Open Channel-Hydraulics PDF

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OPEN CHANNEL FLOW

Chapter -6 Open channel flow An open channel flow may be defined as a passage through which water flows under atmospheric pressure. In open channels the flow of water takes place with a free surface which is subjected to atmospheric pressure, where as pipe flow has no free surface. Pipe flow being confined in a closed conduit, exerts no direct atmospheric pressure but hydraulic pressure only. Classification of flow The flow in channels can be classified as 1- Steady flow and unsteady flow 2- Uniform flow and non- uniform flow 3- Laminar flow and turbulent flow 4- Sub critical flow, critical flow and super critical flow The first three categories are discussed in preceding sections. Let’s define sub critical, critical and super critical flows. In open channel flow gravity force is the predominate force. Due to the relative effect of gravity and inertia forces the channel flow may be designated as sub critical, critical or supercritical. The ratio of inertia force to gravity force is called Fraud’s number, which is a dimension less parameter. V

Fr= gD when Fr=1, the flow is critical Fr< 1 , the flow is sub critical Fr> 1 , the flow is supercritical. Uniform flow When water flows in an open channel resistance is offered to it, which results in causing a loss of energy. The resistance encountered by the flowing water is generally counteracted by the component of gravity force acting on the body of the water in the direction of the motion. A uniform flow will be developed if the gravity force balances the resistance. Among the different uniform flow formula, the Chezy’s and the Manning’s equations are most widely used ones. o Chezy’s formula V= C RS where V= Velocity of flow R= hydraulic mean depth S= the slope of the channel C= constant

LECTURE NOTE ON HYDRAULICS

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OPEN CHANNEL FLOW

o Manning’s formula 1 2/3 1/2 R S n 1 1/6  C= R n

V=

where n= coefficient of roughness

Best Hydraulic OR Most Efficient cross sections -

The best hydraulic section is one that has the least wetted perimeter or its equivalent, the least area for the type of the section. The channel section is said to be most efficient if it gives the maximum discharge for the given shape, slope, area and roughness. The most efficient cross section offers a little resistance to flow .

V= f(R,S) Q= A f(R,s) Rectangular channels Let Band D be the bed width and depth respectively. Then, A= BD -------------(1) P= B+ 2D ---------(2) From (1) , B= P= -

A , substituting in to equation (2) D

D

A +2D ------(3) D

B For the section to be the most efficient, the wetted perimeter p must be minimum

dp =0 dD dp A ( +2D) =0  dD D

 A +2 =0 D2  A = 2D2  BD = 2D2  B=2D



 D=

B 2

Thus the discharge in a rectangular channel of a given cross sectional area is maximum when the depth of water is one-half of the width. Example: water flows in a rectangular channel at a depth of 1.2m and a flow rate of 5.7m3/s. Determine the minimum channel width if the flow is to be sub critical

So/n :

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OPEN CHANNEL FLOW

Q=5.7m3/s

y=1.2m

v b

Q 5 .7 4.75   A 1 .2 * b b 4.75 1.38 Thus,Fr= V  b  b 9 . 81 * 1 . 2 gy

V=

Note: As b decreases, F r increases. Set Fr=1 for minimum width for sub critical flow Hence 1=

1.38  b 1.38m b

Trapezoidal Section -

The best hydraulic section for trapezoidal channel is when the side slope z:1 is

3 :1 3 3 i.e  = tan -1 ( ) = 300 and 3

equal to



y

P = 23 y --------- (1) b= 2

P 3 ------- (2) yb= 3 3

A=

3

b

y2-------- (3)

Example : Determine the dimensions of the most economical trapezoidal brick lined channel to carry 200m3/s with a slope of 0.004 and n=0.016 So/n:

R=

A 3 y2 y   P 2 2 3y

 1 2 / 3 1/ 2  Q  R S  * A  n 2/3

1 y *   * (0.0004)1 / 2 * 3Y 2 0.016  2  Y2/ 3 1 * 2 / 3 * (0.004)1 / 2 * 3 y 2 200  0.016 2 200 * 0.0016 * 22 / 3  * 3 Y 8 / 3 (0.004)1 / 2 200 

 y= 6.49m From (z) above b= 2

3 3 *y = 2 * 6.49 3 3

= 7.5m Specific energy and critical depth The total energy of a channel flow referred to a datum is given by

LECTURE NOTE ON HYDRAULICS

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OPEN CHANNEL FLOW

H= Z+ Ycosθ + α

V

2

2g

For a very small bed slope (θ =0) and kinetic energy correction factor energy of a channel flow is

 =1, the total

V2 H= Z+Y+ 2 g

TEL

v2 2yg

Sf

liquid surface

Sw

Bottom line Z

So  Datum

Fig. Energy in gradually varied open channel flow. If the datum coincides with the channel bed at the section, the resulting expression is known as specific energy and is denoted by E. Thus, E= Y+

Q V2 , substituting for V= 2g A

E= Y+

Q2 2gA 2

The concept of specific energy is very useful in defining critical depth and in the analysis of flow problems. Critical depth The specific Energy is given by E= Y+

Q2 ---------(1) 2gA 2

For a channel of a given shape A=f(y) and thus equation (1) may be written as E= f(y) . The E-Y relation commonly called specific energy diagram (as shown below) can be constructed by giving different values of y in equation Y

E=Y Q1 F...