Engineering Low-Head Dams for Function and Safety

Fritz R. Fiedler

Department of Civil Engineering

University of Idaho

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

Why are they dangerous?

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

• Side view

• Front view

Flow in rectangular channels

QV y

w

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 ftw = 1.5 ftA = 3 ft2

V = 3 ft/sQ = 9 ft3/sq = 6 ft2/s

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

Hydraulic Jump

12

Q = V1A1

= V1y1w

Image source: http://www.engineering.usu.edu/classes/cee/3500/openchannel.htm

Hydraulic Jump

Q = V2A2

= V2y2w

Note: Q is constant, so V1y1 = V2y2 (if w constant also)

• Ratio of inertia forces to gravity forces

• F = V / (gy)0.5

• G = gravitational acceleration• Subcritical flow: F < 1 (gravity forces larger)• Supercritical flow: F > 1 (inertia forces larger)• Critical flow: F = 1

Froude Number

Froude Number

12

Image source: http://www.engineering.usu.edu/classes/cee/3500/openchannel.htm

Hydraulic Jump

F1 = V1 / (gy1)0.5

F1 > 1F2 = V2 / (gy2)0.5

F2 < 1

Initial and Sequent Depths

• Relationship between depths before (initial) and after (sequent) a hydraulic jump

• If y1 and V1 are known, can compute y2

211

2 8F112

1

y

y

Flow over a dam (weir)

y0

y2y1

ycHydraulic

JumpP

H

As water flows over dam, goes through critical depth, yc at which F = 1

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

subcriticalsupercritical

subcritical

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?

Submerged Hydraulic Jump

y0

y2y1

yc

P

H

yt

• When yt exceeds y2 the jump becomes submerged• Degree of Submergence = S = (yt – y2) / y2

• When S < 0, jump occurs downstream• When S > 0, jump is submerged• If yt becomes large enough, dam will be submerged too• In the flume, we can control yt

y0

P

H yc

waves travel upwaves travel down

y1yt

y2

y

Project Steps

1. Analysisa. Measure variables at two discharges

b. With and without tailwater submergence

2. Designa. Objectives: maintain upstream depth, allow

safe passage, create surf wave, minimize cost

b. Method: simple calculations, physical model studies and testing

Analysis1. At low discharge

a. With no tailwateri. Measure: H, P (dam height), yc (must locate), y1,

y2, y

ii. Compute: Vc, Q, q, F1, C

iii. Evaluate: measurement accuracy, sequent depth equation, floating object passage

b. With tailwater submerging jumpi. Measure: yt, y, and compute S

ii. Evaluate: measurements, floating object passage

2. Repeat 1., a., b., … for high discharge

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.

Design1. Conceptual

a. What makes the hydraulic dangerous?i. Uniformity, y, reverse flow velocity, aeration

b. How can this knowledge be used to meet objectives?

2. Analytical / Mathematicala. Difficult!

b. Computer models

c. Simple equations (e.g., V-notch weir)

3. Physical models…

Physical Models

Image source: http://www.usbr.gov/pmts/hydraulics_lab/about/index.html

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)

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

Other (Important) Considerations

• Water Quality– Sediment and contaminants

• Physical– Sediment and stream morphology– Dissolved oxygen– flooding

• Ecological– Fish passage– Effects on aquatic life