CONTENTS Channels. 1 Introduction

Transcription

1 CONTENTS Channels Introduction Flow classification Steady uniform flow Unsteady non-uniform flow Unsteady uniform flow Laminar and turbulent flow Flow equations Factors which influence Manning's roughness coefficient Roughness coefficients (n) for various channel types Channel design Non-erodible channels Erodible channels Design of grassed channels Permissible flow velocity Choice of grass type Design procedure References All rights reserved Copyright 00 ARC-Institute for Agricultural Engineering (ARC-ILI) ISBN

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3 Channels 7. Introduction Free flow is considered as any flow in a channel, river or pipe flowing partially full. In such cases flow can only be created due to differences in geometric height and pressure differences do not occur. The type of free flow can be described in a number of different ways. The following description is based on variations in flow depth with respect to time and distance. Flow classification Flow classification is done according to two parameters, namely a time and distance scale. The flow based on the time scale, is subdivided into steady and unsteady flow. Open channel flow is steady when the flow depth and velocity do not change with time or if they can be considered constant during the specified time interval. Flow is unsteady if the flow depth varies with time, e.g. flow increases or decreases or waves are formed. Q = v A (7.) where Q = flow rate [m /s] v = average flow velocity [m/s] A = cross sectional flow area [m ] With steady flow the flow conditions remain unchanged at any point. Based on the time scale, the flow is subdivided into uniform and non-uniform flow. Flow is uniform when the parameters, flow depth and velocity remain constant at all sections (positions). Flow is classified as non-uniform where fluid is added or removed along the flow path. Steady and uniform flow are not exclusive. Some flows show changes with time as well as position while others vary only with time or position. Free flow may thus be divided into the following groups:. Steady uniform flow This flow depth is constant with time and position, in other words channel friction forces and the force of gravity are in equilibrium. Steady uniform flow is the basic flow type considered in open channel flow, therefore the flow depth does not vary during the time interval under consideration. Figure 7.: Steady uniform flow

4 7. Irrigation Design Manual. Unsteady non-uniform flow Unsteady non-uniform flow occurs when the flow depth varies over the channel length with time. Unsteady non-uniform flow can change rapidly if the depth suddenly changes over a short distance, e.g. a hydraulic jump (see Figure 7.). Otherwise it is gradually varied flow (see Figure 7.) Figure 7.: Flood-wave (gradually varied flow) Figure 7.: Tidal wave (rapidly varied flow) This flow type will not be dealt with in this chapter.. Unsteady uniform flow This free flow depth changes from time to time. Figure 7.4: Unsteady uniform flow

5 Channels 7. Any flow type may be sub-critical, critical or super critical. Critical flow occurs with the minimum specific energy for a given flow rate. The Froude number (F r ) is used to determine if the flow is critical or not. = F r v g y (7.) where F r = Froude number [dimensionless] v = average flow velocity [m/s] g = gravitational acceleration (0 m/s ) y = flow depth [m] Sub-critical flow: F r < Critical flow: F r = Super-critical flow: F r > Earth channels or planted channels are usually designed for sub-critical flow. Critical flow should be avoided in channel design as a small change in energy height can cause a large change in the flow depth. However, critical flow forms the basis for the design of control sections and measuring plates as a definite height-flow relationship exists under these flow conditions. Super-critical flow should be avoided in channels as obstructions or channel changes may result in a hydraulic jump. Laminar and turbulent flow The relationship between viscous and retarding forces determines whether flow is laminar, turbulent or between the two. Flow is laminar when the viscous forces are so much stronger than retarding forces that viscosity plays a meaningful role in the flow behaviour. With laminar's flow it appears as if water particles move in definite smooth lanes or stream lines and that infinitely thin layers of fluid slide over each other. Flow is turbulent when the viscous forces are weak compared to retarding forces. With turbulent flow, water particles move in uneven lanes which are neither smooth nor fixed, but where the average movement still represents the forward motion of the stream. The influence of viscosity can be described using the Reynolds number (R e ) : R e = R v = R v (7.) where R e = Reynolds number [dimensionless] v = average flow velocity [m/s] R = hydraulic radius [m] = fluid density [kg/m³] = kinematic viscosity [m²/s] = dynamic viscosity [kg/m.s] For laminar flow R e (channel) < 500 and turbulent flow R e (channel) > 000. Channel flow falls in the rough turbulent area which allows the use of empirical equations.

6 7.4 Irrigation Design Manual 4 Flow equations Many equations have been developed to describe channel flow. The best known are those of Chezy (775) and Manning (889). In South Africa, the Manning equation is mostly used to describe steady uniform flow: = AR n Q S (7.4) where Q = flow rate [m /s] n = Manning's roughness coefficient R = hydraulic radius [m] S = channel slope [m/m] A = cross sectional flow area [m²] R = A/P where P = wetted perimeter [m] See Section 5 for a detailed description of the symbols. Although the Manning equation is straight forward, its correct application is difficult as there is no precise method to determine the "n"-value. To ultimately give an indication as to the choice of suitable n-values, firstly factors which influence roughness are discussed, followed by tables with n-values for different channels. 4. Factors influencing Manning's roughness coefficient The roughness coefficient of a channel (n-value) is never constant but varies with different flow depths as well as physical, seasonal and time changes in the channel. The n-value should therefore be chosen to allow for the worst possible condition, when the maximum or design flow occurs. Flow depth The n-value for most channels decreases with an increase in flow depth and flow rate. The effect of an uneven channel floor is more pronounced with shallow flow than with deep flow. The sides, however, also influence the retardation of the water. Where plentiful plant growth and an uneven surface occur just above the normal flow depth, the retarding effect of the plant growth on the sides increases the n-value with an increase in flow depth. Surface roughness The surface roughness of the wetted perimeter is caused by the size and shape of the material particles. Channels in fine materials like silt, clay or fine sand have a lower n-value than those in gravel and stone. Plant growth Plant growth on the floor and against the channel sides increase the n-value. The type of plant has a significant influence as some plants like grass flatten during large floods, decreasing the n-value. Seasons influence the state and nature of the plant growth and therefore also the surface roughness. Channel shape Long even curves in a channel will not significantly increase the n-value whereas short, sharp

7 Channels 7.5 curves would. Meandering can increase the n-value by up to 0%. Sediment Water needs energy to transport sediment, therefore water containing sediment will flow slower than clear water. It follows that the sediment load effectively increases the n-value. Unevenness The n-value of a channel is increased by unevenness in the floor and changes in width. Gradual changes may be ignored. Wind Prevailing winds that blow against the direction of flow will have a retarding effect while winds blowing with the flow direction will tend to increase the water flow. The wind velocity will determine the magnitude of the effect. 4. Roughness coefficients (n) for different channel types Table 7.: Roughness coefficient values for channel flow Nature of channel and description Minimum Normal Maximum A. Channels or pipes that flow partially full. Metal (ferrous) (a) Cast iron (i) Black (ii) Galvanized 0,0 0,0 0,04 0,06 0,05 0,07 (b) Corrugated iron (i) Drainage pipe (ii) Stormwater pipe 0,07 0,0 0,09 0,04 0,0. Non-metal (a) Cement (i) Smoothly finished surface (ii) Mortar 0,00 0,0 0,0 0,0 0,0 0,05 (b) Concrete (i) Passage straight without sediment (ii) Passage with sediment, curves, joints (iii) Finished off (iv) Unfinished steel formwork (v) Unfinished, smooth wooden formwork (vi) Unfinished, rough wooden formwork 0,00 0,0 0,0 0,0 0,0 0,05 0,0 0,0 0,0 0,0 0,04 0,07 0,0 0,04 0,04 0,04 0,06 0,00 B. Synthetic channels. Non-metal (a) Cement (i) Neat surface (ii) Mortar 0,00 0,0 0,0 0,0 0,0 0,05 Table 7. (continued)

8 7.6 Irrigation Design Manual Nature of channel and description Minimum Normal Maximum (b) Concrete (i) Trowel finish (ii) Bonded layer finish (iii) Finished off with gravel floor (iv) Unfinished (v) Shotcrete, good section (vi) Shotcrete, undulating section (vii) On well excavated rock (viii) On uneven excavated rock 0,0 0,0 0,05 0,04 0,06 0,08 0,07 0,0 0,0 0,05 0,07 0,07 0,09 0,0 0,00 0,07 0,05 0,06 0,00 0,00 0,0 0,05 (c) Bonded layer finish or floor with sides of: (i) Grouted stone pitching (selected stone) (ii) Grouted stone pitching (uneven stone) (iii) Plastered concrete masonry (iv) Cement masonry (v) Dry rip rap 0,05 0,07 0,06 0,00 0,00 0,07 0,00 0,00 0,05 0,00 0,04 0,04 0,05 (d) Gravel floor with sides of: (i) Cast concrete (ii) Uneven grouted rock (iii) Dry rip rap 0,07 0,00 0,0 0,00 0,0 0,0 0,05 0,06 0,06 (e) Brickwork (i) With cement mortar 0,0 0,05 0,08 (f) Mortar (i) Cemented undressed stone (ii) Dry undressed stone 0,07 0,0 0,05 0,0 0,05 (g) Worked freestone 0,0 0,05 0,07 (h) Planted C. Excavated (a) Earth, straight and uniform (i) Clean, recently completed (ii) Clean, weathered (iii) Gravel, uniform section, clean (iv) Short grass with few weeds 0,06 0,08 0,0 0,0 0,08 0,0 0,05 0,07 0,00 0,05 0,0 (b) Earth, meandering, slow flow (i) No plant growth (ii) Grass with some weeds (iii) Thick weeds or water plants in deep channels (iv) Earth floor with gravel sides (v) Rocky floor with weedy sides (vi) Round boulders on floor with clean sides 0,0 0,05 0,08 0,05 0,05 0,05 0,05 0,0 0,05 Table 7. (continued)

9 Channels 7.7 Nature of channel and description Minimum Normal Maximum (c) Dragline excavated or dredged (i) No plant growth (ii) Sides lightly bushed 0,05 0,05 0,08 0,0 0,060 (d) Cut into rock (i) Smooth and uniform (ii) Coarse and uneven 0,05 0,05 0,05 (e) Unmaintained channels, weeds and bush uncut (i) Thick weeds as high as flowing water (ii) Clean floor, sides lightly bushed (iii) The same, very deep flow (iv) Thick bush, deep flow 0,045 0,080 0,080 0,070 0,00 0,0 0,080 0,0 0,40 D. Natural streams. Smaller streams (a) Streams on a plain (i) Clean, straight without ridges or pools (ii) As (i) with few small bushes and rocks (iii) Meandering with occasional pools and sand banks (iv) As (iii) with rocks and small bushes (not many) (v) As (iii) but flatter slopes and smaller diameter (vi) As (iv) but with more rocks (vii) Slow flowing with deep pools (viii) Very thickly bushed 0,05 0,0 0,05 0,045 0,075 0,05 0,045 0,048 0,070 0,00 0,0 0,045 0,055 0,060 0,080 0,50 (b) Mountain streams (i) Gravel and few rocks on floor (ii) Clay stone with large rocks 0,070. Flood plain (a) Pasture without bushes (i) Short grass (ii) Long grass 0,05 0,05 0,05 (b) Fields (i) No plants (ii) Developed, planted rows (iii) Developed, harvest crop 0,00 0,05 0,05 0,045

10 7.8 Irrigation Design Manual Table 7. (continued) Nature of channel and description Minimum Normal Maximum (c) Bush (i) Sparse bush, many weeds (ii) Sparse bush and trees during winter (iii) Sparse bush and trees during summer (iv) Medium to thick bush during winter (v) Medium to thick bush during summer 0,05 0,05 0,045 0,070 0,060 0,070 0,00 0,070 0,060 0,080 0,0 0,60 (d) Trees (i) Thick willows (ii) Cleared field with tree stumps (iii) As (ii) but with many sprouts (iv) Thick forest with few bushes (v) As (iv) but floodline above branches 0,0 0,080 0,00 0,50 0,060 0,00 0,0 0,00 0,080 0,0 0,60 5 Channel design Channels may be divided into two broad categories: Non-erodible channels here the wetted perimeter is lined with a resistant material, e.g. concrete. Erodible channels earth channels. The following geometric properties apply to all channel types (see Table 7.): Flow depth (y) = the vertical distance from the floor of the channel section to the water surface [m]. Cross sectional area (A) = the cross sectional flow area perpendicular to the flow direction [m²]. Wetted perimeter (P) = the length of the wetted perimeter measured perpendicular to the flow direction [m]. Top width (W) Hydraulic radius (R) = the width of the channel section at the flow surface [m]. = the ratio of the area to the wetted perimeter (A/P) [m]. Hydraulic mean depth (D m ) = the ratio of the area to the top width (A/W) [m]. Wetted angle () = the angle between the wetted depth and the centre of a circular channel or pipe [degrees]. Horizontal side slope dimension (z) Diameter (d i ) Dry board = the horizontal dimension which together with a vertical dimension forms the side slope of a trapezoidal channel [dimensionless]. = the inside diameter of a pipe being used as a channel section [m]. = the vertical distance between the water surface and the top of the channel under design conditions [m].

11 Channels 7.9 Table 7.: Geometric properties of general channel shapes Sketches Cross sectional shape Rectangular Trapezoidal Circular (> ½ full) Triangular Parabolic Area (A) b y (b + z y) y d i sin 80 z y yw Wetted perimeter (P) b + y b + y + z di (60-60 ) y z + W + 8 y W Top width (W) b b + z y (sin ) d i A zy y Hydraulic radius (R) b y b + y (b + z b + y y)y + z Hydraulic mean (b + z y)y depth (Dm) y b + z y 8 45 d zy i - + sin (60 - ) 80 + z d i ( - +sin ) 80 sin ( ) yw W + 8 y y y NB: is measured in degrees

12 7.0 Irrigation Design Manual Table 7. Best hydraulic sections Sketches Cross sectional shape Rectangular Trapezoidal Circular Triangular Parabolic Area (A) y,7y,57y y,886y Wetted perimeter (P) 4y,464y,4y,88y,77y Hydraulic radius (R) 0,5y 0,5y 0,5y 0,54y 0,5y Top width (W) y,09y y y,88y

13 Channels Non-erodible channels These channels are lined with materials that do not erode easily, e.g. concrete, stone pitching, steel, wood, glass, plastic, etc. The choice of material depends on availability and cost of respective materials. The advantage of nonerodible channels is that lower roughness values allow higher velocities to be maintained in a specific channel resulting in the building of a smaller, cheaper structure. Costs must be minimized when designing non-erodible channels. Two aspects need to be taken into consideration, namely the quantity of lining material and excavation required. To minimize the quantity of lining material required, the maximum hydraulic radius should be used, therefore the wetted perimeter should be the minimum for a specific area. This is known as the best hydraulic section. A semi-circle is the most effective hydraulic section as the wetted perimeter is the smallest of all sections with the same area. For practical reasons, semi-circle channels are not recommended for waterdepths < 0,5 m. See Table 7. for the best hydraulic section of the five most common channel shapes. The best hydraulic section does not, however, always require the smallest amount of excavation. The quantity of excavation will depend on whether the channel is partially or fully underground. For a partially underground channel the excavation will be less provided that the section is wider than the best hydraulic section and for a sunken channel the excavation will be less if the channel is narrower than the best hydraulic section. Generally channels are designed so that, for the chosen profile, the cut and fill balance out. The part of the channel that carries the water should be in excavation. The maximum lining depth for parabolic channels is two metres if manual labour is used during construction, the reason being that the freshly placed concrete tends to slide down the channel sides. For larger parabolic channels it is recommended that the floor be made horizontal with the sides parabolic. If the flow should decrease along the length of this type of channel, the floor width can be reduced while the parabolic shape of the sides remains the same. Practice has shown that in stable, well-drained soil, the side slopes of parabolic channels should not exceed :. Trapezoidal channels are usually used where flows are > 8 m /s, with side slopes of :,5 generally being used. Rectangular channels should only be used where space is limited and where small quantities of water are to be transported. In such cases rectangular channels have the advantage of being more stable than trapezoidal channels, therefore also requiring less maintenance. With large channels the cost of a rectangular channel may be up to three times more than the equivalent trapezoidal channel. The dry board of a channel is chosen such, that the distance is sufficient to prevent overtopping due to waves or variations in water level. There is no generally accepted rule for determining dry board, as wave action and variations in water level are caused by uncontrollable factors. A dry board variation of 5% 0% of the normal flow depth is generally accepted. Table 7.4: Guidelines for the dry board Canal depth [m] Dry board height [mm] < 0,5 50 0,5 0,4 75 0,4 0, ,65 0,9 5 > 0,9 50

14 7. Irrigation Design Manual Example 7.: The normal flow depth in a trapezoidal concrete channel is m. The base width is 5 m with side slopes :. The channel slope is 0,00 and Manning's n = 0,05. Determine the flow rate and average flow velocity. Solution: From Table 7.: W = b + zy = 5 + ( ) = m A = (b + z y) y = (5 + ) = 8 m P = b + y + z = =,94 m From equation 7.4: Q = n A P = 0,05 AS ( 8,94 ) 8 (0,00 ) = 45 m From equation 7.: v = Q = A 45 =,5 m/s 8 Check: From Table 7.5: v permissible = 4,5 m/s Example 7.: Determine flow depth and average flow velocities for a concrete channel with slope : 500 changing to : 000. Assume Manning's n-value = 0,07. The channel is rectangular with a base width of m and must be able to handle a flow rate of m /s. Solution: From Table 7.: A = by en R = by b + y From equation 7.4: = (R ) AS n Q

15 Channels 7. For : 500 slope: = 0,07 y + y y 500 Iterate to determine: y = 0,85 m and v= Similarly for : 000 slope: Q A = 0,85 = 0,78 m/s = 0,07 y + y y 000 Iterate to determine: y = 0,9 m and v = 0,9 = 0,7 m/s Therefore the total channel depth will be the maximum flow depth of 0,9 m + a free board (50 mm from Table 7.4). Total channel depth = 0,9 + 0,5 =,06 m If the same flow depth was maintained over the : 000 sloped section the flow rate would decrease. From equation 7.4: = (R ) AS n Q 0,85 = ( ) 0,07 + 0,85 =,8 m /s 0, Therefore the flow rate will decrease by 9% if the same flow depth is maintained throughout.

16 7.4 Irrigation Design Manual 5. Erodible channels Present design methods for channels in erodible materials like earth should act as guidelines and good engineering judgement and experience should play a leading role in any channel designs in erodible material. Methods like maximum safe flow velocity, maximum allowable floor shear tension and minimum stream force are based on the hydraulic properties of the channel. The stability of channels, which is the most important factor, is however more dependant on the physical and chemical properties of the soil than hydraulic properties. Present information on the erodibility of different soils is limited. Experience with existing, stable channels should therefore serve as a basis for the design of erodible channels. The following combined seepage and evaporation losses are accepted for earth channels:, /s per 000 m for channels in clay loam soils,7 /s per 000 m for channels in sandy loam soils Side slopes of these channels depend mainly on the type and erodibility of the material. See Table 7.5 for suitable side slopes for different materials. Table 7.5: Safe side slopes Material Side slopes (vert:hor) Hard rock Weathered, cracked or soft rock Clay and hard gravel Clay loam and gravel loam Sandy loam Sandy soil Vertical Vertical :0,5 : :,5 : Table 7.6 shows the maximum average flow velocities used during the design procedure to guard against erosion. Table 7.6: Maximum average flow velocities to guard against washing out Material Very light flowing sand Very light loose sand Coarse sand or light sandy soil Normal sandy soil Sandy loam soil Loamy alluvial soil Firm loam, clay loam Stiff clay and gravely soil Coarse and rocky gravel Conglomerate, soft shale, soft rock formation Hard rock Concrete Average flow velocity [m/s] 0, 0, 0, 0,4 0,4 0,6 0,6 0,7 0,7 0,8 0,8,0,0,,,5,0,5,0,5,0 4,5 4,5 6,0

17 Channels 7.5 Note however that these velocities apply to straight channels. For meandering channels the flow velocities are reduced: 5% for slight meandering % for medium meandering % for much meandering A minimum flow velocity of 0,6 m/s is recommended to keep sediment in suspension and it helps to reduce plant growth in channels. A silt trap must be designed for lower flow velocities. Example 7.: Determine the floor width (b) and safe flow depth (y) of a trapezoidal spillway with a floor slope of 0,006 and a flow rate of m³/h. The spillway is built in sandy loam soil. Solution: From Table 7.5: v permissible = 0,8 m/s Table 7.4: z =,5 Table 7.: n = From equation 7.4: Q = R n and v = Q = R n =,5 m 0,8 = R R = 0,465 m /s AS S m /h (0,006 ) From equation 7.: Q = va,5 A = 0,8 =,69 m From equation 7.4: A R = P A P = R,69 = 0,465 = 5,79 m From Table 7.: P = b+ y + z = 5,79 m...(i) and A = (b+ zy)y =,69m With z =,5 and from (ii) : b...(ii),69 = -,5y...(iii) y

18 7.6 Irrigation Design Manual Substitute (iii) in (i) :,69 y -,5y +,6y = 5,79 Therefore and y = 0,59 m b =,67 m This size and shape of spillway is not recommended for a channel as high infiltration losses will occur in the sandy loam soil. Example 7.4: The n-value of a trapezoidal channel in sandy soil weakens from 0,05 to 0,0 as a result of bad maintenance (no weed control). The channel was initially designed to handle a flow rate of m /s. Channel slope is : 500. Determine the reduction in flow rate with the new n-value. Solution: From Table 7.6: v permissible = 0,6 m/s Table 7.5: z = From equation 7.: Q = v A = =, m 0,6 A From equation 7.4: Q = R n AS = R, 0,05 R = 0,65 m 500 For a n-value = 0,0 From equation 7.4: Q = 0, 65 0,0 =,66 m /s, 500 Therefore the flow rate will reduce by 7%. 5. Design of grassed channels The presence of grass leads to turbulence which causes energy losses and flow retardation. A grasslined channel has the following advantages: Channel stabilisation, soil consolidation and erosion control. Manning's n-value changes for grass channels: The deeper the flow depth, the smaller becomes the influence of the grass resistance. Graphs have been compiled, showing a solution of Manning equation for specific changes of n-value. The resistance is determined by the condition and type of grass. The length and coverage varies within a grassed area, therefore grass channels must not erode when the grass is at its weakest and should still be able to accommodate the water when the grass is at its best. Therefore firstly design for stability with weak coverage and then for capacity with good coverage.

19 Channels Permissible flow velocity The permissible flow velocity in a grass channel is such that, after a reasonable passage of time, no serious erosion will occur. Table 7.7 shows permissible flow velocities for different grass types, well established on erodible soil with a flow depth < 0,5 m and channel slope < 5%. 5.. Choice of grass type The choice of grass depends mainly on the climate and soil as the grass must survive and grow under these conditions. Hydraulic properties should, however, also be considered. Tuft grasses should be avoided on steep slopes as channels are formed between the tufts. Preference should be given to fine, well spreading, sodforming grasses. However, sod-grasses may be used together with tuft grass where silt deposits create problems. The sod grass protects the channel and the channelisation between the tufts prevents the velocity from dropping below sedimentation velocity. Table 7.7 Maximum permissible flow velocities in grass channels Plant Pennisetum clandestinum (Kikuyu) Digitaria diversinervis (Richmond grass) Digitaria valida Digitaria Swaziland ensis Stenotaphrum secundatum (St Augustine) Dactyloctenum australe (Durban grass) Chloris gayana (Rhodes) Cynodon plectostachyus (Star grass) Stipgrostis namaquensis (Kalahari grass) Paspalum motatum Sorghum halepense (Johnson grass) Digitaria abyssinica (Abyss. finger grass) Panicum repens ( Panicum grass) Acroceras macrum (Nile grass) Hemathria altissima (Red grass) Imperata cylindrica (Cotton wool grass) Leersia hexandra (Rice grass) Velocity [m/s],,0,0,7,7 Remarks Grass mat only formed when well grazed Weeds in orchards and cultivated fields Weeds in orchards and cultivated fields Marsh grass Marsh grass. Feared weed in tropics Marsh grass, grows in water Cenchrus ciliaris (Buffalo grass) Lolium pyrenne (Perennial rye) Eleusine africana (Young ox tuft grass) Aragrotistel,5,5,5 0,9 Sow teff grass for rapid coverage

20 7.8 Irrigation Design Manual 5.. Design procedure Stability Choose suitable flow velocity from Table 7.7 and calculate A from equation 7.. Choose the resistance group (Table 7.8) of the grass for its worst condition. Depending on the resistance group, R can then be read off from Figures 7.5, 7.6, 7.7, 7.8 or 7.9. Use Figure 7.0 to determine the channel cross section. Capacity For the same channel choose greater depths and check if the deeper flow conditions are sufficient for the thickly grassed areas. Table 7.8: Guide to velocity reduction in grassed channels Grass condition Length of grass [m] Figure no/resistance group Good Medium > 0,75 0,5 0,60 0,5 0,5 0,05 0,5 < 0,05 > 0,75 0,5 0,60 0,5 0,5 0,05 0,5 < 0,05 Figure 7.5 Very high resistance Figure 7.6 High Figure 7.7 Medium Figure 7.8 Low Figure 7.9 Very low Figure 7.6 High Figure 7.7 Medium Figure 7.8 Low Figure 7.8 Low Figure 7.9 Very low Example 7.5: Design a trapezoidal grassed channel with side slopes (:) for a flow of 000 /s. The channel slope is 0,00 m/m. Assume blue buffalo grass with condition varying from medium 50 mm 50 mm to good 50 mm 600 mm. Solution: Stability: From Table 7.7: v permissible =,5 m/s From equation 7.: Q = = = 0,67 m v,5 A From Table 7.8: Choose Figure 7.8. From Figure 7.8: With v =,5 m/s and S = % it follows that R = 0,5 m R /A = 0,09 From Figure 7.0: For a trapezoidal channel with z = W/y = 6,5...(i)

21 Channels 7.9 From Table 7.: W = P = b + zy b + y + z (ii) (iii) From(i) W = 6,5y...(iv) Substitute(iv) in (ii): 6,5y = b + 4y b =,5y...(v) R = A,therefore P = P 0,67 = 0,5 A R =,68 m...(vi) Substitute(vi) in (iii) :,68= b+ y 5...(vii) Substitute (v) in (vii):,68 =,5y + 4,47y y = 0,84 m b = 0,96 m and W =,496 m Capacity: Choose y = 0,5 m From Table 7.: (b+ zy)y R = b+ y + z (0,96 + 0,5)0,5 = 0,96 + 0,5 5 = 0,46 m For a good condition of grass for a length of mm, choose Figure 7.6: From Figure 7.6: v =,5 m/s Therefore the permissible velocity is not exceeded.

22 7.0 Irrigation Design Manual Figure 7.5: Very high resistance group

23 Figure 7.6: High resistance group Channels 7.

24 7. Irrigation Design Manual Figure 7.7: Medium resistance group

25 Figure 7.8: Low resistance group Channels 7.

26 7.4 Irrigation Design Manual Figure 7.9: Very low resistance group

27 Figure 7.0: Determining channel cross section Channels 7.5

28 7.6 Irrigation Design Manual 6 References. Jensen, M. E. 98. Design and operation of farm irrigation systems. The American Society of Agricultural Engineers.. Chadwick, A. and Morfett, J Hydraulics in Civil Engineering. Department of Civil Engineering. Brighton Polytechnic.. Ven te Chow Open channel hydraulics. McGraw-Hill Publishing Company.