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 Q V y w Variables: y = flow depth (L) w = channel width (L) A = flow area = yw (L 2 ) V = flow velocity (L/T) Q = discharge = VA (L 3 /T) q = Q/w (L 2 /T) Example: y = 2 ft w = 1.5 ft A = 3 ft 2 V = 3 ft/s Q = 9 ft 3 /s q = 6 ft 2 /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 1 2 Q = V 1 A 1 = V 1 y 1 w Image source: Hydraulic Jump Q = V 2 A 2 = V 2 y 2 w Note: Q is constant, so V 1 y 1 = V 2 y 2 (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

1 2 Image source: Hydraulic Jump F 1 = V 1 / (gy 1 ) 0.5 F 1 > 1 F 2 = V 2 / (gy 2 ) 0.5 F 2 < 1

Initial and Sequent Depths Relationship between depths before (initial) and after (sequent) a hydraulic jump If y 1 and V 1 are known, can compute y 2

Flow over a dam (weir) y0y0 y2y2 y1y1 ycyc Hydraulic Jump P H As water flows over dam, goes through critical depth, y c at which F = 1 Q = CwH 1.5 or q = CH 1.5 where C is a weir coefficient that varies with dam type and H – but we are going to find and measure y c subcritical supercritical subcritical

Critical Flow At critical flow, F = 1 = V c / (gy c ) 0.5 V c = (gy c ) 0.5 Measure y c at dam, compute V c then Q = V c y c w How is the location of y c found?

Submerged Hydraulic Jump y0y0 y2y2 y1y1 ycyc P H ytyt When y t exceeds y 2 the jump becomes submerged Degree of Submergence = S = (y t – y 2 ) / y 2 When S < 0, jump occurs downstream When S > 0, jump is submerged If y t becomes large enough, dam will be submerged too In the flume, we can control y t

y0y0 P H ycyc waves travel up waves travel down y1y1 ytyt y2y2 yy

Project Steps 1.Analysis a.Measure variables at two discharges b.With and without tailwater submergence 2.Design a.Objectives: maintain upstream depth, allow safe passage, create surf wave, minimize cost b.Method: simple calculations, physical model studies and testing

Analysis 1.At low discharge a.With no tailwater i.Measure: H, P (dam height), y c (must locate), y 1, y 2,  y ii.Compute: V c, Q, q, F 1, C iii.Evaluate: measurement accuracy, sequent depth equation, floating object passage b.With tailwater submerging jump i.Measure: y t,  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.

Design 1.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 / Mathematical a.Difficult! b.Computer models c.Simple equations (e.g., V-notch weir) 3.Physical models…

Physical Models Image source:

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