47

5. WEIRS

5.1. GENERAL

5.1. Introduction

A weir or low head dam is a barrier across the width of a river that alters the flow characteristics of water

and usually results in a change in the height of the river level. They are also used to control the flow of water

for outlets of lakes, ponds, and reservoirs. There are many weir designs, but commonly water flows freely

over the top of the weir crest before cascading down to a lower level.

Dams are structures that cover the entire valley other than its bed and affect the regime of the stream. Weirs

are structures that generally only cover the bed of the stream, raise the water level to a certain level rather

than accumulate water, turn the water in a certain direction and provide the desired amount of water from the

desired level. Weirs are also called regulators or in a broader sense translation structures.

Weirs are structures that swell the water in the streambed and turn it into a transmission structure. Therefore,

it includes both the elements necessary for taking water and the elements required to transfer the excess

water harmlessly to the downstream when the water is excessive. Although it swells the water to a certain

amount, unlike dams, there is no important accumulation. Weirs contain control elements such as grids and

covers include elements such as a settling basin, the structure in which the sediment is settled. The sediment

accumulated in the sedimentation pool is cleaned intermittently by opening the cover of the washing

channel. Weirs may be made with a fixed concrete mass called fixed weirs (Figure 5.1a) or with lids placed

on a lower called movable (gated) weirs (Figure 5.1b). Sometimes, both kinds of weirs may be used together

(combined weirs).

Significant changes may occur in the flow conditions in the downstream region of the stream after the

construction of the weirs. As the waters passing downstream through the weir leave most of the sediment

they carry, bed and bank erosion occurs in the downstream region. Since the construction of the weirs cause

elevation difference between the upstream and downstream water levels, some special structures should be

made to ensure the access between upstream and downstream.

5.1.2. Construction Aims

Weirs may be constructed one of or a number of the following purposes:

To increase the upstream water to a certain level, ensuring that it receives water at the desired level,

To reduce the water level changes in front of the water intake,

To obtain drop height by swelling the water,

To reduce the flow velocity in order to prevent shore and bottom erosion in the streambed and to

protect the related structures against scouring,

To provide the required water depth in transport streams, especially at minimum discharges,

To keep the bed and suspension sediment back, even to a limited extent,

To regulate flows, because there is limited storage in the swelling of water.

48

a. Fixed Weir

b. Movable (Gated) Weir

Figure 5.1. Types of Weirs.

5.1.3. Factors that Affect the Type of Weirs

a. Topography of the Weir Place: In the case of fixed weir in flat and plain streams, since swelling will be

high in the passage of flood waters, agricultural land, access roads and basements of residential areas may be

submerged. In such places, the swelling level can be kept constant to some extent by choosing the movable

weir. The choice of fixed or mobile weir in mountainous rivers and valleys with steep slopes is decided by

looking at other factors. Generally, fixed weirs are more economical in such cases. Planning a fixed weir

wide valleys and movable weirs in narrow valleys is appropriate in terms of the passage of the flood flow.

b. Sediment Discharge: In streams carrying a large amount of sediment, the upstream side of the fixed weir

fills in a short time and a large amount of bed material enters from the water intake. In movable weirs, it is

possible to wash the solid materials accumulated on the upstream side by opening the lids, especially during

flood, and eliminating the aforementioned drawbacks for fixed weirs. For this reason, the choice of mobile

weir is appropriate in rivers with high solid material transport.

c. Minimum and Maximum Discharges: If the difference between the maximum and minimum discharge of

the stream is too large, the choice of movable weir is appropriate, since the swelling level will increase

during the flood in fixed weirs.

49

d. Operation and Maintenance Costs: Since additional energy is needed to open the gates in movable weirs,

the operation and maintenance costs of these types are higher than the fixed weirs.

e. Comparison of Costs: The points mentioned above are examined one by one and compared with each

other. The advantages and disadvantages of each type are determined; The most appropriate weir type to be

built is decided by calculating the initial investment costs and estimated maintenance and operating costs.

5.1.4. Determination of Backwater Elevation

When a weir body is constructed (for fixed weir) or weir gates (for gated weir) are constructed upstream of

the structure water level will swell; the water profile at upstream of a weir is called backwater (Figure 5.2).

As going from weir to upstream, the water level will descend and the swelling will be zero enough far from

weir. When the water level difference between before and after swelling is 2 cm, it is supposed that the

effect of the weir will end (no swelling upstream this point). This point is called swelling (backwater)

boundary and the distance between swelling boundary and weir is named as backwater length.

Figure 5.2. Backwater Profile

Backwater elevation is determined according to: The flooding condition of the backwater (swelling) zone,

the permissible seasonal peak values of the ground and surface water levels in the upstream region,

foundation conditions, the costs of the energy breakers (dispersion structures). In particular, the selection

should be made by considering the lands with high agricultural value, the settlements in the swelling zone,

the drainage status of the region, the water supply and wastewater networks and the existing water rights in

the region and by considering the goals that serve everyone.

The swelling elevation, which determines water level upstream of the weir, is calculated by adding friction

and local energy (head) losses at the transmission channel and local losses at the water intake. Low weirs are

not suitable as they will lose their effect in a short time as a result of sediment accumulation. High

agricultural value lands can be protected by constructing berms. It should be noted that the swelling

elevation will increase over time as a result of sediment accumulation in the swelling zone.

4.1.5. Weir Foundations

Foundation soils at the weir place are classified into 3 groups; a. Rock, b. Sand-Gravel and c. Clay-Mud.

Rock is the most suitable and inexpensive foundation type. However, the weirs were mostly built on

sand-gravel ground. If the sand-gravel layer is of sufficient thickness, there is no problem in terms of

transferring the loads to the ground and the stability of the structure. If the permeability is large, serious

problems are encountered as a result of bottom leakage. In this case, special measures such as cutoff wall

and sheet pile are required to increase the infiltration length. The foundations planned on clay-mud are the

most expensive and difficult. Clay soils can be used as a weir foundation, taking into account the swelling,

shrinkage properties and pore water pressure and reinforcing it. If the soil is mud, it should be removed and

the ground with high bearing capacity should be filled instead.

50

5.2. FIXED WEIRS

5.2.1. Definitions

The fixed weir is essentially a wall that blocks the front of the water, is resistant to the pressure of the water

that will swell behind it and the pressure of the accumulated sediment material; and has a hydraulic suitable

cross section. The swell level and the passage of waters from upstream to downstream are provided by a full

body that covers the stream bed. The top of the full body is fixed. If discharge changes, the water level in the

upstream region also changes greatly. For this reason, fixed weirs are planned in places where the harmful

effects of swelling level changes are not observed. The solid body also acts as a spillway to discharge flood

waters downstream. Since the accumulation of sediments in front of the water intake will cause clogging

over time, it is necessary to leave a covered section near the connecting body. This section is called the

undersluice (gravel passage). After high discharges, the covers of the undersluice is opened and cleaned.

Some terms related to fixed weirs are given below (Figure 5.2):

Water Nappe: A layer of water that passes over the weir and has a lower and an upper surface.

Weir Load: Height difference between the weir crest elevation and the water level passing over the weir.

Weir Crest Elevation: It is found by subtracting the minimum sluice load from the swell level.

Swelling Level: Minimum swelling level of the water that is desired to be swelled by weir.

Maximum Swelling Level: It is found by adding the maximum weir load to the weir crest elevation.

Weir Height: It is found by subtracting the stream base elevation from the weir crest elevation.

5.2.2. Elements of Fixed Weirs

The main elements of a fixed weir are the main weir structure, water intake structure and special structures.

Information on intake structures and special structures will be given later. Here, information is given about

parts of the main weir structure (Figure 5.3 and 5.4).

a. Weir Body: It is the structure that allows the adjustment of the upstream water level by closing the stream

bed from one end to the other. If a service bridge that provides passage from one shore to another is

necessary, the bridge piers are placed on the weir body.

b. Undersluice (Gravel Passage): These are the covered passages planned at the lowest level (thalweg) of the

stream bed in order to prevent the accumulation of bed sediment in front of the water intake. The gravel pass

is separated from the full body by the separation (guide) wall that guides the sediment.

c. Abutments: They are the retaining walls that restricts the weir with the coasts, resists the soil effects here

and acts as a support for the service bridge.

d. Fall Bed (Apron): It is the protective layer that is planned as the continuation of the full body in order to

prevent the water passing over the weir from damaging the connection by breaking the energy and

preventing the river bed from being eroded.

e. Riprap: It is the part protected by stones and rock fragments of certain length, at the downstream side the

fall bed in order to prevent scouring in the stream bed.

f. Sealing Structures: The leakage under weir is controlled by sealing structures; such as cutoff wall, sheet

pile, injection curtain, upstream cover, reverse filter, etc.

g. Other Facilities: Depending on the purpose of weir, structures such as water intake structure, power plant,

fish passage, ship passage etc. are planned.

51

Plan

a-a Section

b-b Section

c-c Section

d-d Section

Figure 5.3. Plan and Sections of a Fixed Weir

52

Figure 5.4. Elements of a Fixed Weir

5.2.3. Calculation Principles

Calculation principles of fixed weirs are examined in four main sections: Determination of weir height and

width, and profile of the sluice, and design of undersluice. In order for the desired amount of flow to enter

from the water intake, the water level at the upstream of weir should not fall below a certain level. This level

is called swell level and is calculated as follows:

Swell Level = Elevation of water arrival +

Energy losses in transmission facilities + Energy losses in water intake (5.1)

5.2.4. Determination Crest Elevation and Length of Weir

The discharge passing on sluice crest is calculated as:

5.1CbhQ (5.2)

Where, Q is discharge (m3/s), C is sluice coefficient (between 1.7 and 2.2), b is crest length of sluice (m) and

h is the water depth on weir (m). Since the critical situation in receiving the demand flow (Qd) into the

transmission channel occurs at minimum discharge (Qmin), the following steps are taken in determining the

weir crest elevation:

Case 1: 0'Q minmin QQd : In this case, the sluice load (water depth of sluice) that will occur when the Q

discharge passes over the weir is calculated. The weir crest elevation level is found by subtracting the sluice

load from the swell elevation.

Case 2: 0Qmin dQ In this case, since the water will not pass over the weir, the weir crest elevation is

taken as swelling elevation by adding 0.1 m safety margin for wave swelling effect.

The weir body is the most expensive part of the facility, so it is desirable to keep its length as short as

possible. If the weir length is chosen large, the maximum swelling level during the flood is small, but the

weir cost is large. The opposite happens if the weir length is chosen small. For this reason, it is necessary to

examine from which swelling elevation the settlement and agricultural areas in the upstream region will be

damaged and submerged, and to what extent this situation can be prevented by berms; thus, the technically

and economically most suitable weir length should be determined. The fixed weir length can be determined

to be q = 5 m3/s/m flow per unit length as a rough approximation. In principle, the weir length should not be

less than 0.5-0.6 times the width of the streambed to prevent ice accumulation and erosion.

53

5.2.5. Undersluice

Undersluices are the gated passages arranged to transfer the gravels to the downstream from time to time in

order to prevent gravel entering the settling basin and blockage of the water intake mouth due to excessive

accumulation in front of the sill. It is appropriate to keep the undersluice width between 3 to 3.5 m. Since the

cost of large gates is high, it is also economically beneficial not to make the gate very wide. In the weirs up

to 2.5 m height, the gate height may be equal to weir height. For high weirs, it is suitable to use a breast wall

(a reinforced concrete curtain extending into the water) together with the gate.

5.2.6. Determination of Hydraulic Profile of Sluice

The fixed weir crest over which the water flows freely is called sluice. The upper and lower nappe values of

the sluice should be determined to avoid excessive stresses on the body. Two different methods are used to

determine the hydraulic profile of sluice: Creager Profile and Ogee Profile.

a. Creager Profile: The lower and upper nappe elevations (y) corresponding to various x horizontal distances

from the starting point of the weir are given in Table 5.1 and Figure 5.5 for the unit sluice load (water depth)

(h0 = 1 m). The calculated coordinates for other sluice loads are multiplied by the sluice load.

Figure 5.5. Creager Profile

Table 5.1. Coordinates of Creager Profile

x/h0 0.00 0.10 0.20 0.30 0.40 0.60 0.80 1.00 1.20

y/h0 Lower .126 .036 .007 .000 .007 .063 .153 .267 .410

Upper -.831 -.803 -.772 -.740 -.702 -.620 -.511 -.380 -.219

x/h0 1.40 1.70 2.00 2.50 3.00 3.50 4.00 4.50

y/h0 Lower .590 .920 1.315 2.100 3.110 4.260 5.610 7.150

Upper -.030 .305 .693 1.500 2.500 3.660 5.000 6.540

54

b. Ogee Profile: The lower nappe elevation is found as follows (Figure 5.6):

85.185.0

00.5hy x

(5.4)

Figure 5.6. Ogee Profile

5.2.7. Static Calculations of Weirs

5.2.7.1. Acting Forces:

a. Main Forces: Hydrostatic force at maximum swelling level, own weight of the weir and uplift force.

b. Secondary Forces: Downstream water force, earthquake force, ice pressure, soil pressure, dynamic force

of water passing over sluice.

5.2.7.2. Investigations:

a. Tilting: The ratio of resisting moments (Mr) to overturning moments (Mo) should be at least 1.5.

b. Body Slip: The ratio of net horizontal forces (H) to net vertical forces (weight-lift = G-U) should be

smaller than the friction coefficient (f) between the weir body and the foundation surface. The friction

coefficients can be 0.8 for solid rock, 0.7 for cracked rock, 0.4 for gravel and coarse sandy ground, and 0.3

for sandy ground.

c. Soil Safety Stress: The maximum stress on the soil must be less than the soil safety stress (allowable

bearing value) and the minimum stress must be positive (pressure).

5.1M

M

o

r , fU-G

H,

I

My

A

N1,2 , e 1 , 02 (5.5)

In these equations, M is moment, N is normal force, A is weir base area, y = b/2, b is weir base width, I is

moment of inertia, e is soil safety stress . Apart from the body, similar investigations should be made for

the fall pool where the energy is broken.

55

5.3. MOVABLE WEIRS

5.3.1. Main Elements

Movable weirs are planned to achieve one or more of many different purposes, such as keeping the upstream

water level constant or precisely adjusting it, ensuring the passage of floating bodies, ice, sediment and flood

discharges downstream. The main structural elements of a movable weir are (Figure 5.7):

a. Gates: They are movable structural elements that undertake the function of the solid body in fixed weirs;

there are many types of gates.

b. Piers and Abutments: They are fixed structures that act as a support to the gates and service bridge and

transfer their loads to the ground. Their height is approximately twice the height of the gate.

a. General View

56

b. Main Elements

Figure 5.7. Movable Weir

c. Fall Bed (Apron): A protective layer of stone or riprap at the downstream of gates to break the water

energy and to protect soil from scouring.

d. Sealing Structures: Structures to prevent water transmission from bed, such as cutoff wall and sheet pile.

5.3.2. Piers

Piers (middle columns), which are one of the most important structural elements of mobile weirs; undertake

important tasks such as supporting the gates, transferring the gate loads to the soil and carrying the

mechanisms that move the gates. The minimum height of the piers legs is found by adding 0.5-1.0 m of

safety (air) margin to the maximum swelling height. The pier width is largely dependent on the type of the

gate, with a minimum width of 2 m and a maximum width of 6-7 m.

The gap between the piers is closely related to the gate sizes. The largest gap is selected considering the gate

type and the bearing capacity of the foundation. Since the upstream end (nose) of the piers will meet the

water, it is designed to show minimum resistance against flow. Usually it is made in the form of a

combination of circle or circle parts. In case of large flow velocities between piers, it is necessary to cover

with hard stones to prevent the concrete on the pier surface from erosion.

The main vertical forces affecting the piers are the weight of the pier, the weight of the mechanism that

moves the gate, the weight of the gate, the weight of the service bridge and the ground water pressure. The

main forces acting in the horizontal direction are the water pressure, ice and wind pressure forces acting on

the gate and the pier. The greatest stresses occurring on the piers are found as:

y

y

x

x

W

M

W

M

A

N (5.6)

Where, N is total vertical forces, A is section area of pier, Mx and My are bending moments and Wx and Wy

are moment of resistance; parallel and perpendicular to the flow direction, respectively.

57

5.4. WEIR CONSTRUCTION IN PERMEABLE SOILS

5.4.1. Introduction

Leakage in the ground cause important problems in weirs, resting on permeable soils. Water leaking to the

ground causes the fine grains in the ground to be washed. Larger grains are also transported from the pores

formed by the movement of these grains. If this process continues, the ground becomes porous and small

pipes are formed. This phenomenon, called piping, affects the stability of the fall bed and therefore the weir.

Another problem that leakage causes is that it causes large ground water pressures. The large ground water

pressure requires the construction of heavier and therefore more expensive structures. The piping effect of

the leakage can be prevented by lengthening the leak path.

5.4.2. Determination of Flownet

The flows, in which at each point the rotation is zero, are called potential (irrotational) flow. All the

characteristic values of water leaking under the binding can theoretically be studied with the potential

current theory. The mathematical expressions of the current network are given by the following Laplace

Differential Equations:

02

2

2

2

yx

, 0

2

2

2

2

yx

(5.7)

Here, and ψ functions are potential and stream functions, respectively. (5.7) equation can be solved

analytically or numerically. Here, the flow net, which is one of the important application areas of the

graphical solution of the equations, will be discussed. A collection of lines consisting of flow ( ) and

equipotential ( ) lines drawn in a two-dimensional and potential flow field is called a flow net. A flow net is

drawn by trial and error to suit the boundary conditions of the problem to be solved, by paying attention to

the followings:

• The spacing of the streamlines is chosen such that equal discharge must flow between each line,

• Equipotential lines should be perpendicular to the streamw lines at each point,

• Changes in both lines must be equal, ie .

As a result, the flow net consists of approximately curved squares. With the aid of the flow net, the discharge

of water that flows under a weir (regulator), for example, can be calculated. It is considered here that the

boundary condition is the foundation of the weir, sheet pile and impermeable soil, all of them are flow lines

and equipotential lines will be perpendicular to these boundaries. The flow discharge through the unit weir

width is calculated as follows:

N

NHkq (5.8)

Where, k is the permeability coefficient of the soil, H is the water level difference between the upstream

and downstream of the weir, N is the number of flow lines and N is the number of equipotential line

intervals. The flownet under a fixed weir is presented in Figure 5.8. Flownets under a fixed weir, with sheet

piles and a movable weir are given in Figure 5.9.

58

Figure 5.8. Flownet under a Fixed Weir

a. Fixed Weir b. Movable Weir

Figure 5.9. Flownet under Weirs

5.4.3. Ground Water Pressure

Ground water pressure may be determined by means of flownet under weir. The pressure value at any point

A is calculated by (Figure 5.10):

yH

n

nP i1

(5.9)

Where, H is the difference of upstream and downstream water levels, n: The total number of gaps of the

potential lines, ni: The gap number of the point A of the potential line numbered from upstream to the

downstream, y: is the depth measured from the downstream water surface of point A.

5.4.4. Critical Leakage Length

If the flow velocity of the water leaking from the bottom of the weir rises above a certain critical value, it

causes erosion under the foundation by dragging the soil particles with it, and the ground mass on the

downstream may rise upwards and tunnel-shaped passages (water veins) may be formed due to the seepage

pressure effect. Piping that occurs in this way can be prevented by extending the leakage length. In order to

prevent piping, the minimum leakage length (L) is found with the following equation:

HCL (5.10a)

Where, C is a leakage coefficient, which depends on soil type.

59

Figure 5.10. Ground Water Pressure Distribution

Lane has found that, at the piping event, the vertical parts of the leakage line are 3 times more effective than

the horizontal parts. In the Lane method, the critical infiltration length is based on the vertical lengths itself

and one-third of the horizontal lengths as follows. Lane’s C coefficients are given in Table 5.2.

3/horizvert LLL (5.10b)

Table 5.2. Lane Coefficients (C)

SOIL TYPE C SOIL TYPE C

Very fine sand, silt 8.5 Fine sand 7.0

Medium sand 6.0 Coarse sand 5.0

Fine gravel 4.0 Medium gravel 3.5

Coarse gravel 3.0 Rock (Stone and Gravel) 2.5

Loam (Mix of sand, silt an clay) 3.0-1.6 Clay 3.0-1.6

5.4.5. Reduction of Ground Water Pressure

Main measures to reduce ground water pressure (uplift force) for weirs are (Figure 5.11):

To decrease the permeability of soil,

To increase the leakage length (cutoff wall, sheet pile, impermeable upstream cover etc.),

To decrease the difference between water levels of upstream and downstream,

To apply inverted filter at bed.

Figure 5.11. Measures to Decrease Ground Water Pressure

60

5.5. WATER INTAKE STRUCTURES

5.5.1. Description and Planning Principles

Structures that take water from water sources such as streams and reservoirs and give them to transmission

systems are called water intake structures. The following points are taken into consideration when arranging

a water intake structure:

The required amount of water should always be available.

Floods should be prevented from damaging the transmission system and other structures.

The entry of floating objects, sediment and fish into the transmission system must be prevented.

Head (energy) losses in the water intake structure should be low.

The amount of water to be taken when necessary should be able to be controlled and measured.

The operation and maintenance of the water intake structure should be easy.

5.5.2. Classification

Intake structures are classified according to various criteria:

a. Classification According to Building Status:

Direct water intake from the streambed (by gravity or a pump system)

Taking water from the stream with a relief facility (weir or dam)

b. Classification According to Flow Status:

Free surface water intakes: Taking water from the side, from the bottom and from the front,

Pressurized water intakes.

Here, information will be given only about free surface water intakes, which are common in practice.

5.5.3. Main Elements of Free Surface Intakes

The main elements of a free surface water intake structure are given in Figure 5.12.

Figure 5.12. Main Elements of Free Surface Intakes

1. Panel Wall, 2. Coarse Grid, 3. Entry Sill, 4. Settling Basin,

5. Sluiceway (Washing) Channel, 6. Fine Grid, 7. Grid Washing Platform, 8. Auxiliary Gate

61

5.6. SETTLING BASINS

5.6.1. Introduction

Entrance structures built on streams are designed to prevent sediment entering into the canal. However, no

matter how many measures are taken, it will not be possible to completely prevent sediment entering. After

the coarse-grained material has been deposited with measures such as check dams in the upper basin, settling

basins are designed to settle the remaining fine-grained sediment (Figure 5.13). They are made to protect

conveyance elements and turbines in irrigation and hydroelectric energy structures from the corrosive effect

of the sediment. In the design of settling basins, it is important to keep a certain size of sediment and it is

assumed that sediment below this size will not harm.

5.6.2. The Need for Settling Basin

Settlement is carried out on the basis of the smallest grain diameter desired to be settled. It is allowed to pass

grains smaller than 0.1-0.2 mm in hydropower plants. In drinking (potable) water plants, grains with a size

of 0.02 mm are settled. It can be more tolerant in irrigation systems. In these systems, the grain diameter to

be deposited is calculated based on the critical drag stress in the channel:

)(06.0

s

RJD (5.11)

Where, J: The slope of the conveyance channel, R: The hydraulic radius of the channel, D: The grain

diameter, s: The specific gravity of the grain, : The specific gravity of the water.

Figure 5.13. Settling Basin

In hydroelectric power plants, settling basins are designed when the amount of sediment exceeds 0.2 kg/m3,

which is thought to damage the turbines. In this case, particles that are thought to damage the turbines and

cause serious wear on the blades are quartz larger than 0.25 mm or softer particles over 0.4 mm. Angular

fine sand grains carried especially in wild (large sloped) streams cause rapid wear on the penstock and the

steel parts of the turbine. The particle size that will cause damage depends on the turbine type and the head.

Considering the economic loss that will occur in turbines and penstock under high operating velocities and

high head conditions, settling of the fine sediment particles, such as silt, becomes more important. The grain

sizes that can cause damage are given in Table 5.3.

62

Table 5.3. The Grain Sizes That Can Cause Damage, Depending on Height of Drop

HEIGHT OF

DROP (m)

GRAIN

DIAMETER (mm)

80 - 100 0.7

100 - 200 0.6

200 - 300 0.5

300 - 500 0.3

500 – 1 000 0.1

5.6.3. Planning Principles

Planning principles of a settling basin are:

There must be an entry and an exit sill with height of at least 0.5 m and 0.7 m, respectively. The

sediment accumulated in front of the exit sill should be washed and flowed to washing channel.

There must be a panel wall and grid in the entrance.

Bed slope should be between 1% and 3%.

Flow velocity in sluiceway (washing) channel should be between 3 to 8 m/s.

Second grid to trap sediment entering the settling basin and energy breaker rods to reduce turbulence and

increase settling may be placed. In order to allow the settled sediment to flow, the bottom of the basin is

tilted both vertically and horizontally. Washing channel and sliding cover are made at the outlet of the basin

and the accumulated sediment is given back to the stream bed through the washing channel. The washing

channel and the number of caps, may be more than one according to the project design, and the cells

(screens) are designed in the section (Figure 5.14). When directing water to the settling basin, to reduce the

generation of secondary flows, curbs should be avoided as much as possible. Secondary flows that will occur

when curb design cannot be avoided, causes coarse-grained sediment to enter the basin. In this case, the

coarse grained material can be cleaned with the sill and washing channel.

5.6.4. Design Principles

Settling basins are generally made by rectangle section (Figure 5.15). In this figure, B is net width of the

basin, H is depth, L is effective settling length, Q is discharge, V is mean flow velocity in the basin, W is the

fall velocity of the sediment particles, t is the time, x is horizontal and y is vertical axis. The flow discharge

is found as VBHVAQ . It is assumed that the velocity of the particle is equal to flow velocity. Sediment

particle moves by the effect of its weight in vertical axis. So, the horizontal and vertical distances of a

particle in t time are Vtx and Wty . By the geometry of the basin, the followings are written and settling

basin length are calculated as:

W

V

y

x

W

Vyx

W

VHL (5.12a)

Effect of Turbulence: If the turbulence is not significant and not considered, the basin length is raised 50%

for being safe, then the basin length is found as:

W

VHL 5.1 (5.12b)

If the effect of turbulence is important and should be taken into account, the fall velocity decreases. The

amount of decrease is calculated by:

H

VW 132.0' (5.12b)

63

In this case, the basin length is found as, by adding 20% for safety:

'2.1

WW

VHL

(5.12c)

Horizontal flow velocity (V) should be low enough to permit the sediment particles settle. The formula between

V (cm/s) and sediment diameter (D, mm) is as follows. Coefficient a is given as follows depending on D:

DaV (5.13)

D > 1 mm ia = 36 , 0.1 mm < D < 1 mm a = 44, D < 0.1 mm a = 51

In general, long and wide basins are more economical than deep basins. In hydro power plants, horizontal

flow velocities are generally between 0.4 to 0.6 m/s and basin depths are between 1.5 to 4 m. Basin width is

calculated by continuity equation.

VH

QBVBHVAQBHA , (5.14)

Figure 5.14. Plan View of Multi-Cell Settling Basin

a. Plan

b. Longitudinal Section

Figure 5.15. Design of a Settling Basin

64

EXAMPLES

Example 5.1: Determination Creager Profile:

Calculate upper and lower nappe coordinates of Creager Profile for h0= 2.5 m sluice load and for x = 0.5 m,

1.5 m, 5.0 m and 7.5 m distances and draw the profile.

Solution: x/ho = x/2.5 values are calculated for the given x values, the corresponding y/h0 values are found

by Table 5.1 by calculating 0

0

0

5.2h

yh

h

yy . For example, for x = 1.5, the elevations of lower and upper

nappe are found as:

6.05.2

5.1

0

h

x 063.06.0

00

h

y

h

x alt

myalt

158.0063.0*5.2

my

h

yüst

üst 55.1)62.0(*5.2)(620.00

Example 5.2: Determination of Ogee Profile:

Sluice load h0=1.5m, calculate lower nappe coordinates for x = 1, 2, 3, 4 and 5 m and draw the profile.

Solution:85.185.0

0 *5.0 xhy 85.1

0 354.05.1 xyh

x(m) 0.5 1.5 5.0 7.5

x/h0 0.2 0.6 2.0 3.0

y/h Lower .007 .063 1.315 3.11

Upper -.772 -0.62 .693 2.50

y(m) Lower .018 0.158 3.29 7.8

Upper -1.93 -1.55 1.73 6.25

x(m) 1 2 3 4 5

y(m) .35 1.28 2.70 4.60 6.96

65

Example 5.3: Calculations of an Irrigation Fixed Weir:

Given: Bed elevation, length and slope of conveyance channel are 600 m, 10 000 m and 0.0005 (1/2 000),

respectively. Total local losses at water intake are 0.40 m, thalweg elevation of the weir is 595 m, sluice

coefficient is 2.0, Lane coefficient is 4.0 (fine gravel), net length of the weir is 50 m, maximum, minimum

and demand discharges are 200, 30 and 10 m3/s, respectively, specific gravity of concrete is 2.4 t/m3, friction

coefficient is 0.75, Manning coefficient is 83.3, soil safety stress is 15 kg/cm2, other data are given on figure.

Find:

a. Design of conveyance channel, which side slopes are 1/1.5 and bed width is b = 4y

b. Calculate crest elevation and height of the fixed weir,

c. Make the necessary investigations (tilting, body slip and soil safety stress).

Solution:

a. İletim kanalı:

,1 2/13/2 AJRn

Q A = 4y2 + 1.5y2 = 5.5y2, U = 4y + 3.61y = 7.61y, R = A/U = 5.5y2 / 7.61y = 0.723y,

,075.15.5*0005.0*723.0012.0

110 22/13/2

myyyQQ a

b = 4*1.075 = 4.3 m, B = 4.3 + 3*1.075 = 7.525 m,

Kanal üst kotu yüksekliği: y + 0.15 (hava payı) = 1.075 + 0.15 = 1.225m.

1.5y

1.5

1 y

b=4y 1.5y

B

0.15m

66

b. Bağlama Kotları:

yüksekliğü

su

üzerindeki

Bağ

kaybı

yük

yüksekliğü

su

kanalı

isale

kotu

taban

kanalı

iletim

kotu

kret

Bağ.

.

Minimum debi için hesap yapılmalıdır, çünkü bu durumda bağlama üzerindeki su yüksekliği en az,

dolayısıyla bağlama kret kotu maksimum olur.

Q = Qmin – Qalınan = 30 – 10 = 20 m3/s, Q = CbH 3/2 20 = 2.0*50*H1.5 H = 0.34m = Hmin

Bağlama kret kotu = Kanal tab. kotu + Su yüks.+ Yersel yük kayıpl. + Sürekli yük k. - Savak yüks.

= 600 + 1.075 + 0.40 + 10 000*0.0005 - 0.34 = 606.14 m

Bağlama yüksekliği: BY= BKK – Talveg Kotu = 606.14 – 595 = 11.14 m bulunur.

c. Tahkikler:

Maksimum debi halinde taşkın olduğundan, sulama suyuna ihtiyaç yoktur; alınan debi Qa = 0’dır.

Q = Qmaks. 200 = 2*50*H3/2 H = Hmaks = 1.59 m bulunur.

Memba ve mansap su seviyeleri arasındaki fark ΔH = BY + H - Hmansap

Mak s.s. ΔH1 = 11.14 + 1.59 – 1.5 = 11.23 m

Min s.s. ΔH2 = 11.14 + 0.34 – 1.0 = 10.48m . Emniyetli tarafta kalmak için büyük değer seçilir, ΔH=11.23 m

(5.10a) Gerekli minimum (teorik) bağlama boyu Lteorik = Clane*ΔHmaks = 4*11.23 = 44.92 m ,

(5.10b) Mevcut bağlama boyu Lşekil = 1.5 + (6+8+1 )/3 + 1.5 = 8.0m

Lteorik > Lşekil → Palplanş gereklidir.

Palplanş boyu ; Lp = (Lt – Lş)/2 = (44.92 – 8 )/2 = 18.46m 18.5m.

(Su palplanş boyunu bir aşağı bir yukarı dolaşıyor, bu sebeple 2’ye bölünür.)

Bu palplanş derinliği çok büyüktür. Bu sebeple yarı boydaki palplanşı membada, yarı boydakini de mansapta

yapmak uygundur.

(Lp)memba = (Lp)mansap = Lp / 2 = 18.5 / 2 = 9.25m,

Hidrolik eğim = Birim boydaki yük kaybı J = ΔHmaks / Lt = 11.23 / 44.92 = 0.25 m/m

Stabilite hesapları sadece ana gövde için yapılacaktır.

67

1 - 4 arasında, 1m boyda 0.25 m yük kaybı vardır. Bir noktadaki net (gerçek) basınç, brüt basınçtan

(hidrostatik) yük kaybı çıkarılarak bulunur. L boyu düşeyde kendisi, yatayda 1/3’ü alınır.

Pnet = Pbrüt – hk = Pbrüt – JL = Pb – 0.25L,

1 noktasında P1brüt = 1.59 +11.14 = 12.73 m,

2 noktasında P2brüt = 1.59 + 11.14 + 1.5 + 9.25 = 23.48 m,

3 ve 4 noktalarında P3.4brüt = 1.59 + 11.14 + 1.5 = 14.23 m,

1 noktasında Pnet = P1b – 0.25L = 12.73 – 0.25*0 = 12.73m.

Nokta L JL (m) Pbrüt (m) Pnet (m)

1 0 0 12.73 12.73

2 10.75 (=1.5+9.25) 2.69 23.48 20.79

3 20 (=10.75+9.25) 5 14.23 9.23

4 22 (=20+6/3) 5.5 14.23 8.73

68

Etkiyen kuvvetler ve bu kuvvetlerin 4 noktasına göre momentleri şöyledir.

X 1= 1.59*12.64 = 20.1 t. M4 = 20.1*12.64/2 = 127 tm.

X 2= 12.642 / 2 = 79.88 t, M4 = 79.88*12.63 / 3 = 336.6 tm.

Y1 = 2*11.64*2.4 = 55.87 t, M4 = 55.87*5 = 279.4 tm

Y2 = 11.64* 4*2.4 / 2 = 55.87 t, M4 = 55.87*8/3 = 149 tm

Y3 = 6*1*2.4 = 14.4 t, M4 = 14.4*3 = 43.2 tm

U1 = 8.73*6 = 52.4 t, M4 = 52.4*3 = 157.2 tm.

U2 = 0.5*6 / 2 = 1.5 t, M4 = 1.5*4 = 6 tm.

Kayma tahkiki: ,10088.791.2021 tXXX

tUUYYYY 3.725.14.524.149.559.5521321

Kayma Faktörü: 75.038.13.72/100/ fYXFk Kaymaya Karşı Emniyetsiz.

Devrilme tahkiki: Mk = MY1+Y2+Y3 = 279.4 + 149 + 43.2 = 471.6 tm.

Md = MX1+X2+U1+U2 = 127 + 336.6 + 157.2 + 6 = 626.8 tm,

Devrilme Faktörü : Fd = Mk / Md = 471.6 / 626.8 = 0.75 < 1.5 Devrilmeye Karşı Emniyetsiz.

0.5

11.14

0.5

8.73

U2

. 4

1.59 12.64 4.0m

12.64

Y3

X1

X2

Y1

Y2

U1

2.0m

0.5

1.0

69

Gerilme Tahkiki :

O noktasına göre momentler;

,3721*5.10*4.520*4.143/1*87.552*87.556.336127 tmMo

,3.72 tUYN A = 6 x 1 = 6 m2,

,*

2,1I

yM

A

N o y = 6 / 2 = 3, I = 1 x 63 / 12 = 18 m4,

0/0.5/5018

3*372

6

3.72 22

1 cmkgmt (Çekme) Emniyetsiz.

222

2 /15/41.7/1.7418

3*372

6

3.72cmkgcmkgmt zem Emniyetli,

Sonuç: Kayma, Devrilme ve Gerilme tahkikleri sağlamadı. Beton gövdenin taban boyutları büyütülerek

(B > 6m, B 8 ~ 10 m ) hesaplar tekrar edilmelidir.

Example 5.4: Calculations of an Irrigation Fixed Weir:

Given: Qmax = 300 m3/s, Qmin = 20 m3/s, Qdemand = 10 m3/s, Csluice = 2.0, CLane = 3.0, bed elevation of the

conveyance channel entry is 10 m, its slope is 0.0003, soil safety stress is 45 t/m2, ,/4.2 3mtb f = 0.6,

weir net length is 50 m, k = 1/n = 62, trapezoidal conveyance channel, bed width is 4 m and side slopes are

1/1.5, total local and friction energy losses are 0.15 m.

Find: a. Design of conveyance channel,

b. Calculate crest elevation and height of the fixed weir,

c. Make the necessary investigations.

1m

Qmaks.

1.2m

1.0m

8.0m

1.0m

Qmin.

8m 12m

1m

3.01m

70

Solution:

b. Q = Qmin – Qa = 20 – 10 = 10 m3/s , Q = CLH 3/2 10 = 2.0*50*H1.5 H = 0.22 m = Hmin

BKK = Kanal Taban Kotu + y + hk - H = 10 + 1.5 + 0.15– 0.22 = 11.43 m olur.

Bağlama yüksekliği: BY= BKK – Talveg Kotu = 11.43 – 8 = 3.43 m bulunur.

c) Q = Qmaks. 300 = 2*50*Hmax3/2 Hmaks = 2.08 m bulunur. Q=Qmaks. ΔH = 3.43 + 2.08 – 3.01 = 2.5 m,

Q = Qmin. ΔH = 3.43 + 0.22 – 1.2 = 2.45 m büyük olan değer seçilir. ΔH = (ΔH )maks = 2.5m,

Lteorik = CLane*ΔHmax=3*2.5 = 7.5 m , Lşekil = 1.0+(8 + 12 )/3 + 1.0 = 8.67m > Lt = 7.5 m Palplanş Gerekmez.

J = ΔH / L 2.5 / 8.67 = 0.288 m/m Birim boydaki yük kaybı. Gerçek (net) basınç = Brüt basınç – Yük

kaybı Pnet = Pbrüt – JL , L = Ld + Ly/3, Pb = h ( Hidrostatik Basınç )

Etkiyen kuvvetler ve bu kuvvetlerin A ve O noktasına göre momentleri şöyledir.

X 1= 2.08 x 4.43 = 9.21 t. MA = MO = 9.21 X 4.43/2 = 20.41 tm.

X 2= 4.432 / 2 = 9.81 t, MA = MO = 9.81 x 4.43 / 3 = 14.49 tm.

Y1 = 1 x 4.43 x 2.4 = 10.63 t, MA = 10.63 x 7.5 = 79.73 tm, MO = 10.63 x 3.5 = 37.205 tm,

Y2 = 4.43 x 7 x 2.4 / 2 = 37.212 t, MA = 7.212 x7x 2/3 = 173.66 tm, MO = 24.83 tm,

U1 = 5.45 x 8 = 43.6 t, MA = 43.6 X 4 = 174.47 tm, MO = 0,

U2 = 0.5 x 0.77 x 8 = 3.08 t, MA = 3.08 X 8 x 2/3 = 16.43 tm, MO = 4.11 tm.

Kayma tahkiki: ,02.1981.921.921 tXXX tUUYYY 16.108.36.43212.3763.102121

Kayma Faktörü: 60.04.1616.1/02.19/ fYXFk Kaymaya Karşı Emniyetsiz

Devrilme tahkiki: Mk=MY1+Y2=79.73+173.66 = 253.39 tm. Md = MX1+X2+U1+U2 =20.4+14.49+174.47+16.43 =

225.79tm,

Devrilme Faktörü : Fd = Mk / Md = 253.39 / 225.79 = 1.12 < 1.5 Devrilmeye Karşı Emniyetsiz.

1.5y

1.5

1 y

4 1.5y

Q = Qa = 10 m3/s = 62*( 0.0003)1/2*R2/3*A

A = 4y + 1.5y2, U = 4 + 3.606y, R = A / U,

10 = 1.0739*(4y+1.5y2)*

3/22

606.34

5.14

y

yy

Deneme-yanılma ile y = 1.5 m bulunur.

Deneme-yanılma ile y = 1.5m bulunur.

71

Gerilme Tahkiki :

,025.2311.483.24205.3749.1441.20 tmM o MO = 23.025 tm,

↓ ,16.1 tUYN A = 8 x 1 = 8 m2, y = 8 / 2 = 4, I = 1 x 83 / 12 = 42.67 m4,

,2,1I

yM

A

N o 0/013.267.42

4025.23

8

16.1 2

1

mt (Çekme) Emniyetsiz.

22

2 /45/30.267.42

4025.23

8

16.1mtmt zem

Emniyetli.

Sonuç: Zemin emniyet gerilmesi sağlıyor. Kayma, Devrilme sağlamıyor. Zeminde çekme gerilmesi oluyor.

Beton gövdenin taban boyutları büyütülerek (B > 8 m, B 12 ~ 130 m ) hesaplar tekrar edilmelidir.

.O 1m

0.77

5.45

U2

.O .A

2.08 4.43 7.0m

4.43 X1

X2

Y1

Y2

U1

1.0m

4m 3

Nokta L(m) JL Pb(m) PN(m)

1 0 0 5.51 5.51

2 1 0.288 6.51 6.22

3 3.67 1.056 6.51 5.45

2.08

3

1

2

1.5m

3.43

L = 8m

8m

72

Example 5.5: Calculations of an Irrigation Fixed Weir:

Given: Qmax = 85 m3/s, Qmin = 8 m3/s, Qdemand = 3 m3/s, Csluice= 1.75, CLane= 3.0, water surface elevation at the

entrance (beginning) of the conveyance channel is 100 m, weir thalweg elevation is 96 m, weir net length is

20 m, γconcrete = 2.4 t/m3, total energy losses are 1.0 m, friction coefficient is 0.70, soil safety stress is 30 t/m2.

Find: Calculate the weir height and make the necessary investigations.

Solution:

Q=Qmin = 8-3 = 5 m3/sn = 1.75*20*Hmin1.5 Hmin= 0.27 m bulunur.

Bağlama kret kotu = 100 + 1 -0.27 = 100.73 m olur.

Bağlama yüksekliği = 100.73 – 96 = 4.73 m bulunur.

Q=Qmaks = 85 m3/sn = 1.75*20*Hmaks1.5 Hmaks= 1.817 m bulunur.

Q=Qmaks H= 4.73+ 1.81 – 1 – 2 = 3.54 m, Q = Qmin H= 4.73+ 0.27 – 1 – 0.4 = 3.6 m,

büyük olan seçilir H = 3.6 m.

Lteorik=3.*3.6 = 10.8 m, Lşekil = (5+10)/3 + 1 = 6 m, Lt>Lş

Palplanş Gereklidir. Lp = (10.8 – 6)/2 = 2.4 m,

Birim boydaki yük kaybı J = H /L = 3.6/10.8 = 0.333 olur.

Bir noktadaki brüt basınç Pb = hidrostatik basınç = h,

net basınç ise brüt basınç – yük kaybı = Pn=Pb - JL şeklinde bulunur.

NOKTA Pb L

(m)

JL

(m)

Pn

(m)

1 6.54 4.8 1.6 4.94

2 6.54 6.47 2.16 4.38

73

Her kuvvetin büyüklüğü, A ve O noktalarına uzaklığı ve momenti hesaplanıp aşağıda sunulmuştur:

KUVVET BÜYÜKL.

(t)

A’YA

UZ. (m)

MA (tm) O’YA

UZ. (m)

MO (tm)

X1 8.56 2.365 20.24 2.365 20.24

X2 11.19 1.58 17.64 1.58 17.64

Y1 17.03 4.25 72.37 1.75 29.80

Y2 19.87 2.33 46.36 0.167 3.31

U1 21.9 2.5 54.75 0 0

U2 1.4 3.33 4.67 0.833 1.17

KAYMA TAHKİKİ: Y = 17.03 + 19.87 – 21.9 – 1.4 = 13.6 t, X = 8.56 + 11.19 = 19.75 t

70.045.16.13/75.19/ YX KAYMAYA KARŞI EMNİYETSİZDİR

DEVRİLME TAHKİKİ: tmM K 73.11836.4637.72 , tmM D 3.9767.475.5464.1724.20

5.122.13.97/73.118/ DK MM DEVRİLMEYE KARŞI EMNİYETSİZDİR

GERİLME TAHKİKİ:

tmMO 56.1217.131.38.2964.1724.20 , A = 5 m2, I = 1*53/12 = 10.42 m4, y=5/2 = 2.5 m

N = 13.6 t, 2

2

2

11,2 /73.5,/29.042.10

5.2*56.12

5

6.13mtmt

I

My

A

N

01 ÇEKME GERİLMESİ VAR EMNİYETSİZDİR , 2

,2 /30 mtEMZ EMNİYETLİDİR.

74

Example 5.6: Determination of Minimum Particle Diameter to be Settled for Irrigation:

Given: Parameters of trapezoidal concrete conveyance channel: Bed slope 0.0003, discharge 2.5 m3/s, side

slopes 1/2, bed width 1.4 m, k = 62.5 (n=1/62.5 = 0.016), specific gravity of the particles is 2.6 t/m3.

Find: Particle diameter to be settled.

Solution:

Example 5.7: Design of Settling Basin without Considering (Omitting) Turbulence Effect:

Given: Particle diameter to be settled is 0.5 mm, its fall velocity is 100 m/hour, discharge is 8 m3/s, basin

width is 15 m.

Find: Depth and length of the settling basin, omitting the turbulence effect.

Solution:

75

Example 5.8: Design of Three- Cells Settling Basin by Considering (Not Omitting) Turbulence Effect:

Given: Particle diameter to be settled is 0.09 mm, its fall velocity is 2 cm/s, discharge is 6 m3/s, basin will be

planned as 3 cells (screens), the thickness of the walls between cells is 0.35 m, basin depth is 2.0 m.

Find: Width and length of the settling basin and draw the cross section of the basin.

Solution:

76

Example 5.9: Design of a Settling Basin by Considering (not Omitting) Turbulence Effect:

Given: Particle diameter is 0.15 mm, its fall velocity is 2.3 cm/s, discharge is 8 m3/s, basin depth is 2.5 m.

Find: Width and length of the settling basin.

Solution: