1

Open Channel Flow

Fluid develops a free surface exposed to atmospheric pressure. Can also occur in par8ally-full closed conduits. Associated energy losses are also important but ow here is governed by gravity forces.

2

Head Losses in Open Channels

Energy Equa8on: where y = ow depth

3

Head Losses in Open Channels

Cri8cal ow:

Rectangular channels

Circular Pipes

4

Head Losses in Open Channels

Similar to pressurized pipes, fric8on losses are caused by shearing forces associated with the channel roughness.

Impact of resistance on free surface ow: Manning Formula:

Chezy (KuPer) Formula:

Where Sf = Slope of EGL; R = Hydraulic radius

5

Flow Classification steady/unsteady; uniform/non-uniform Examples:

I. Euent owing over a weir over a short-5me

II. Flow through a long, submerged intake pipe

III. Open Channel ow through a screen

IV. Flow through a pipe where an upstream valve is being closed

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Uniform Flow

Open Channel Flow

v Velocity remains constant over prescribed length. v Geometric proper5es are not constrained as in closed pipes. v Free surface ow ul5mately reaches uniform ow: normal depth yn.

v Gravity forces are balanced with resis5ng shear forces. v HGL is parallel to EGL (Sf) and the channel invert (S0).

7

Varied Flow

Open Channel Flow

v The depth and velocity vary longitudinally along the channel. v Common in short channels, at changes in channel grade or geometry & near hydraulic structures e.g. weirs, gates, transi5ons...

v If changes are gradual, resis5ng shear forces con5nue to be important and the eect of accelera5on on ow between 2 adjacent

sec5ons is negligible.

v However, in rapidly-varied ow, iner5al forces dominate and pressure distribu5ons can no longer be assumed hydrosta5c Large

losses are incurred.

8

Gradually varied ow:

Assump5ons Fric8on loss iden8cal to that in uniform ow. The pressure distribu8on remains hydrosta8c. Velocity distribu8ons at one sec8on are constant. Prisma8c channel (constant shape and slope). Resistance coecients are independent of ow depth.

Open Channel Flow

9

Terminology:

Head Losses in Open Channels

Zone 1

Zone 2

Zone 3

10

Open Channel Flow Water Surface Profiles

11

Open Channel Flow Water Surface Profiles

12

Direct Step Method:

Solves for the distance over which a specied change in

depth occurs. Ideally suited for

prisma8c channels.

Does not directly yield the depth at the end of a known

channel length.

Open Channel Flow

Standard Step Method:

Itera8vely solves for the unknown depth at one end of

the channel.

CHANNEL TRANSITIONS

Cylinder quadrant inlet transi8on from trapezoidal to rectangular channel

18

SHARP-CRESTED WEIRS:

Rectangular suppressed

19

Rectangular contracted

SHARP-CRESTED WEIRS:

20

BROAD-CRESTED WEIRS:

FREE JUMP

FORCED JUMP

SUBMERGED JUMP

Types of Hydraulic Jump

Key parameters in energy dissipa8on: i) Headwater ra8ng curve ii) Energy line for headwater iii) Tailwater ra8ng curve iv) Energy line for tailwater

FLIP BUCKET ON OVERFLOW SPILLWAY

~ Safety valve of the dam-reservoir system Oken indispensible: it is not economical to have a reservoir capacity larger than the dierence between inow and oumlow

Percent of total cost varies e.g. 4 % for unlined rock spillways 22 % for earth and rock ll dams

Libby and Dwoskak dams: 5 M $ repair cost due to reduced # of spillways

SPILLWAYS:

Classification of Spillways

Classica8on according to:

Most prominent feature Ogee, Chute, Labyrinth, side channel, tunnel, shak, siphon, stepped

Func8on Service, Auxiliary, Fuse

Control Structure Gated, Ungated, Orice

Classification of Spillways

OR Classica8on according to:

Inlet Overow, collec8ng channel, shak, siphon, orice

Regula8on Sluicegate, radial gate, ap gate, unregulated

Outlet S8lling basin, roller bucket, sky jump, plunge pool

Spillway Design

2 steps:

Find type and size to t the requirements of the specic site Hydraulic and structural design

Prepara8on for design Evalua8on of date: topogaphy, geology, ood hydrography, storage and

release requirements

Crest type, size and eleva8on Control Alterna8ve arrangements + cost analysis Analysis of exis8ng spillways (trends for a given set of condi8ons)

Aspects involved in design

1) Inow design ood e.g. ood formulae, sta8s8cal methods,

numerical modeling of rainfall-runo rela8ons

2) Spillway design ood: previously based on dam height, storage

volume, downstream development; now based on consequences of

dam failure ( most complicated issue): each country has its standards

3) Spillway oumlow discharge: Flood-rou8ng analysis requires:

Full reservoir level Crest Level # of spans Dsicharge ra8ng curves

Aspects involved in design

Based on 3)

Crest prole Downstream protec8on Energy dissipa8on

4) Frequency of usage: depends on runo characteris8cs of drainage

area and reservoir capacity

Ogee Spillway design charts