AEG-101-Class-17,18: Wind erosion

Introductory Soil and Water Conservation Engineering

II Semester 3^rd Feb to 30^th June 2020, 2019-20

Teacher Information

Professor	Email	Phone
Dr. K. C. Shashidhar	shashidhar.kumbar@gmail.com	9448103268

Class-17,18 Reference material

Wind erosion

Movement of soil particles is caused by wind force excerpted against or parallel to surface of the ground.

Gradient in velocity, which determines the magnitude of the force, excreted.

Wind erosion occurs where soil is exposed to the dislodging force of wind. The intensity of wind erosion varies with surface roughness, slope and types of cover on the soil surface and wind velocity, duration and angle of incidence. Fine soil particles can be carried to great heights and for (may be) hundreds of kilometers. The overall occurrence of wind erosion could be described in three different phases. These are initiation of movement, transportation and deposition.

1. Initiation of Movement: The initiation of the movement of soil particles is caused by several factors acting separately in combination. In the course of collision of grains rolling and bumping on the surface, some particles may be bounced up. It occurs when the wind force or the impact of moving particles is strong enough to dislodge stationary soil particles.

2. Transportation: The transportation of the particles once they are dislodged take place in three ways:

i) Saltation – In saltation soil particles of medium size (0.10-0.15 mm diameter) are carried by wind in a series of short bounces. These bounces are caused by the direct pressure of the wind on soil particles.

ii) Soil Creep – saltation also encourages soil creep (rolling or sliding) along the surface of the particles (0.5-1.0 mm diameter). The bouncing particles carried by saltation strike the large aggregates and speed up their movement along the surface.

iii) Suspension – When the particles of soil are very small (less than 0.1 mm) they are carried over long distances. Finer suspended particles are moved parallel to the ground surface and upward.

3. Deposition: Deposition of the particles occurs when the gravitational force is greater than the forces holding the particles in air. Deposition could occur when the wind velocity is decreased due to surface obstructions or other natural causes.

Principle of movement	Partial size	% contribution to erosion by wt.
Saltation	0.06 – 0.6 mm	50-75
Suspension	< 0.05	3-40
Surface creep	0.5 – 2 mm	5-25

  

Factors influencing wind erosion

The movement of soil by wind is a complex process influenced by the conditions of wind, soil and nature of the eroding surface. The various factors may be classified into the following.

1. Features of wind: Speed, direction, structure, temperature, humidity and burden carried.
2. Character of surface: Rough, plant cover, other obstructions
3. Topography: Flat, undulating and broken
4. Characters of soil: Texture structure, organic matter content, and moisture content.

Three most important factors are:

• Soil cloudiness
• Surface roughness
• Crop residues

Studies have shown that 75% of the variability in amount of erosion can be attributed to these three.

• Aridity of climate. Wind erosion can also take place in high-rainfall climates when certain months of the year are particularly dry (but only if the soil is tilled with techniques that crush the surface fine).

Wind-speed also has to exceed about 20 km/in or 6 m/s over dry soils. Wind erosion phenomena will increase proportionately in the presence of strong, regular prevailing winds or gusts.

• Soil texture. Loamy sand, rich in particles between 10 and 100 microns in size, is the most vulnerable soil (Bagnold 1937). More clayey soil is much stickier, better-structured, and hence more resistant. Coarse sand and gravelly or rocky soils are also more resistant, since the particles are too heavy to be removed by wind erosion. The optimum size for wind erosion is about 80 microns.

• Soil structure. The less structure-improving matter a soil has on the surface (organic matter, iron and free aluminium, lime), the more fragile it will be, while the presence of sodium or salt often leads to formation of a layer of dust on the surface, which fosters wind erosion.

• State of the soil surface. If the soil surface is stony, forming a "pavement", the risks of wind erosion are lower - as, for example, in regs.

A rough surface, left by cloddy tillage or ridges perpendicular to the prevailing wind, slows down the wind at ground level, thus reducing saltation.

• Vegetation. Stubble and crop residues in the soil cut wind-speed at ground level.

• Soil moisture increases cohesion of sand and loam, temporarily preventing their erosion by wind.

Measures to control soil erosion by wind on the basis of the mechanics of wind erosion process, four basic methods of control are evident.

1. Protect the soil surface with a cover of vegetation or vegetative residues
2. Produce or bring to the surface, soil aggregates or clods which are larger enough to resist the wind force
3. Roughen the land surface to reduce wind velocity and trap drifting soil.
4. Establish barriers or trap strips at intervals to reduce wind velocity and soil drifting.

Wind Erosion Control Measures

Wind erosion is the process of detachment, transportation and deposition of soil particles by the action of wind. It occurs in all parts of the world and is a cause of serious soil deterioration. In India, Rajasthan has severe wind erosion problem. A large part of area the state is affected by sand dune formation. Some parts of coastal areas also have such problems. It most commonly occurs in the regions where soil is loose, finely divided and dry, soil surface is smooth and bare, and where wind is strong to detach the soil particles from the surface.

Wind Erosion Control: A suitable surface soil texture is the best key to wind erosion protection. Properly managed crop residues, carefully timed soil tillage, and accurately placed crop strips and crop barriers can all effectively reduce wind erosion. Proper land use and adaptation of adequate moisture conservation practices are the main tools which help in wind erosion control. In arid and semiarid regions where serious problem of wind erosion is common, several cultural methods can help to reduce the wind erosion. In the absence of crop residue, soil roughness or soil moisture can reduce the wind erosion effectively.

Three basic methods can be used to control wind erosion:

• Maintain Vegetative Cover (Vegetative Measures) 
• Roughen the Soil Surface by Tillage Practices (Tillage Practices or may be called Tillage Measures) 
• Mechanical or Structural Measures (Mechanical Measures)

There is no single recipe for erosion control as many factors affect the outcome. However, with an understanding of how soil is eroded, strategies can be devised to minimize erosion.

Vegetative Measures

Vegetative measures can be used to roughen the whole surface and prevent any soil movement. The aim is to keep the soil rough and ridged to either prevent any movement initially or to quickly trap bouncing soil particles in the depressions of the rough surface. A cover crop with sufficient growth will provide soil erosion protection during the cropping season. It is one of the most effective and economical means to reduce the effect of wind on the soil. It not only retards the velocity near the ground surface but also holds the soil against tractive force of wind thereby helping in reduction of soil erosion.

From the basic concept, the velocity of wind decreases near the ground surface because of the resistance offered by the vegetation. The variation in wind velocity with respect to height above the land surface increases exponentially.

Vegetative measures can be of two types:

1. Temporary Measures

2. Permanent Measures

The use of these measures depends upon the severity of erosion.

Tillage Practices

 The tillage practices, such as ploughing are importantly adopted for controlling wind erosion. These practices should be carried out before the start of wind erosion. Ploughing before the rainfall helps in moisture conservation. Ploughing, especially with a disc plough is also helpful in development of rough soil surface which in turn reduces the impact of erosive wind velocity. Both the above effects are helpful in controlling the wind erosion.

Surface roughening should only be considered when there is insufficient (less than 50%) vegetation cover to protect the soil surface or when the soil type will produce sufficient clods to protect the surface. Roughening can be used in both crop and pasture areas. Surface roughening alone is inadequate for sandy soils because they produce few clods. Tillage ridges, about 100 mm high, should be used to cover the entire area prone to erosion. Ridges that are lower than 100 mm get quickly filled with sand, whilst the crest of the ridge that is higher than 100 mm tends to erode very quickly.

The common tillage practices used for wind erosion control are as under: 

• Primary and Secondary Tillage 
• Use of Crop Residues 
• Strip Cropping

Mechanical Measures

This method consists of some mechanical obstacles, constructed across the prevailing wind, to reduce the impact of blowing wind on the soil surface. These obstacles may be fences, walls, stone packing etc., either in the nature of semi-permeable or permeable barriers. The semi-permeable barriers are most effective, because they create diffusion and eddying effects on their downstream face. Terraces and bunds also obstruct the wind velocity and control the wind erosion to some extent. Generally, in practice two types of mechanical measures are adopted to control the wind erosion; i) wind breaks and ii) shelter belts.

Wind Breaks

This is a permanent vegetative measure which helps in the reduction of wind erosion. It is most effective vegetative measure used for controlling severe wind erosion. The term wind break is defined as any type of barrier either mechanical or vegetative used for protecting the areas like building apartments, orchards or farmsteads etc. from blowing winds. The wind break acts as fencing wall around the affected areas, normally constructed by one row or maximum up to two rows across the prevailing wind direction.

A further use for "windbreaks" or "wind fences" is for reducing wind speeds over erodible areas such as open fields, industrial stockpiles, and dusty industrial operations. As erosion is proportional to the cube of wind speed, a reduction in wind speed by 1/2 (for example) will reduce erosion by over 80%. The largest one of these windbreaks is located in Oman (28 m high by 3.5 km long) and was created by Mike Robinson from Weather Solve Structures.

Shelter Belts

A shelterbelt is a longer barrier than the wind break, is installed by using more than two rows, usually at right angle to the direction of prevailing winds. The rows of belt can be developed by using shrubs and trees. It is mainly used for the conservation of soil moisture and for the protection of field crops, against severe wind erosion.

Shelterbelt is more effective for reducing the impact of wind movement than the wind break. Apart from controlling wind erosion, it provides fuel, reduces evaporation and protects the orchard from hot and cold winds.

Woodruff and Zingg (1952) developed the following relationship between the distance of full protection (d) and the height (h) of wind break or shelter belt. 

d = 17h( v_m / v ) cos∅

Where, d is the distance of full protection (m), h is the height of the wind barrier (wind break or shelter belt) (m), vm is the minimum wind velocity at 15 m height required to move the most erodible soil fraction (m/s), v is the actual velocity at 15 m height, and θ is the angle of deviation of prevailing wind direction from the perpendicular to the wind barrier.

This relationship (equation) is valid only for wind velocities below 18 m/s. This equation may also be adapted for estimating the width of strips by using the crop height in the adjoining strip in the equation. The value of vm for a bare smooth surface after erosion has been initiated and before wetting by rainfall and subsequent surface crusting is about 9.6 m/s.

Sand Dunes Stabilization

A ‘Dune’ is derived from English word ‘Dun’ means hilly topographical feature. Therefore a sand dune is a mount, hill or ridge of sand that lies behind the part of the beach affected by tides. They are formed over many years when windblown sand is trapped by beach grass or other stationary objects. Dune grasses anchor the dunes with their roots, holding them temporarily in place, while their leaves trap sand promoting dune expansion. Without vegetation, wind and waves regularly change the form and location of dunes. Dunes are not permanent structures.

Sand dunes provide sand storage and supply for adjacent beaches. They also protect inland areas from storm surges, hurricanes, flood-water, and wind and wave action that can damage property. Sand dunes support an array of organisms by providing nesting habitat for coastal bird species including migratory birds. Sand dunes are also habitat for coastal plants. For example: ‘The Seabrook dunes’ are home to 141 species of plants, including nine rare, threatened and endangered species.

There are three essential prerequisites for sand dune formation:

(1) An abundant supply of loose sand in a region generally devoid of vegetation (such as an ancient lake bed or river delta);

(2) A wind energy source sufficient to move the sand grains.

(3) A topography whereby the sand particles lose their momentum and settle down.

The best method by which the sand dunes can be stabilized is to reduce the erosive velocity. Therefore, various methods which are employed for sand dune stabilization are based on the principle to dissipate the erosive power of wind, so that the detachment and transportation of soil particles cannot take place. Some methods employed for sand dune stabilization are:

• Vegetation/Vegetative Measures
• Mechanical Measures
• Straw (Checkerboard and Bales)/Mats and Netting
• Chemical Spray

Vegetative Measures: This method is most common and preferred worldwide for sand dune stabilization. It is a most effective, least expensive, aesthetically pleasing method which mimics a natural system with self‐repairing provision. However, it has some disadvantages as the plant establishment phase is critical, it needs irrigation and maintenance until self-sustaining system is developed. Most common practices adopted under this are:

Raising of Micro Wind Breaks: It is preferred in those areas where wind velocity is intensive and rainfall is less than 300 mm per year. The raising of wind break should be completed before the onset of monsoon. Twigs or brush woods are inserted into the soil parallel to one another at about 5 m spacing. The spacing depends on the intensity of erosive wind velocity, if the velocity is more spacing is less and vice versa. The fencing of dunes using brush woods reduces evaporation loss and also enriches the humus content in the soil.

Retreating the Dunes: In this, the micro wind breaks are treated again by planting tree saplings and grasses in the space left. The grasses grown in the intersection of plants of wind break reduce the soil loss from the dune surface significantly.

Mechanical Measures: Wind breaks, shelterbelts, stone pitching, fences etc., either manmade or natural barriers are helpful to reduce the wind velocity thereby favoring the stabilization of sand dunes.

Straw Checker Boards: This technique of sand dunes stabilization is extensively used in China since 1950’s. Wheat or rice straw or reeds (50 – 60 cm in length) are placed vertically to form the sides of the checkerboard, which are typically 10 to 20 cm high. Optimum grid size of checker ranges from 1 x 1 m to 2 x 2 m, depending on local wind and sand transport conditions. Smaller grids are used in areas where winds are stronger.

Chemical Spray: Sometimes crude oils are used for the successful stabilization of sand dune. The oil is heated to 50 °C and sprayed on the dune at the rate of 4 m3/ha. It is a temporary measure, lasting only for 3-4 years and during those years, it is expected that the vegetation growth will take place in that area. This method is costly and suitable only for small areas.

Effects of wind erosion

1. The first effect is the winnowing of light particles. Wind erosion is very selective, carrying the finest particles - particularly organic matter, clay and loam - many kilometres.
2. The most spectacular forms are dunes - mounds of more or less sterile sand - which move as the wind takes them, even burying oases and ancient cities.
3. Degradation of sedimentation crusts on the surface of stripped soils, or the weathering of rocks at their base where they are in contact with the soil (abrasion).
4. Sheets of sand travelling close to the ground (30 to 50 metres) can degrade crops (particularly millet or cotton seedlings in semi-arid zones).
5. Wind erosion reduces the capacity of the soil to store nutrients and water, thus making the environment drier.
6. Crops, particularly in the seedling stages, are often damaged by abrasion of windblown soil particle.
7. Sufficient soil is removed to expose the plant roots or seed. – Leads to complete crop failure.
8. Drifting soil often buries and ruins established crops, shrubs fences, wells, ditches and channels.
9. Insects and weed seeds are blown far and wide with drifted soil, to in best clean fields.
10. Drifting sand or soil sometimes blocks railways and roads and this incurs added maintenance costs.

AEG-101-Class-14 : Grassed Waterways

Introductory Soil and Water Conservation Engineering

II Semester 3^rd Feb to 30^th June 2020, 2019-20

Teacher Information

Professor	Email	Phone
Dr. K. C. Shashidhar	shashidhar.kumbar@gmail.com	9448103268

Class-14 – Reference Material

Grassed Waterways

Classroom Video

 

Grassed waterways and outlets are natural or constructed waterways shaped to required dimensions and vegetated for safe disposal of runoff from a field, diversion terrace or other structures.

The grass lined waterway is one of the basic conservation practices. Waterways subject to constant or prolonged flows require special supplemental treatment, such as grade control structures, stone center or subsurface drainage capable of carrying such flows. After establishment, protective vegetative cover must be maintained. Vegetated outlets and waterways are used for the following purposes:

• as outlets for diversion and terraces;
• as outlets for surface and subsurface drainage systems on sloping land;
• to dispose of water collected by road ditches or discharged through culverts; and
• To rehabilitate natural drains carrying concentration of runoff.

The waterway or outlet may be protected by using a combination of the following steps:

• Construct the waterway in advance of any other channel that will discharge into it, and divert the

Flow during the period of stabilization.

• Establish and maintain the vegetative cover.

Shape

Grassed waterways may be built to three general shapes-parabolic, trapezoidal or V-shaped. Parabolic waterways are the most common. The successful vegetated waterway is dependent on good conservation treatment on its watershed, which reduce the peak rate of runoff and the volume of runoff to be carried by the waterway.

Profile and cross-section 

The original ground surface should be surveyed for longitudinal and cross-section in detail, to permit dividing the waterway into reaches of approximately uniform slope and shape.

Design

In designing a grassed waterway, care should be taken to see that its size is sufficient to carry all the runoff water from the contributing catchment and the gradient is such that the runoff will flow non-erosive velocities.

Design data

The following information is required for designing a waterway:

• Water shed area (ha) together with soil characteristics, cover and topography.

This information is needed to estimate peak rate of runoff.

• Grade of the proposed waterway (in per cent slope). This is fixed considering the outlet elevation.
• Vegetal covers adapting to site condition (for selecting roughness coefficient).
• Erodibility of the soil in the waterway (the information is necessary for protecting the waterway till the vegetation or grass gets established).
• Permissible velocity for the condition encountered.
• Allowance for space that will be occupied by vegetative lining.
• Free-board.

Non-erosive velocity of flow

The non-erosive velocity of flow depends usually on site conditions. However, following velocities of flow can be considered safely for design purposes.

• a velocity of 0.9 m/sec should be maximum where only a sparse cover can be established or maintained;
• a velocity of 0.9 to 1.2 m/sec should be used where vegetation is to be established by seeding;
• velocity of 1.2 to 1.5 m/sec should be used only in areas where dense, vigorous sod is established quickly;
• a velocity of 1.5 to 1.8 m/sec may be used on well- established sod of excellent quality; and
• Velocity of 1.8 to 2.1 m/sec may be used on well- established quality and conditions under which the flow cannot be handled at lower velocity. Also special maintenance measures are needed.

For situations where waterways are without vegetation, following values of critical velocity may be used (critical velocity is the velocity of water flowing in the channel, such that no silting or scouring takes place).

Nature of soil	Critical velocity (m/sec)	Nature of soil	Critical velocity (m/sec)
Earth	0.3-0.6	Boulder	1.5-1.8
Ordinary murrum	0.6-0.9	Soft rock	1.8-2.4
Hard murrum	1.2	Hard rock	More than 3.0

Cross-section

The area of cross-section (A), wetted perimeter (P) and top width (T) of trapezoidal section can be obtained by using the formula:

Trapezoidal
A = bd + Zd² 

P = b + 2d √(1 + Z²)

T = b + 2dZ

where, b = bottom width; d = depth of channel; z = side slope.

In area of cross-section (A), wetted perimeter(P) and top (T) of parabolic and triangular sections can be obtained, by using the following formulae:

Parabolic

A = (2/3) Td

And P = T + (8/3) x (d²/ T)

T= Top width

Triangular (Fig.3.36)

A = Zd² 

P = 2d √(1 + Z²)

T = 2dZ

The wetted perimeter (P) in the above equations is the length of line of inter-section of the plane of the cross-section with the wetted surface of the channel.

The hydraulic radius (R) is the ratio which is obtained by dividing area of cross-section (A) by the wetted perimeter (P). This is necessary to determine (R) to compute the velocity of flow of water in the channel using Manning’s formula.

STEPS FOR DESIGN

Step 1. The area drained, A (ha) may be obtained from the contour maps.

Step 2. Estimate the peak rate of runoff(cumecs) for the area to be drained using the rational formula.

Q=CIA/360

Step 3. Permissible velocity of flow, V (m/sec) in the vegetated and non-vegetated waterways can be obtained as discussed earlier.

Step 4. Compute approximate area of cross-section of the channel using the formula, Q =A.V., where V = the permissible velocity as obtained under Step 3 and q = peak rate of runoff.

Step 5. Knowing the cross-section from Step 4, determine the channel dimension in such a way that the area of cross-section equals the area of cross-section computed as in Step 4. (Use of different formulae given to compute area of cross-section for different shaped channels).

Step 6. Compute hydraulic radius (R) from the cross-section obtained in Step 5.

Step 7. Compute the grade of the channel using the Manning’s formula,

V = (1 / n) R^2/3S^1/2

where, V = permissible velocity (m/sec) (Step 3),

R = hydraulic radius (m)

n = roughness coefficient (refer Tables 1 and 2)

Step 8. The channel gradient obtained under Step 7 may be rounded for convenience of layout. The outlet elevation obtained by computing with this channel gradient should coincide with field outlet elevation.

Step 9. From the rounded off value of grade (S), we calculate the velocity of flow for the section under consideration. If needed, cross-section is to be adjusted (by adopting the channel dimensions) and it is to be verified whether the computed velocity is approximately equal or less than the velocity as assumed under Step 3.

Example 20: Determine the dimensions of a grassed waterway for stability and capacity, with a trapezoidal cross-section using the following data:

Peak rate of runoff = 3.5 cumec

Grade = 0.3 per cent

Vegetative cover = Blue grass

n = 0.045

Classroom Video

Table 1 Values of Manning’s roughness co-efficient, n. To be used with Manning’s formula

Surface	Best	Good	Fair	Bad
Uncoated cost iron pipe	0.012	0.013	0.014	0.015
Coated cast iron pipe	0.011	0.012	0.013*
Commercial wrought iron pipe, black	0.012	0.013	0.014*	0.015
Commercial wrought iron pipe, galvanized	0.013	0.014	0.0.15	0.017
Smooth brass and glass pipe	0.009	0.010	0.011	0.013
Rivoted and spiral steel pipe	0.013	0.015*	0.017*
Vitrified sewer pipe	0.010	0.013*	0.015	0.017
	0.011
Common clay drainage till	0.011	0.012*	0.014*	0.017
Glazed brick work	0.011	0.012	0.013*	0.015
Brick in cement mortar, brick sewers	0.012	0.013	0.015*	0.017
Neat cement surfaces	0.010	0.011	0.012	0.013
Cement mortar surfaces	0.011	0.012	0.013*	0.015
Concrete pipe	0.012	0.013	0.015*	0.016
Concrete lined channels	0.012	0.014	0.016*	0.018
Cement rubble surface	0.025	0.030	0.033	0.035
Dry rubble surface	0.025	0.030	0.033	0.035
Semi-circle metal flumes, smooth	0.011	0.012	0.013	0.015
Semi-circle metal flumes, corrugated	0.0225	0.025	0.0275	0.030
Canals and ditches
Earth, straight and uniform	0.017	0.020	0.0225*	0.025
Rock cuts, smooth and uniform	0.025	0.030	0.033*	0.035
Rock cuts, jagged and irregular	0.035	0.040	0.045
Winding sluggish canals	0.0225	0.025*	0.0275	0.030
Dredged earth channels	0.025	0.0275*	0.030	0.033
Canals with rough stony beds, Weeds on earth banks	0.025	0.030	0.035*	0.040
Earth bottom, rubble sides	0.028	0.030*	0.033*	0.035
Natural Stream Channels
Clean, straight, bank, full stage, No rifts or deep pools	0.025	0.0275	0.030	0.033
Same as above but some weeds and stones	0.030	0.033	0.035	0.040

*Values commonly used in designing.

Soil moderately erodible
Side slope, Z=2.
Solution
Assume B = 2m
Area of cross-section,

A = BD + ZD²

Wetted Parameter

P = 2D√(1+Z²)

A + (2x1) + (2x1²) = 4m²

P=2 + 2√(1+2²) = 2 + 4.47 = 6.47m

Hydraulic radius

R = A / P = 4 / 6.47 = 0.62m

Using the Nomograph below

Velocity of flow in the channel section is approximately equal to 0.9m/sec

Q = A x V = 4.0 x 0.9 = 3.6cumec 

Hence, the design can be accepted.

Table 2 Values of Manning’s roughness co-efficient, n. To be used with Manning’s formula

Kind of pipe	Variation		Use in designs
	From	To	From	To
Clean uncoated cast iron pipe	0.011	0.015	0.013	0.015
Clean coated cast iron pipe	0.010	0.014	0.012	0.014
Dirty or tuberculated cast iron pipe	0.0.15	0.035
Riveted steel pipe	0.013	0.017	0.015	0.017
Lockbar and welded pipe	0.010	0.013	0.012	0.013
Galvanized iron pipe	0.012	0.017	0.015	0.017
Brass and glass pipe	0.009	0.013
Wood stave pipe	0.010	0.014
Wood stave pipe, small diameter			0.011	0.012
Wood stave pipe, large diameter			0.012	0.013
Concrete pipe	0.010	0.017
Concrete pipe with rough joints			0.016	0.017
Concrete pipe, ‘dry mix’ rough forms			0.015	0.016
Concrete pipe, ‘wet mix’ steel forms			0.012	0.014
Concrete pipe, very smooth			0.011	0.012
Vitrified sewer pipe	0.010	0.017	0.013	0.015
Common clay drainage tile	0.011	0.017	0.012	0.014

Source: Handbook of Hydraulics, King, McGraw-Hill Book Company, INC(Fourth edition) (1954) pages 6.12)

Example 21: Design a grassed waterway of parabolic shape to carry a flow of 2.6 m3/s, down a slope of 3 per cent. The waterway has a good stand of grass and a velocity of 1.75 m/s can be allowed. Assume the value of n in Manning’s formula as 0.04.

Solution
Using Q = AV, for a velocity of 1.75 m/s, a cross-section of 2.6/1.75 = 1.5 m2 is needed.
Assuming

t = 4m, d = 60cm

A = (2/3) t d = (2/3) x 4 x 60 = 1.6m² 

P = t + (8d² / 3t) = 4 + (8.062 / (3 x 4)) = 4.24m

R = A / P = 1.6 / 4.24 = 0.377

V = R^2/3S^1/2 / n = ((03.77)^2/3 x (0.03)^1/2) / 0.04 = (0.522 x 0.173) / 0.04 
   = 2.6m/s

The velocity exceeds the permissible limit. Assuming a revised value of t=6 m and d=0.4m

A = (2/3) x 6 x 0.4 = 1.6m² 

P = 6 + (80.4² / (3 x 6)) = 6.45m

R = 1.6 / 6.45 = 0.248

V = (0.248^2/3 x 0.03^1/2 ) / 0.04 =1.70m/s

The velocity is within permissible limits

Q = 1.6 x 1.7 = 2.72m³ /s


Hence Satisfactory. A suitable freeboard to the depth is to be given in the final dimensions.

Classroom Video

Example 22: Design a parabolic shaped grassed waterway to carry a peak flow of 3.0 m3/sec down a slope of 4.0%. An excellent stand of dub grass is maintained in the waterway.

Manning’s Coefficient n = 0.04
initially assume a top width T = 4.0 m (Fig. 3.38)
Depth of flow d = 0.60

The section is much higher in size. Therefore, assuming that T=4.15 m and depth of flow as 0.475 m and adopting the above method, Q = 3.007 cumec. This is satisfactory.

DESIGN OF A DIVERSION CHANNEL
A case is met where in an area to be improved by contour bunding receives runoff from an outside catchment. It is necessary to devise a diversion channel before undertaking contour bunding project.

Classroom Video

Design Example 23:
Outside catchment = 15 ha
Slope = 8%
Coefficient of runoff may be assumed as 0.75
Intensity of rainfall = 25 mm/hr.
Assume a coefficient of roughness = 0.05
Peak rate of runoff,

Q = CIA / 360 = (0.75 x 25 x 15) / 360 = 0.78cumec

Solution design of diversion drain

First trail-Assume b=2m, d=0.3m,Z=2
Area of cross section= bd+Zd2 = (2 x 0.3 ) + (2 x 0.3² ) = 0.78m²

Wetted perimeter = b + 2d√(1+Z²) = 2 + ( 2 x 0.3√(1+2² )) = 3.338m



Hydraulic radius, R = 0.78 / 3.338 = 0.233m

V = (1/n) x (R^2/3 x S^1/2 ) = (1/0.05) x (0.233^2/3 x 0.08^1/2 ) = 2.12m/s

Q = A x V = 0.78 x 2.12 = 1.65cumec





The requirement being 0.78cumec the size of diversion drain is very big. Hence the dimension can be lowered

2nd trail-b=0.6m: d=0.3m, Z=2

Area of cross section of flow,
A= bd+Zd² =  (0.6 x 0.3) + (2 x 0.3 x 0.3) 
  = 0.36m²

Wetted perimeter P = b +  2d√(1+Z²) = 0.6 + ( 2 x 0.3√(1+4) ) = 1.94m

Hydralic radius  R = A / P = 0.36 / 1.94 = 0.185m

V = (1/n) (R^2/3 x S^1/2 ) = (1 / 0.05) x 0.185^2/3 x 0.08^1/2  = 1.05m/s


Manning’s formula

Q = A V = 0.78 x 1.05 = 0.81cumec

This is satisfactory. Here channel dimensions of bottom width of 0.6m and depth 0.3m with side slopes of 2:1 can be adopted.