HYDRAULICS

UNIFORM FLOW IN OPEN CHANNELS

ByErni Syuhada Bt Mazwil Ishan

HYDRAULICS ENGINEERING

• A scientific fluid flow particularly in water thoroughly in pipe, open channel, orifice and embankment, including the problem related to energy and pressure.

• Related to water or fluid in dynamic condition.

CONTENT

What is Open Channel Types of Open ChannelTypes of flowing water and controlSolution of uniform flow in Open Channel

OPEN CHANNEL

An open channel :a)The stream not completely enclosed by solid

boundaries b)It has free surface subjected only to

atmospheric pressure.c) Referred as free-surface flow or gravity flow

Open Channel

TYPES OF OPEN CHANNEL

Natural ChannelIrregular shape

i.e : river, hillsides rivulets, tidal etuaries

Artificial ChannelRegular shape

i.e : drains, culverts, sewer, tunnels

TYPES OF OPEN CHANNEL

TYPES OF FLOWING WATER AND ITS CONTROL

Rapidly Varied Flow

i.e : hydraulic jump

Non-Uniform Flow

≠ 0

Uniform Flow

= 0

Gradually Varied flow

i.e : upstream of obstruction

Open Channel

Steady Flow

= 0

Open ChannelUnsteady Flow

≠ 0

TYPES OF FLOWING WATER AND ITS CONTROL

Steady• y (depth of water) and v (velocity) remain constant

with respect to time

Unsteady Flow• y and v change with time

TYPES OF FLOWING WATER AND ITS CONTROL

Uniform• y (depth of water) and v (velocity) remain constant

along the channel. Figure 2.0

Non - uniform Flow• y and v change along the length of the

channel

Figure 2.0

• Flow Classifications1) Depending on the Reynolds number, Re

– Laminar Flow (if Re < 500): very slow and shallow flowing water in very smooth open channels.

– Turbulent Flow (if Re > 1000): ordinary flow in ordinary open channels.

– Transition Flow (if 500 < Re < 1000)

TYPES OF FLOWING WATER AND ITS CONTROL

V = average channel velocityL = length of channelv = kinematic viscosity of fluid

2) Depending on Froude number, Fr

– Fr = 1 : Critical Flow

– Fr < 1 : Subcritical Flow – slow flowing water

– Fr > 1 : Supercritical Flow – fast flowing water

TYPES OF FLOWING WATER AND ITS CONTROL

V = average channel velocityg = gravity acceralationD = hydraulics water depth

TURBULENT

LAMINAR

TYPES OF FLOWING WATER AND ITS CONTROL

Critical Section (In uniform and non-uniform flow)1) If So < Sc, y > yc : Subcritical flow2) If So = Sc, y = yc : Critical flow3) If So > Sc, y < yc : Supercritical flow

Figure 3.0

Bernoulli’s Equation

Lhzg

Vpz

g

Vp 2

222

1

211

22

Open Channel

GEOMETRIC PROPERTIES OF OPEN CHANNELS

RECTANGULAR CHANNEL TRAPEZOIDAL CHANNEL

• The terminology of geometric elementsy : depth of flow T : top width b : bottom channel widthm : side slope So : channel bottom slope v : average flow density

Fr : Froude number Re : Reynold number L : length of channelQ : flow rates , Q = AV A : area of the flow P : wetted perimeterR: hydraulic radius at cross section

D : hydraulics water depth V : volume

ν : velocity E : specific energy ∆z : weir height : flow temperature q = discharge over width

(m)

GEOMETRIC PROPERTIES OF OPEN CHANNELS

Type of channel

TOP WIDTH, T

AREA, A WETTED PERIMETER, P

RECTANGULAR B By B + 2yTRAPEZOIDAL B+2my By + my2 B+2y √ 1+m2

GEOMETRIC PROPERTIES OF OPEN CHANNELS

Where,

UNIFORM FLOW IN OPEN CHANNEL

Uniform flow is an equilibrium condition that flow tends to if the channel :

a)constant slopeb)constant cross sectionc)constant roughnessd)depth, water area, velocity and discharge at every section of channel are constante)channel bed, water surface and energy line are parallel, So = Sw = Sf)y1 = y2 , V1 = V2

• CHEZY FORMULA :

UNIFORM FLOW IN OPEN CHANNEL

Where ; V = mean velocity (m/s)C = Chezy’s factor of flow resistance (m1/2/s)R = hydraulic radiusSo = slope of energy lineQ = Discharge (m3/s)

• MANNING FORMULA :Where ; V = mean velocity (m/s)

n = Manning’s coefficient of roughness (s/m1/3) R = hydraulic radiusSo = slope of energy lineQ = Discharge (m3/s)

UNIFORM FLOW IN OPEN CHANNEL

Closed conduits flowing partly fullCorrugated metal storm drains 0.010Concrete culvert 0.024Unfinished concrete 0.013Clay drain tile 0.014Lined or built up channelsUnpainted steel 0.012Planed wood 0.012Unplaned wood 0.013Trowel – finished concrete 0.013Rough concrete 0.017Glazed brick 0.020Brick in cement mortar 0.013Excavated channelsClean earth (straight channel) 0.022Earth with weeds (winding channel) 0.030Natural streamsClean and straight 0.030Weedy reaches, deep pools 0.100

Typical values of Manning’s coefficient, n

SOLUTION IN OPEN CHANNEL

• Conveyor FactorFrom eq

We obtain ; For Chezy

For Manning

• Section Factor, Z For Chezy ;

For Manning;

SOLUTION IN OPEN CHANNEL

• Thus, normal depth, yo can be obtain by using trial and error method

SOLUTION IN OPEN CHANNEL

• Example :Given trapezoidal channel 10m wide with side slope of 1:1.5. Bed slope is 0.0003. The channel with concrete lining, n = 0.012. Calculate the velocity, V and flow rate, Q when the flow depth is 3.0m. If the flow rate is 50m/s, determine the slope, So of channel.