
1
F1 V1 / (gy1)0.5 F1 gt 1
F2 V2 / (gy2)0.5 F2 lt 1
Image source http//www.engineering.usu.edu/class
es/cee/3500/openchannel.htm
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Initial and Sequent Depths

• Relationship between depths before (initial) and
  after (sequent) a hydraulic jump
• If y1 and V1 are known, can compute y2

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Flow over a dam (weir)
As water flows over dam, goes through critical
depth, yc at which F 1
subcritical
H
yc
Hydraulic Jump
y0
subcritical
P
supercritical
y2
y1
Q CwH1.5 or q CH1.5 where C is a weir
coefficient that varies with dam type and H but
we are going to find and measure yc
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Critical Flow

• At critical flow, F 1 Vc / (gyc)0.5
• Vc (gyc)0.5
• Measure yc at dam, compute Vc then
• Q Vcycw
• How is the location of yc found?

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Submerged Hydraulic Jump
H
yc
y0
P
y2
y1
yt

• When yt exceeds y2 the jump becomes submerged
• Degree of Submergence S (yt y2) / y2
• When S lt 0, jump occurs downstream
• When S gt 0, jump is submerged
• If yt becomes large enough, dam will be
  submerged too
• In the flume, we can control yt

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waves travel up
waves travel down
H
yc
y0
Dy
P
y1
y2
yt
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Project Steps

• Analysis
• Measure variables at two discharges
• With and without tailwater submergence
• Design
• Objectives maintain upstream depth, allow safe
  passage, create surf wave, minimize cost
• Method simple calculations, physical model
  studies and testing

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Analysis

• At low discharge
• With no tailwater
• Measure H, P (dam height), yc (must locate), y1,
  y2, Dy
• Compute Vc, Q, q, F1, C
• Evaluate measurement accuracy, sequent depth
  equation, floating object passage
• With tailwater submerging jump
• Measure yt, Dy, and compute S
• Evaluate measurements, floating object passage
• Repeat 1., a., b., for high discharge

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Notes

• We can mark, with tape and markers, the water
  levels right on the flume
• Mark the height of the tailwater gate
• We will keep flume slope, discharges constant
  throughout semester
• Group Assignment create a data sheet based on
  previous slide before next class.

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Design

• Conceptual
• What makes the hydraulic dangerous?
• Uniformity, Dy, reverse flow velocity, aeration
• How can this knowledge be used to meet
  objectives?
• Analytical / Mathematical
• Difficult!
• Computer models
• Simple equations (e.g., V-notch weir)
• Physical models

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Physical Models
Image source http//www.usbr.gov/pmts/hydraulics_
lab/about/index.html
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Physical Model Testing

• Measure variables as in Analysis (and more?)
• What has changed?
• Compare upstream pool elevations
• Aim for little or no difference at both
  discharges
• Test object passage
• Surf spot?
• Describe the hydraulic
• Iterative process! (a.k.a., trial and error)

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Practicality and Economics

• What types of materials would be required to
  build your design? (concrete, rip rap, )
• How and when could it be constructed?
• If volume of material added is the primary cost,
  and the cost of this material per unit volume is
  known how much would it cost?
• Minimum volume minimum cost estimate the
  volume change in your design

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Other (Important) Considerations

• Water Quality
• Sediment and contaminants
• Physical
• Sediment and stream morphology
• Dissolved oxygen
• flooding
• Ecological
• Fish passage
• Effects on aquatic life

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