1BFC 21103 Hydraulics

Section 4

Instructor: Tan Lai Wai (Office: D1-309)

Lecture: Mondays, 3 pm to 5 pm Wednesdays, 8 am to 10 am

Chapter 1. Flow in Open Channel

Learning Outcomes:1. Differentiate between open channel flow and

pipe flow2. Define and explain on the types of flow3. Identify the state of flow and flow regimes4. Define open channel geometries

2Chapter 1. Flow in Open Channel

Stormwater Management and Road Tunnel (SMART), Kuala Lumpur, Malaysia

Tahan river rapids

Siberian meandering river

Open channel flow is flow of a liquid in a conduit with a free surface subjected to atmospheric pressure.

Examples: flow of water in rivers, canals, partially full sewersand drains and flow of water over land.

Free surface

Flow

Datum x

y

uyA

B

T

Figure. Sketch of open channel geometry

3Practical applications are the determination of:a. flow depth in rivers, canals and other conveyance conduits,b. changes in flow depth due to channel controls e.g. weirs,

spillways, and gates,c. changes in river stage during floods,d. surface runoff from rainfall over land, e. optimal channel design, andf. others

1.1 Flow Parameters and Geometric Elementsa. Depth of flow y is the vertical measure of water depth.

Normal depth d is measured normal to the channel bottom.d = y cos

For most applications, d y when 10%. cos 0.1 = 0.995.

Free surface

Flow Q

Datum x

y d

So = bottom slope

Sw = water surface slope

b. Flow or discharge Q is the volume of fluid passing a cross-section perpendicular to the direction of flow per unit time.Mean velocity V is the discharge divided by the cross-sectional area A

QV =

41.1 Geometric Elementsc. Wetted perimeter P is the length of channel perimeter that is wetted or

covered by flowing water.

A = cross sectional area covered by flowing water

B = bottom width

T = top width

AP

y

1.1 Geometric Elementsd. Hydraulic radius R is the ratio of the flow area A to wetted perimeter P.

B

T

AP

y

PAR =

e. Hydraulic depth D is the average depth of irregular cross section.

TAD ==

widthtopareaflow

5Wetted perimeter P

Top width T

Area A

Channel shape

By B B + 2y

Table. Open channel geometries

yB

T

Rectangular

yz

T

Triangular

1 zy2 2zy212 zy +

By + zy2 B + 2zy 212 zyB ++yz

T

Trapezoidal

1

B

y

T

Circle2

D ( ) sin282

D DsinD

1.2 Types of Open Channel Prismatic and non-prismatic channels

Prismatic channel is the channel which cross-sectional shape, size and bottom slope are constant. Most of the man-made (artificial) channels are prismatic channels over long stretches. Examples ofman-made channels are irrigation canal, flume, drainage ditches, roadside gutters, drop, chute, culvert and tunnel.All natural channels generally have varying cross-sections and therefore are non-prismatic. Examples of natural channels are tiny hillside rivulets, through brooks, streams, rivers and tidal estuaries.

Rigid and mobile boundary channelsRigid channels are channels with boundaries that is not deformable. Channel geometry and roughness are constant over time. Typical examples are lined canals, sewers and non-erodible unlined canals.Mobile boundary channels are channels with boundaries that undergo deformation due to the continuous process of erosion anddeposition due to the flow. Examples are unlined man-made channels and natural rivers.

6Canals - is usually a long and mild-sloped channel built in the ground, which may be unlined or lined with stoned masonry, concrete, cement, wood or bituminous material.

Griboyedov Canal, St. Petersburg, Russia

Terusan Wan Muhammad Saman, Kedah

This flume diverts water from White River, Washington to generate electricity Bull Run Hydroelectric Project diversion flume

Open-channel flume in laboratory

Flumes - is a channel of wood, metal, concrete, or masonry, usually supported on or above the surface of the ground to carry water across a depression.

7Chute - is a channel having steep slopes.

Natural chute (falls) on the left and man-made logging chute on the right on the Coulonge River, Quebec, Canada

Drop - is similar to a chute, but the change in elevation is within a short distance. The spillway of Leasburg Diversion Dam is

a vertical hard basin drop structure designed to dissipate energy

Stormwater sewer - is a drain or drain system designed to drain excess rain from paved streets, parkinglots, sidewalks and roofs.

Storm drain receiving urban runoff

Storm sewer

81.3 Types / Classification of Open Channel FlowsOpen channel flow conditions can be characterised with respect to space(uniform or non-uniform flows) and time (steady or unsteady flows).Space - how do the flow conditions change along the reach of an open

channel system.

Time - how do the flow conditions change over time at a specific section in an open channel system.

a. Uniform flow - depth of flow is the same at every section of the flow dy/dx = 0

b. Non-uniform flow - depth of flow varies along the flow dy/dx 0

c. Steady flow - depth of flow does not change/ constant during the time interval under consideration dy/dt = 0

d. Unsteady flow - depth of flow changes with time dy/dt 0

1.3 Types / Classification of Open Channel Flowsa. Uniform flow

b. Non-uniform flow

c. Steady flow

d. Unsteady flow

y y Constant water

depth

y1y2 Depth changes

along the

channel

y

Time = t1

y

Time = t2

y1

Time = t1

y1

Time = t2

y

t3

t2t1

yt3

t2t1

9Open channel flow

Steady flow Unsteady flow

Uniform flow Non-uniform flow

Gradually-varied flowRapidly-varied flow

Various types of open-channel flow

The flow is rapidly varied if the depth changes abruptly over a comparatively short distance. Examples of rapidly varied flow (RVF) are hydraulic jump, hydraulic drop, flow over weir and flow under a sluice gate.

The flow is gradually varied if the depth changes slowly over a comparatively long distance. Examples of gradually varied flow (GVF) are flow over a mild slope and the backing up of flow (backwater).

RVF RVFGVF RVFGVF RVFGVF

SluiceHydraulic jump Flow over weir

Hydraulic drop

Contraction below the sluice

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1.4 State of FlowThe state or behaviour of open-channel flow is governed basically by the viscosity and gravity effects relative to the inertial forces of the flow.

Effect of viscosity - depending on the effect of viscosity relative to inertial forces, the flow may be in laminar, turbulent, or transitional state.

- Reynolds number represents the effect of viscosity relative to inertia,

VR=Re

where V is the velocity, R is the hydraulic radius of a conduit and is the kinematic viscosity (for water at 20C, = 1.004 106 m2/s, dynamic viscosity = 1.002 103Ns/m2 and density = 998.2 kg/m3).

Re < 500 , the flow is laminar

500 < Re < 12500, the flow is transitionalRe > 12500 , the flow is turbulent

Re < 500 , the flow is laminar

500 < Re < 12500, the flow is transitionalRe > 12500 , the flow is turbulent

The flow is laminar if the viscous forces are dominant relative to inertia. Viscosity will determine the flow behaviour. In laminar flow, water particles move in definite smooth paths.

VR=Re

The flow is turbulent if the inertial forces are dominant than the viscous force. In turbulent flow, water particles move in irregular paths which are not smooth.

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1.4 State of Flow

Effect of gravity - depending on the effect of gravity forces relative to inertial forces, the flow may be subcritical, critical and supercritical.

- Froude number represents the ratio of inertial forces to gravity forces,

gDV

=Fr

where V is the velocity, D is the hydraulic depth of a conduit and g is the gravity acceleration (g = 9.81 m/s2).

Fr < 1 , the flow is in subcritical stateFr = 1 , the flow is in critical state

Fr > 1 , the flow is in supercritical state

gDV

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1.5 Regimes of FlowA combined effect of viscosity and gravity may produce any one of the following four regimes of flow in an open channel:a. subcritical - laminar , when Fr < 1 and Re < 500b. supercritical - laminar , when Fr > 1 and Re < 500c. supercritical - turbulent , when Fr > 1 and Re > 12500d. subcritical - turbulent , when Fr < 1 and Re > 12500

Assignment No. 1 (due date September 21, 2011)Q1. [Final Exam Sem. 1, Session 2010/2011]

Justify the difference between:(a) uniform flow and nonuniform flow(b) state of flow using Reynolds number Re and Froude number Fr

Q2. [Final Exam Sem. 1, Session 2008/2009](a) What is:

(i) Wetted perimeter(ii) Gradually varied flow(iii) Non-uniform flow(iv) Froude number

(b) Explain the differences between canal and sewer.

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Q3. [Final Exam Sem. 1, Session 2006/2007]What is:

(a) Reynolds number(b) Froude number(c) Hydraulic radius(d) Prismatic channel(e) Uniform flow

Q4. A discharge of 16.0 m3/s flows with a depth of 2.0 m in a rectangular channel of 4.0 m wide. Determine the state of flow based on (i) Froude number, and (ii) Reynolds number. Determine the flow regime.

Q5. A triangular channel of apex angle 120 carries a discharge of 1573 L/s. Calculate the critical depth.