Headrace Canal General

DESIGN GUIDELINES

3.1.1.3 Headrace Canal General

3.1.1.3 Headrace Canal

e) For not allowing the entry of rainwater from the sloppy terrain to headrace canal, the provision of catch drain in the side of upstream slopes is essential.

• Canal Alignment

The practical alignment is the economically shortest route. It will lie in between the routes following the contour of the side hill from dam / weir to forebay with a minimum excavation or fill and a straight line between dam / weir and forebay which would usually result in excessive cuts and fills.

• Basic Geometry

The design of a power canal as with any design problem, aims at determining the size and configuration that meets the criteria for the least cost. The best form of cross-section of a canal is a section which gives maximum discharge for a minimum cross-section for a given bed slope. The cross-section should also correspond to the section with the least loss of water from absorption (i.e.

with minimum of wetted perimeter) and evaporation (considered only if the canal is very big in size and alignment is located in very hot and low humid area). Theoretically, a circle for a closed canal, a semi-circle for open canal, half a square (i.e. depth equal to half the width) for rectangular canal and semi-hexagon for trapezoid canal are the best discharging canals. In practice for ease of construction, cross-sections close to the theoretical one will have to be adopted. Depending upon the location, humidity and size of the canal, an evaporation loss is considered^∗.

In the Nepalese conditions, the derivation type of hydropower projects have prospects in the mountainous regions, because in the Terai region very little head could be concentrated at a given location even with very long water conveyance system. The terrain conditions in the mountainous regions are such that there are topographical limitations for constructing wide, but shallow canals. On the other hand for irrigation development which has larger prospect in the Terai, due to flatness of topography, wide and shallow canals will have more prospect. Thus, the topographical conditions could be considered as the major criteria for determining whether the canal should be shallow or deep.

The most efficient proportions of the rectangular, trapezoidal and parabolic canal are:

For rectangular Canal h

b=2 --- (3.3) 2

/ h P / A

R= = --- (3.4) For the case of section that is relatively wide in comparison with depth (Width>25 x depth), R= h, more generally the value of R is between h and h/2.

For trapezoidal canal

(

^{z z}

)

h

b =2 1+ ² − --- (3.5)

Where,

b = Width of the canal h = Depth of the canal

z

= Side slopes

R = Hydraulic radius P = Wetted perimeter, and

A

= Area

∗ Please refer “Hydrology in Practice” Elizabeth M. Shaw – Third Edition – Stanley Thornes Publishers Ltd.

United Kingdom, for the calculation of absorption and Evaporation losses in headrace canal.

The most efficient hydraulic section is when the top width is twice the length of the sloping side.

For Parabolic Canal h

T =2 2 --- (3.6) where,

T

= Top width

h = Depth

Geometric Elements of Channel Sections

Unlike the natural channels which are usually irregular in shape, man-made channels (artificial channels) are usually designed with sections of regular geometric shape. Some of the commonly used geometric sections and corresponding formulas are given below in the tabular form.

Geometric Sections and Corresponding Formulae

Formula/Shape Rectangular Trapezoidal

(“z”-Side Slope) Circular Parabolic T-Top width

Area-“A” b *h

(

b+zh

)

h

(

sin

)

²

8

1

φ

−

φ

D Th

3 2 Wetter

Perimeter-“P” b+2h b+2h 1+z² 12

φ

D

T b h

3 8 ² + Top Width of

Section-“T” b = T b+2zh 2 h(D−h)

T

Hydraulic

Radius-“R”

b h

bh

+ 2

2 1 ²

) (

z h b

h zh b

+ +

+

⎟⎟ ⎠ D

⎜⎜ ⎞

⎝

⎛ − φ

φ 1 sin 4 1

2 2

2

8 3

2 h T

h T

+

Hydraulic Depth-

“D” h

zh b

h zh b

2 ) (

+

+

D

sen ⎟⎟⎟⎟

⎠

⎞

⎜⎜

⎜⎜

⎝

⎛ −

2 sin 8

1

φ φ

φ h

3 2

Section Factor bh^1.5

[ ( ) ]

zh b

h zh b

2

5 . 1

+

+

^{1.5 2.5}

12 sin 32

) sin (

2 D

φ φ φ−

5

6 1

9

2 _.

Th

The typical sections of the lined and unlined canals are shown in the Figure 3.3 below.

Figure 3.3: Typical Sections of the Canal

• Design for Transition

Transitions are required to alter the basic canal geometry. Sidewall angles for transitions should follow the basic criteria outlined previously. It is important to check if the transition requires a change in state of flow, from sub-critical to super-critical or vice versa. Special design considerations like energy dissipation systems are required at such change. In general, transitions should be smooth and gradual as possible to minimize turbulence and hydraulic losses. Rounded corners are preferable to sharp edges.

Hydraulic Transition –Transition between sub-and Super-Critical flow: If sub-critical flow exists in a channel of a mild slope and this channel meets with a steep channel in which the normal depth is super- critical there must be some change of surface level between the two. In this situation the surface changes gradually between the two. The flow in the joining of the two channels the depth passes through the critical depth (Fig. 3.4a).

hc = critical depth Sc = critical slope So = canal slope

Figure 3.4: Transition of Sub to Super-Critical Flow and Vice Versa

If the situation reversed and the upstream slope is steep (super critical flow) and the downstream mild (sub-critical), then there must occur a hydraulic jump to join two (Fig. 3.4b). Also, there may occur a short length of gradually varied flow between the channel junction and the jump.

Structural Transition: The terminology transition structure implies a designed channel appurtenance whose purpose is to change the cross sectional shape of the channel. The function of such structures is to:

¾ Avoid excessive losses of energy

¾ Eliminate cross waves, standing waves, and other turbulences

¾ Provide safety for both the transition structures and the waterway.

The geometric form of a transition structure can vary from a rather simple straight line design to a complex, streamlined design involving warped surface. The common types of transitions are generally used at the inlet and outlet of structures and where changes occur in the water section. An accelerating water velocity usually occurs in the inlet transitions and a decelerating velocity in outlet transitions. The most common type of open transitions where a change of section from the trapezoidal canal to the rectangular opening of structures occurs, are the streamlined warp, straight warp, broken back and vertical walled type.

There are considerable difficulties in constructing those sloping parts of the sloping warped which are steeper than the natural slope of the retained materials, but not so steep that the lining can stand unaided to allow backfilling behind. Accordingly, in Nepal either broken back “dog leg” or a vertical walled transition should be used. Hydraulically broken back transition is the better solution. In a vertical walled solution, to reduce head losses to a minimum the wing walls are flared at 45^o to the canal centre line and lead into the abutments via a horizontal circular arc.

For minimum hydraulic loss and smooth operation, a small submergence of the opening in the headwall should be provided at inlet transition, and no submergence of the opening in the headwall should normally be provided at outlet transitions. If the submergence exceeds one sixth of the depth of the opening at the outlet, the hydraulic loss should be computed on the basis of the sudden enlargement rather than as an outlet transition. The hydraulic loss in a transition will depend primarily on the difference between the velocity heads at the open end of the transition and at the normal centerline section of the closed conduit at the headwall. Hydraulic loss coefficients in some transitions are tabulated below:

Type of open transition to closed conduit Inlet Outlet

• Streamline warp to rectangular opening

• Straight warp to rectangular opening

• Straight warp with bottom corner fillets to pipe opening

• Broken back to rectangular opening

• Broken back to pipe opening (closed)

• From Trapezoidal canal to rectangular opening through vertical walled transition

• From trapezoidal canal to pipe opening through vertical walled transition

Closed Transition

• Square or rectangular to round (Maximum angle with centerline =7.5⁰)

0.1 0.2 0.3 0.3 0.4 0.5 0.6

0.4

0.2 0.3 0.4 0.5 0.7 0.8 1.0

0.7

Open transitions to multiple closed conduits will involve some additional hydraulic loss. Average friction loss should be added for large transitions, but it may be neglected for small transitions. The slope of the floor on the broken back outlet transitions should be 1:6 or flatter. The maximum angle between the water surface and the centerline should not exceed 27.5⁰ for inlet transitions and 22.5⁰ for outlet transitions for the best hydraulic conditions. In some structures it may prove economical to use 25⁰ to allow the same structure to be used for both inlets and outlets. A 30⁰ angle is often used on inlet transitions with checks, in which case an additional loss is allowed for the check. Design should

provide for a loss through most check structures of about 0.5 times the difference in velocity head through the check opening and the upstream channel section.

Transmission sections of canal are normally designed for minimum head loss. The basic two methods are generally adopted as a formula for the transition (refer the figure given below):

( ^{B B} ) ^x

B L

L B B B

f c c f

f f c

x

× − − ×

×

= ×

--- (3.7)

and

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎟⎟⎠

⎜⎜ ⎞

⎝

−⎛

−

= × ²

3

3 3

3

1

2 2

2

x f f f

cc c f

B B B

B B

x L --- (3.8)

where

Bx = Width of transition

Bc = Width of the normal canal section Bf = Width of the flamed section Lf = Total length of the transition x = Distance of transition

An inlet transition connects to a free flow closed conduit in such a way that the conduit inlet is sealed the quantity of water that is passed should be determined by the orifice equation. The head should be

measured from the center of the opening to the inlet water surface and an orifice coefficient of c=0.6 should be used. A small correction factor is theoretically required when the submergence is less than the height of the opening. When the inlet to a long conduit may operate without sealing, a hydraulic jump may occur that can result in blowback and undesirable operation. Transitions to free flow conduits can have the control point anywhere between the inlet cutoff and the headwall. If control at any flow is at the inlet cutoff, the upstream channel must be protected from erosion or the design changed to move the point of control to the transition.^∗

• Head Losses due to Friction and Structural Transition

Water flowing through a conveyance system with entrances, bends, sudden contraction and enlargements, racks, valves and other (in case of pipe) experiences, in addition to the friction loss, a loss due to the inner viscosity. This loss depends on the velocity and is expressed by an experimental coefficient K multiplying the kinetic energy v²/2g.

Calculation of head losses is based upon the following general equation.

t f

L h h

H = + --- (3.9) where,

HL= the total head loss or energy loss;

hf

= the loss due to frictional resistance, and

ht = the loss due to transitions or changes in direction, also called local losses.

The friction loss

( )

hf in length is calculated by the equation:

3 / 4

2

2* *

R L V

h_f = n --- (3.10) where,

hf = friction loss V = velocity in m/s.

R = hydraulic radius in m,

n

= Manning’s roughness coefficient, the typical values of which are given in Table-3.1^#, and L = length of canal in m.

∗ For more detailed information about the structural transition refer to standard hydraulic books such as (Water Power Development – Emil Masonyi, Hydraulic Design – Ven Te Chow, Hydraulic Design – French, Davi’s Handbook of Applied Hydraulics – ISBN 0-07-073002-4).

# For more Manning’s roughness value –refer to standard hydraulic books such as (Water Power Development – Emil Masonyi, Hydraulic Design – Ven Te Chow, Hydraulic Design – French, Davi’s Handbook of Applied Hydraulics – ISBN 0-07-073002-4).

Table-3.1: Typical Manning’s Roughness Coefficients for Channels

Channel Material or Type Manning’s n

Clean, straight earthen channel 0.022

Straight earthen channel with grass 0.027

Winding and sluggish earthen channel with some weeds 0.030 Winding and sluggish earthen channel with cobble

bottom and clean sides 0.040

Unmaintained earthen channel with uncut weeds and

brush on sides and clean bottom 0.050

Concrete-lined channels 0.013 - 0.017

Asphalt-lined channels 0.013 - 0.016

Gunited channels 0.019 - 0.022

Rubble masonry 0.020 - 0.025

Riprap-lined channel 0.030

Channel with cement plaster 0.011

Brick work 0.014

Rock cut channel 0.035 - 0.040

Channel with gravel 0.022 - 0.030

Older wooden channel 0.015

Natural river bed 0.024 – 0.05

Transition losses (ht) and local losses such as entrance / exit loss, trash rack loss, bend loss, etc. is calculated by the following general equation:

g h_t KV

2

= 2 --- (3.11)

Where,

K

is loss coefficient, and

g

= gravitational constant.

The value of K depends on nature of transition (expansion / contraction), change in direction (shape and angle of bend) and resistance to flow imposed. For other details of head loss calculation and loss coefficient refer Annex-2.

Maximum Permissible Velocity in the canal

The maximum permissible velocity or the maximum allowable bottom shear stress in the power canals will be limited by the resistance of the bed material to erosion or, in case of lined canals, by that of the lining against wear. The latter becomes considerable if the water carries abrasive materials in appreciable quantities.

Some authors relate permissible bottom velocities to the material of bottom and sides or /and lining, while others suggest values for the permissible mean velocity. Maximum permissible velocity have been determined partly by experimental and partly by theoretical research work.

The maximum bottom velocity, i.e. critical scour velocity as regards erosion given by Sternberg is:

d

V_b =

ξ

× --- (3.12) Where,

Vb - Maximum Permissible Velocity

d - Diameter of Particles in m. and in this case

ξ

=4.43

Although a number of other investigators (Kutter, Airy, Hochenberger, Schffernak, Mavis and others) have derived theoretical relations between critical bottom velocity and particles size, the discussion on these relations are not indicated. The practice refuses calculation with the bottom velocity, because its deduction from the data available for designing is uncertain; it would impose a rather difficult task on the designer. In fact it is not yet unambiguously clarified what is meant by bottom velocity. For this reason two other types of relations are commonly used in engineering practice to define the scouring

effect of the flow: the mean velocity or the bottom shear stress versus the particle size. Since the incipient motion of the bed material strongly depends on the intensity of turbulence, the present trend is to take into account this factor by indicating the shear velocity and expressing the critical state as dependence of both parameters; the shear stress and the shear velocity. Since the specified gravity of the grains is of great significance, methods and expressions, which include the influence of this property of the material, can cover a wider range of the erosion phenomena. Accordingly, in several cases, priority can be given to the procedures which relate the incipient scouring to the specific (dimensionless) shear stress:

(

₁

)

*d

*

γ γ

τ τ

= − --- (3.13)

Where,

τ

* - Specific shear stress

γ RS

τ =

= Bottom Shear Stress in Kg/m²

γ

γ

₁, - Specific weight of particles and the water respectively in Kg/m³ d - Mean or representative grain size (diameter) in meter.

R - Hydraulic Radius

S - Slope

Scour velocities for various soil particles sizes based on the American practice are indicated in the figure (Fig. 3.5) below: This figure is created by W.P. Creager and J.D. Justin.

Fig. 3.5: Scour Velocities for Various Soil Particles Sizes

The range of maximum permissible mean flow velocities is given for different soil grain diameters varying from fine clay to gravel of medium fineness (0.001 to 10 mm). The erosion velocities depend on the number of soil properties, beside the average particle size. Safe values are characterized in American practice by a fairly wide range instead of a single curve. Some maximum permissible mean velocities are given below in the tabular form (Table 3.2)⁴:

The Table 3.2 below has been compiled for the loose granular bed material on the basis of velocity distribution pertaining to a depth of 1 meter. In case of depths other than that, corrections are to be introduced. With water depths lower than 1m, tabulated permissible velocities are to be diminished

4 Reference from Low Head Power Plant by Emil Mosonyi

because of the more uniform velocity distribution and vice versa. Actual permissible maximum mean velocities will be obtained from tabulated values V1 (Table 3.3) as:

V1

V =

α

--- (3.14) Where,

V - Actual permissible maximum mean velocity V1 - Maximum Mean Velocity

α

- Coefficient whose value depends on the depth

The maximum permissible velocities for solid rocks are given in Table 3.4 and the same for cohesive soils and for flow in lined canals are given respectively in Tables 3.5 and 3.6.

Table 3.2: Maximum permissible mean velocities for loose granular bed material

Material Diameter of particle

“d” in mm

Maximum mean velocity in case of

h=1 m , V1 m/s Very coarse gravel

Coarse gravel

Cobble Coarse sand

200-150 150-100 100-75

75-50 50-25 25-15 15-10 10-5.0 5.0-2.0 2.0-0.5 0.5-0.1 0.1-0.02 0.02-0.002

3.9-3.3 3.3-2.7 2.7-2.4 2.4-1.9 1.9-1.4 1.4-1.2 1.2-1.0 1.0-0.8 0.8-0.6 0.6-0.4 0.4-0.25 0.25-0.20

0.2-0.15 Table 3.3: Correction coefficients to formula V =

α

V₁

Depth “h” Correction coefficient

α

0.3m 0.6m 1.0m 1.5m 2.0m 2.5m 3.0m

0.80 0.90 1.00 1.10 1.15 1.20 1.25

Table 3.4: Maximum Permissible velocities for solid rocks

Material V1, m/s

• Loose conglomerate, clay loam

• Tough conglomerate, porous lime rock, stratified limestone

• Dolomite sandstone, non stratified limestone, quartzitic limestone

• Marble, granite, syenite, gabbro-coarse

• Same as above - smoothed

• Porphyry, phonolite, andesite, diabas, basalt, quartzite - coarse

• Same as above - smoothed

2.5-3.0 3.0-5.0 4.5-7.0 15.0-25.0 27.0-38.0 24.0-48.0 38.0-45.0

Table 3.5: Maximum permissible mean velocities for cohesive soils

Type of Soil V1, m/s Note

Slightly clayey sand, very fine sand Compacted clayey sand

Loose sandy clay or loess Medium sandy clay Hard sandy clay Soft clay Ordinary clay Rolled clay Silts

0.7-0.8 1.0 0.7-0.8

1.0 1.1-1.2

0.7 1.2-1.4 1.5-1.8 0.5-0.6

Tabulated data apply to hydraulic radius between 1 and 3 m for R>3 increased by (R/3)^0.1

The accuracy obtained by the use of values listed above is limited and sufficient only for the design of projects of smaller significance, or for the preliminary study of greater ones. However for a detailed planning of the latter, a more exact investigation of non eroding mean velocity is advisable.

Table 3.6: Maximum permissible mean velocity for flow in lined canals Type and Strength of lining Permissible velocity,

V, m/s