Module 4

open channel flow
ktu fluid mechanics

1. MODULE 4 OPEN CHANNEL FLOW ATHIRA SURESH I.C.E.T

2. INTRODUCTION Flow of liquid through a free surface Free surface is a surface having constant pressure such as atmospheric pressure Man made or natural

3. DIFFERENCE B/W OPEN CHANNEL FLOW & PIPE FLOW

4. DIFFERENCE B/W OPEN CHANNEL FLOW & PIPE FLOW

5. TYPES OF FLOW IN OPEN CHANNELS Steady flow and unsteady flow Uniform flow and non uniform flow Laminar flow and turbulent flow Sub-critical, critical and super critical flow

6. Steady and Unsteady Flow In an open channel flow, if the flow parameters such as  depth of flow, the velocity of flow and the rate of flow  at a particular point on the fluid do not change with respect to time, then it is called as steady flow If v is the velocity of the fluid, Q is the rate of flow and d is the depth of flow, then for a steady flow: dv / dt = 0; dQ / dt = 0; dy / dt = 0; And is at any point on the open channel flow, the flow parameters like depth of flow, the velocity of flow and rate of flow do change their value with respect to time, then it is called as an unsteady flow. It is hence given by : dv / dt , dQ / dt and dy / dt   not equal to Zero

7. 2. Uniform Flow and Non-Uniform Flow The flow in the channel is said to be uniform, if, for a given length of the channel, the velocity of flow, the depth of flow remains constant. i.e. dy / dS = 0 ; dv / dS =0; In a Non-uniform flow, the flow parameters like velocity, depth of flow, etc do not remain constant for a given length of the channel. dy / dS and dv / dS not equal to zero

8. The Non-uniform flow can be again defined as Rapidly varying flow (R.V.F) and Gradually Varied Flow (G.V.F). In the case of R.V.F, the depth of flow rapidly changes over a smaller length of the channel. It rises up suddenly for a short length and settles back. While in a G.V.F, the depth of flow changes gradually over a longer length of the channel.

9. 3. Laminar Flow and Turbulent Flow Laminar and turbulent flow in open channel flow is defined based on the Reynolds Number, Re. The Reynolds number is given by the relation : If the Reynolds number  Re  is less than 500 or 600, then the flow is called  laminar flow . If the Reynolds number is more than 2000, then the flow is said to be  turbulent . A flow that has Reynolds number between 500 and 2000 is said to be in the transition state.

10. 4 . Critical, Sub-Critical and Super - Critical Flow The open channel flow is categorized as critical or sub-critical or super-critical based on the Froude number  Fe . Froude number is given by the relation : Open channel flow is Sub-critical if the Froude number is less than 1. Sub-Critical open channel flow is also defined as a  tranquil or streaming flow. An open channel flow with a Froude number equal to one is a critical flow. super-critical flow in open channel has a Froude number greater than 1 . A supercritical flow is also termed as  rapid flow or torrential flow or shooting flow.

11. TYPES OF CHANNEL Rigid boundary open channels Loose boundary open channels Prismatic open channels Rigid boundary open channels can be said to be as the open channels with the non-changeable boundaries. While on the other hand if open channel has the boundaries which changes due to scouring action or deposition of sediments, such channels are said to be as loose boundary open channels. The open channels in which shape, size of cross section and slope of the bed remain constant are said to be as the prismatic channels . Opposite o these channels are non-prismatic channels . Natural channels are the example of non-prismatic channels while man made open channels are the example of prismatic channels.

12. Velocity distribution in open channels Velocity is always vary across channel(or not uniformly distributed) because of free surface & friction along the boundary It increases from zeroat the invert of the channel to a maximum value close to the water surface. the maximum velocity usually occurs 0.05-0.25 from the free surface

13. Velocity distribution in open channels To measure velocity of open channel at required depth, Pitot tube or current meter are used. In general, to find average velocity of a particular open channel, velocity at a depth of 0.6 m from free water surface is measured. In the other case, velocity at 0.2 m depth, 0.8 m depth from free water surface is taken and average velocity of these two values is considered as channel average velocity. Mean velocity = (0.2y+0.8y)/2 y= depth of flow

14. Velocity distribution in open channels Mainly depends upon the following factors. Shape of the channel section Roughness of channel Alignment of channel Slope of Channel bed

15. 1. Shape of the Channel Section Open channels may be naturally formed or artificially developed. Natural open channels do not have any particular shape and they contain irregular sections while artificial channels are provided with certain designed shapes such as rectangular, circular, trapezoidal, triangular etc. Contour lines of equal velocities in different shapes of channel sections are shown in below figure

16. 2. Roughness of Channel Roughness of channel is the measure of amount frictional resistance offered by channel bed material against flow of water. In natural channels, the flow velocity is affected by the presence of large angular boulders as bed material, vegetation, obstructions etc. If the channel is made of smooth clay or silt, its roughness is very low and water flows faster. In case of artificial channels, smooth finishing is required to maintain required flow velocity. The average velocity in open channels can be calculated using manning’s formula mentioned below V = Average velocity of channel R = hydraulic radius of channel = Area/Perimeter S = Slope of channel n = Manning’s roughness coefficient

17. 3. Alignment of Channel The velocity of flow in channel also depends up on the alignment of channel. If the channel is straight there will be no change is velocity with respect to alignment. In straight channels, maximum velocity is generally occurs at 0.05 to 0.15 m depth from free water surface. If it is sinuous or meandering, the velocity will vary at bends. At bend, due to centrifugal action of flow the velocity becomes more at convex side compared to concave side.

18. 4. Slope of Channel Bed Slope of channel bed or gradient of channel will also effects the velocity of flow in open channels. At steeper gradients, velocity increases while at normal gradients velocity decreases. Channel Slope

19. GEOMETRIC ELEMNTS OF CHANNEL Flow depth, y -Vertical distance from the channel bottom to the free surface. Top width, T Width of the channel section at free surface. Wetted perimeter, P Length of the interface between the water and the channel boundary. Flow area, A Cross-sectional area of the flow. Hydraulic depth, D Flow area divided by top width, D = A/T. Hydraulic radius, R Flow area divided by wetted perimeter, R = A/P. Bottom slope, S0 - Longitudinal slope of the channel bottom,

20. UNIFORM FLOW

21. DISCHARGE THROUGH OPEN CHANNEL CHEZY’S EQUATION MANNINGS FORMULA KUTTER’S FORMULA

22. CHEZY’S EQUATION

23. DISCHARGE Q = A X V AX

24. MANNING’S FORMULA

25. KUTTER’S FORMULA

26. MOST ECONOMICAL SECTION RECTANGULAR CHANNELS TRIANGULAR CHANNELS TRAPEZOIDAL CHANNELS CIRCULAR CHANNELS