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BFC21103 HydraulicsChapter 1. Flow in Open ChannelSiti Nazahiyah Rahmatnazahiya@uthm.edu.my

Learning OutcomesAt the end of this chapter, students should be able to:

i. Define and explain on types and states of flow

ii.Identify types of open channels

iii.Define open channel geometriesBFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)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 sewers and drains and flow of water over land.Free surfaceFlowDatumxyuyABTFigure. Sketch of open channel geometryBFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)

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

Tahan river rapids

Siberian meandering riverPractical applications:flow depth in rivers, canals and other conveyance conduits,changes in flow depth due to channel controls e.g. weirs, spillways, and gates,changes in river stage during floods,surface runoff from rainfall over land, optimal channel design, and othersBFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)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%, e.g. cos 1 = 0.9998.Free surfaceFlow QDatumxydSo = bottom slopeSw = water surface slopeBFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)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

BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)c. Wetted perimeter P is the length of channel perimeter that is wetted or covered by flowing water.A = cross sectional area covered by flowing waterB = bottom widthT = top widthAPyBFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)d. Hydraulic radius R is the ratio of the flow area A to wetted perimeter P.BTAPy

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

Channel sectionArea ATop width TWetted perimeter PByBB + 2yTable. Open channel geometriesyBTRectangularyzTTriangular1zy22zy

By + zy2B + 2zy

yzTTrapezoidal1ByTCircle2D

BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)Find:(a)Top surface width T, flow area A, wetted perimeter P, and hydraulic radius R.(b)If Q = 2.4 m3/s, determine the state of flow.(c)If longitudinal length L = 50 m, find the cost to construct the channel. Given excavation cost = RM 3/m3 and lining cost = RM 5/m2.Activity 1.13 m2 m1 m60BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)

(a)Top surface width T, wetted area A, wetted perimeter P and hydraulic radius R.BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)(b)If Q = 2.4 m3/s, determine the state of flow.

(c)If the length of the channel is L = 50 m, find the cost to construct the channel. Given excavation cost = RM 3/m3 and lining cost = RM 5/m2.Volume of excavation

Cost of excavation

BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)Area of lining

Cost of lining

Total cost

BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)Find T, A, P, R, and DAdditional Question for Assignment #11.2 m1.5 m321.2 m1.5 m0.3 mBFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)Find:(a)Flow area A (b)Wetted perimeter P (c)Hydraulic radius RActivity 1.23 m4 m2 m1 m2 m2 m1 mA1A2A3A4BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)1.2 Types of Open Channel Prismatic and non-prismatic channelsPrismatic 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 of man-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. BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my) 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 and deposition due to the flow. Examples are unlined man-made channels and natural rivers.BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)Canals 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, KedahBFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)

This flume diverts water from White River, Washington to generate electricity

Bull Run Hydroelectric Project diversion flumeFlumes 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.BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)

Open-channel flume in laboratoryBFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)Chute 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, CanadaBFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)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 energyBFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)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 sewerBFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)1.3 Types and Classification of Open Channel FlowsOpen channel flowSteady flowUnsteady flowUniform flowNon-uniform flowGradually-varied flowRapidly-varied flowVarious types of open-channel flowBFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)Open 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.a. Uniform flow - depth of flow is the same at every section of the flow dy/dx = 0b. Non-uniform flow - depth of flow varies along the flow dy/dx 0BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)a. Uniform flowb. Non-uniform flowy1y2Depth changes along the channelyyConstant water depthxDepth of flow is the same at every section along the channel,

Depth of flow varies at different sections along the channel,

BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)Time - how do the flow conditions change over time at a specific section in an open channel system.c. Steady flow - depth of flow does not change/ constant during the time interval under consideration dy/dt = 0d. Unsteady flow - depth of flow changes with time dy/dt 0BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)c. Steady flowd. Unsteady flowy1Time = t1y2Time = t2y1t3t2t1Depth of flow is the same at every time interval,

Depth of flow changes from time to time,

y1 = y2y1 y2 y3BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)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).BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)RVFRVFGVFRVFGVFRVFGVFSluiceHydraulic jumpFlow over weirHydraulic dropContraction below the sluiceBFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)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 visco sity - 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,

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 = 1.002 103 Ns/m2 and density = 998.2 kg/m3).BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)Re < 500 the flow is laminar500 < Re < 12500 the flow is transitionalRe > 12500 the flow is turbulentThe 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.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.

BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)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,

where V is the velocity, D is the hydraulic depth of a conduit and g is the gravity acceleration (g = 9.81 m/s2).BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)Fr < 1, the flow is in subcritical stateFr = 1, the flow is in critical stateFr > 1, the flow is in supercritical state

BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)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:

subcritical - laminar, when Fr < 1 and Re < 500

supercritical - laminar, when Fr > 1 and Re < 500

supercritical - turbulent, when Fr > 1 and Re > 12500

d. subcritical - turbulent, when Fr < 1 and Re > 12500BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)Assignment #1Q1.[Final Exam Sem I, Session 2010/2011]Justify the difference between:(a)uniform flow and non-uniform flow(b)state of flow using Reynolds number Re and Froude number Fr.

Q2.[Final Exam Sem I, Session 2008/2009](a)Define(i)Wetted perimeter(ii)Gradually-varied flow(iii)Non-uniform flow(iv) Froude number(b)Explain the differences between canal and sewer.BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)Q3.[Final Exam Sem I, Session 2006/2007]Define(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(a)Froude number, and(b)Reynolds number.BFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)Q5.A triangular channel of apex angle 120 carries a discharge of 1573 L/s. Calculate the critical depth.- End of Question -Thank YouBFC21103 Hydraulics Tan et al. (laiwai@uthm.edu.my)