Assessment of Hydroelecric Potentials of Owu and Ero-omola ...

ASSESSMENT OF HYDROELECTRIC

POTENTIALS AT THE OWU AND ERO-OMOLA

FALLS IN KWARA STATE

B. F. Sule

K. M. Lawal

K. A. Adeniran

TECHNICAL REPORT

NO. 7

ISBN: 978-978-915-055-7

MAY, 2011

NATIONAL CENTRE FOR HYDROPOWER RESEARCH AND DEVELOPMENT

ENERGY COMMISSION OF NIGERIA UNIVERSITY OF ILORIN, ILORIN, NIGERIA

Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria

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TABLE OF CONTENTS

1. EXECUTIVE SUMMARY 3

CHAPTER ONE

1.0 Introduction 5

1.1 General Introduction 5

1.2 Sources of Energy 6

1.3 Statement of Problem 6

1.4 Why Small Hydro 7

1.5 Aim of the Study 7

1.6 Objective of the Study 7

1.7 Physical Characteristics and Description of the Study Areas 7

1.8 Demographic Data 8

2. CHAPTER TWO

2.0 Theory of Hydropower Generation 10

2.1 Energy Production 11

2.2 Hydropower System 14

3. CHAPTER THREE

3.0 Study Approach and Technology 14

3.1 Data Collection 14

3.2 Determination of Energy Demand 14

3.3 River Stage Measurement 16

3.4 Measurement of Discharge 16

4. CHAPTER FOUR

4.0 Field Output and Data Analysis 17

4.1 Introduction 17

4.2 Instrumentation Details 17

4.3 Stream Discharge 19

4.4 Development of a Monthly Flood Rating Curve 19

4.5 Extension of Streamflow Data at Ero-omola Fall 23

4.6 Model Development 25

4.7 Determination of the Required Reservoir Capacity 28

4.8 Evaluation of Sediment Load or Sediment transport 29

5. CHAPTER FIVE

5.0 Potential Energy Assessment 31

5.1 Potential Energy Assessment of Ero-omola Fall 31

5.2 Potential Energy Assessment of Owu Fall 33

5.3 Hydropower Power Demand 34

6. CHAPTER SIX

6.0 Financial Justification 35

6.1 Introduction 35

6.2 Engineering Economics 35

6.3 Economics Analysis 35

6.4 Cost of Generation Per Kilowatt 36

6.5 Internal Rate of Return 36

6.6 Amortization Analysis 36

7. APPENDIX 1 40

APPENDIX 2 41

APPENDIX 3 48

APPENDIX 4 49

APPENDIX 5 55

APPENDIX 6 56

APPENDIX 7 57

APPENDIX 8 58

APPENDIX 9 59

APPENDIX 10 60

APPENDIX 11 61

8. REFERENCES 61


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EXECUTIVE SUMMARY

1. General

The study for the assessment of potential hydropower development of Owu and Ero-omola Falls

commenced effectively by 20th

of June, 2009. Various site visits were undertaken to facilitate

gauge installation and hydraulic head survey. Gauge readers were recruited to monitor gauges,

with provision of a motorbike for the gauge reader at Owu Fall, due to long distance of site from

urban centre. Gauge readers were effectively engaged by 26th

of November, 2009 and have since

continued to monitor the gauge till date. Signboards were installed to indicate ownership of the

measuring instrument at both sites. Ero-Omola has recorded about 450 days (15 months) of

records while Owu Fall has about 217 days (7months) of records. The fewer months of records

were due to conflict between the gauges readers employed for the site. Discharge measurement

from both sites were evaluated to generate the discharge rating curves on excel programme and to

establish the minimum and the maximum water level.

2. Discharge Computation Method

There are different methods of determining river discharge. The choice of computation methods

depends upon the equipment and observational method used during the gauging, flow conditions

at the time of gauging, type of stream and the accuracy required. The arithmetic method is

preferred, because it offers sufficient accuracy and quicker to perform than other methods. For

the purpose of this report the Mean Section Method was utilized to evaluate the discharge. The

raw data is presented in the annexure to this report.

3. Hydropower Potential

a. Owu Fall with a hydraulic head of 95.5m has a potential hydro capacity of 8.81MW and annual

generating capacity of 15425.12MWh. The minimum flow available for about 100% of the time

from the flow duration curve is estimated at 9.9m3/s. Therefore a single pelton turbine is

recommended. The total amount of energy so generated can be sold to National grid is estimated

at N216,091,680.00 at N14.00/kWh. The internal rate of return was however negative. Owu Fall

has a difficult terrain with relatively low runoff but consistent runoff yield. It is therefore suitable

for only runoff river system as it is practically difficult to impound water behind the Fall. More so

the distance to the 33kva National Grid at Omu Aran is about 189km, while that of Ero-Omola is

just 48km.

b. Ero-Omola Fall with an averages discharge of 22.8m3/s and a hydraulic head of 59.4m has a

potential hydropower capacity of 8.64MW. The 100% flow rate from Ero-Omola may be

bifurcated by 3 unit draft tube into the turbines at 7m3/s each. The total annual energy was

estimated at 15137.28MWh at an economics cost of N211,921,820.00/annum using the NIPP

multi-year tariff order of N14.00/Kwh. The total amount derivable from the power generation

excluding other charges amount to about N213million with an internal rate of return (IRR) of

18.00%. This IRR although lower than the prevailing interest rate of 21% is still acceptable on the

premise that, the present commercial interest rate in Nigeria is relatively high. Ero-Omola water


Page 4

year is between April to March with a two to three month break of hydrological cycle. It is

therefore necessary to provide a reservoir, sufficient enough to regulate flow for the turbines and

to provide domestic and irrigation water supply to the host communities downstream. This off

course is an additional cost to the investor. The benefit/cost ratio is however encouraging.

4. Constraints

The Centre must collaborate with State Government to see that the only access roads to Owu Fall

are rehabilitated. The deplorable condition of the road makes it un-passable during the rainy

season and make site visit difficult. The present security situation of Owu site does not encourage

installations of expensive instrument for now, due to constant vandalization, removal or theft.

5. Financial Positions

The total budgetary provision for the two sites would have been draw down completely by the end

of April 2011. It is therefore important to provide fund for the salary and wages of the gauge

readers beginning from May 2011. The budgetary provision for the two site is estimated at

N650,000.00 each, bringing the total sum required annually to about N1,300,000.00(this includes

salary and wages of gauge readers, fuelling of motorbikes, instrument maintenance, site visits

etc.). This request becomes necessary if the centre is to continue to sustain continuous and

uninterrupted data acquisition of both sites.

6. Recommendations

a. The next phase of this study is to provide detail topography of the site and to locate position of

power house, fore bay, penstocks with detail engineering drawing and subject the overall cost to

economic analysis.

b. Thereafter this report will be publicly presented to provide the necessary information to investors

to appraise and executes the project.

c. An automatic data logger should be provided at Ero-omola. This is to minimize research cost and

expenditure on data acquisition. Self-recording gauges that maintain a continuous record of stage

are based on various types of sensors. The three most commonly used types of sensors are float-

driven, pressure, and ultrasonic. In a typical installation of a float-driven, water-level sensor, the

vertical movement of a float in a stilling basin, resulting from fluctuations in water level, is

translated by a mechanical movement or an electronic signal. Ultrasonic sensors use acoustic

pulses to sense water levels either by contact or noncontact methods. Stage-discharge relations

may have to be periodically updated due to changes in the hydraulic characteristics of a stream

reach over time, caused by erosion and sedimentation, bank vegetation, and other changes. It is

therefore extremely important to make provision for continuous regular site visits, whenever the

need arises.


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CHAPTER ONE

1.0 INTRODUCTION

1.1 General Introduction

Power is a very important infrastructural development of a nation. It is widely believed that

an appropriate level of energy generation has always gone hand in hand with industrialization

and economic development. Similarly a functional energy generation system often serves as

an effective tool for National Economic Development. The need for comprehensive studies of

hydropower operation of large water resources system is increasing at rapid pace because of

the increasing interest in all facets of resources use and management. Complexity of water

resource planning, design and operations studies, demand for a mathematical procedure that

will select the optimum sizes and characteristics of components to produce a desired result.

Many failures of water related projects are due to project planning on the basis of inadequate

hydrological data, due in part to two factors:

a. Data which are not accurately measured

b. Too short time series of hydrological data not allowing reliable estimates of system

performance

In the later case some scientist suggests the postponement of the project until more reliable and

accurate data are available. Although this suggestion is theoretically sound, it however lacks the

requirement and needs of engineering practice. A better way to solving the problem may be the

use of hydrological data from synoptic station within the same catchment which in combination

with available hydrological data may improve the planning results. This is the basis of the

stochastic theory approach utilized to extend flood data. The purpose of this research is to

demonstrate the value of such deficit data in the optimization process of hydropower

development. Inadequate hydrological data may lead to over or under design of the power plant.

Stochastic theory is applied in order to minimize the risk of such uncertainties. The stochastic

theory provides opportunity to forecast and extend short duration data in a planning process.

In this context we have to distinguish between two types of hydrological uncertainty.

a. The natural uncertainty due to random variation of hydro meteorological processes;

b. If hydro-power project are planned and designed on the basis of rather short time series of

observed hydrological data the danger of inaccurate solutions is high.

1.2 Sources of Energy

The three most important sources, which have become common and therefore referred to as

conventional, are:

(i) Thermal power (ii) Hydro-power (iii) Nuclear power

The other sources of power generation are also valuable but the quantum of power produced

by these sources is limited. Such other sources are: (i) Tidal power (ii) Solar energy (iii)


Page 6

Geo-thermal energy (iv) Wind power (v) Magneto-hydro-dynamic plants and (VI) Biomass

Energy

The focus of this research was limited to design of potentials hydropower generation only.

Table 1.1, 1.2 and shows the status of hydropower generation and Electricity demand

Scenarios in Nigeria.

Table 1.1: Status of Hydropower Generation in Nigeria (Install Capacity)

Year Generation Capacity Actual

generation(Peak)

Losses

2005 5,880 MW 2,500 MW 57%

2009

2009(NIPP)

6,021 MW

6,814 MW

3,700 MW

----------

38%

--------

2011 (P) 11,000 MW ????

Source:Energy Commission of Nigeria

Table 1.2 Nigeria Electricity Demand Scenarios

Scenarios Demand MW

Period 2010 2015 2020 2025 2030

Reference (7%) 15,730 28,360 50,820 77,450 119,200

High Reference (10%) 15,920 30,210 58,180 107,220 192,000

Optimistic (11.5%) 16,000 31,240 70,760 137,370 250,000

Source: Energy Commission of Nigeria (2006)

1.3 Statement of Problem

Fresh water supplies, energy and environmental preservation are three of the most pressing

issues facing humanity. In Nigeria poor planning and under investment had created a huge

generation and supply deficit over time, despite improved routine maintenance for the

existing hydro infrastructures. There is a heavy reliance on public electricity supply while

demand for electricity keeps outstripping supply. The response to address irregular public

power generation and transmission failure was the importation of various brands of gasoline

generators into the country to augment supply, it is however obvious that a new approach and

fresh initiatives to development of energy producing resources and the implementation of

developmental plans has to be accelerated, if vision 2020 target is to be met.

1.4 Why Small Hydro

Hydroelectricity enjoys several advantages over most other sources of electrical power. These

include high levels of reliability, proven technology, high efficiency, very low operating and

maintenance cost, and the ability to easily adjust to load fluctuations. Hydropower project

often provide flood control and recreational benefits. Hydropower does not produce waste


Page 7

products that contribute to air quality problems, acid rain, and green house gases; it is a

renewable resource that minimizes the use of other fuels (oil, gas and coal).

Poverty in Nigeria is associated with high unemployment, poor governance, corruption, lack

of accountability, and gross violation of human rights, nepotism and a skewed income

inordinate distribution. Additional factors include poor infrastructure and impaired access to

productive and financial assets by women and vulnerable groups. In the framework of the

Millennium Development Goals Report, the latest estimates revealed that over 70% of the

population lives below the International income poverty line of $1 a day. (World Bank, 2007)

A common belief is that guaranteeing a sustainable supply of affordable energy is one of the

best ways to address poverty, inequality and environmental degradation everywhere on the

planet. However, energy cannot be affordable unless its production and availability are

sustainable. Increasingly, energy sustainability amongst others also means: connecting the

entire urban and rural poor to reliable, sustainable economical sources of energy. This way we

can guarantee improved living standard for a better quality of life. (World Bank, 2007)

It is in response to these challenges, that the study was initiated

1.5 Aim of the Study

The main purpose of this study is to establish, explore and optimize the hydropower potentials

of Owu and Ero-omola Falls for the use of the rural communities.

1.6 Objectives of the Study

In achieving the main aim stated above, the following objectives are covered.

a. Installation of hydrologic instruments for data collection.

b. Collection of hydrologic data and topographical maps of the two sites and adjoining

catchments.

c. Rainfall and run-off data studies.

d. Development of flood duration curve.

e. Estimation of energy generation potential with the runoff.

f. Determination of potential hydropower generation capacity of Owu Falls.

g. Economic analysis and financial assessment of both hydropower projects.

1.7 Physical Characteristics and Description of the study Areas:

Owu Fall is located at Owa Kajola in Ifelodun LGA of Kwara State near Oro-Ago about

127km from Ilorin, the state capital (figure 1 shows the LGAs of Kwara State). The run-off is

perennial from a hill of about 95.5 m high. Owu Fall lies between Latitude North N08 20 ׳

23.2״ and N08° 2023.1 ׳

״ and between Longitude East E005° 08

׳ 34.8

״and E005° 08

׳34.7

״.


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The rainfall is moderate with general annual average of about 1,250mm with maximum

rainfall occurring in the months of June and August and a low humidity of about 50%. The

Ero-Omola Fall is located along Osi- Isolo-Ajuba Road off Osi-Idofin road in Ekiti LGA,

(Araromi-Opin) about 116 km from Ilorin. The runoff is perennial and of higher unit

discharge than Owu-Falls. The height of the Fall is about 59.4m high. The catchment area of

Ero-omola Fall is about 45km2 with contribution from two rivers namely, Ero-river from

Iddo- Faboro near Ifaki in Ekiti state and Odo-Otun from Ajuba itself. Ero-Omola Falls lies

between Latitude North N08° 09 ׳34.6

״and N08°09

׳ 30.8

״ and between Longitude East E005°

14 ׳07.4

״ and E005° 14

׳ 06.7

״.

1.8 Demographic Data

Population is a major driver of energy demand. The most important determinant of energy

demand is the level of economic activity and its structure, measured by the Gross Domestic

Product (GDP). The evolution of the GDP was guided by the projections assumed in the

National Economic Empowerment and Development Strategy (NEEDS). The local

government areas within the catchment areas of the proposed project are listed in Table 1.4

along with other LGAs in Kwara State.

Table 1.3: Population of Kwara State (NPC, 2006)

LGAs MALES FEMALES POPULATION

Baruten

Kaiama

Moro

Edu

Pategi

*Ifelodun

Ilorin South

Ilorin East

Ilorin West

Asa

Oyun

Offa

*Irepodun

*Isin

*Oke-Ero

*Ekiti

Total

*Study Areas

108153

68240

55630

104944

62639

106056

104504

104402

181875

64982

48601

46266

75539

30833

29515

28402

1220581

101306

55924

53162

96525

49678

99986

104187

99908

182791

61453

45652

43408

73071

28905

28104

26448

1150508

209459

124164

108792

201469

112317

206042

208691

204310

364666

126435

94253

89674

148610

59738

57619

54850

2371089


Page 9

Fig. 1:Map of Kwara State showing Local Government Areas. Owu and Ero-Omola Falls are located

in Ifelodun and Ekiti LGAs.


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CHAPTER TWO

2.0 THEORY OF POWER GENERATION

2.1 Energy Production

Hydroelectric power production from a given reservoir at any time, t depends on the installed

capacity of the turbine (generators), turbine release, generating head, the number of hours of

power generation in a period, the plant factor, the efficiency of the turbine. In hydropower,

the potential energy of the Falling water is converted to mechanical energy which is used in

rotating the turbine.

The Potential energy is given as: (Loucks et al, 1981).

PE= mgh (2.1)

where m =is the mass of the Falling water

g =is the acceleration due to gravity

h =is the Falling head

A cubic meter of water, weighing 103 kg, accelerating at a rate of 9.81m/s

2 over a distance of

one meter, results in 9.81 x 103 joules (Newton-meter) of work. The work done in one second

equals (joules per second) is of power produced in watts. Hence an average flow of tqˆ (m3/s)

Falling a height of Ht (m) in period t yields 9.81 x 103 tqˆ Ht watts or 9.81 tqˆ Ht Kilowatts.

Multiplying by the number of hours in period t yields the kilowatt-hours of energy produced

from an average flow of tqˆ in period t. The total kilowatt-hours of energy KWHt produced in

period t, assuming 100% efficiency is (Sharma, 1979)

E=KWHt =9.81 qˆ H(seconds in period t) (2.2)

3.6 x 103

Since the total flow qt in period t, in units of 106 m

3, equals the average flow rate tqˆ (m

3/s)

times the number of seconds in the period divided by 106, the total kilowatt-hours of energy

produced in period t given a plant efficiency of e is equals

E = KWHt = 2730qtHt (2.3)

Equation (2.3) implies that the kilowatt-hours of energy KWHt produced in period t, are

proportional to the product of the plant efficiency, the productive storage head Ht and the

flow qt through the turbine. The amount of electrical energy produced also depends on the

installed kilowatts of plant capacity P as well as on the plant factor Ft. The plant factor is a

measure of hydroelectric power plant use and is usually dictated by the characteristics of the

power system supply and demand.


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The plant factor F is given as: Ft =Average load on the plan(2.4)

Installed plant capacity

The plant factor accounts for the variability in the flow rate during each period t and this

variability is pre specified by those responsible for energy production and distribution. It may

or may not vary for different period’s t. The total energy produced cannot exceed the product

of the plant factor Ft, the number of hours in the period ht and the plant capacity P, measured

in kilowatts.

KWH = ft ht P (2.5)

FIRM ENERGY = Pdesign x x 24 x 365 kWh (2.6)

= 0.2 (A reduction factor due to streamflow fluctuations)

2.2 Hydropower system.

2.2.1 The major types of hydroelectric power development are (Sharma, 1979):

a. Run-of river development

The runoff river plant are such plant that do not substantially alter the flow regime of the

river, this implies that the river is not diverted materially away from its natural course, since

no impoundment is envisaged.

b. Pondage development (Dam toe based)

Pondage developments are reservoirs developed to provides uninterrupted or balance inflow

for day to day fluctuations in the amount of inflow available for power productions. Most

often the power plant is located at the dam toe.

c. Storage development is similar to pondage development as described above.

d. Regulating development (canal Fall based)

This are the hydropower plant fed through a regulated outlet from the reservoir.

e. Pumped storage development (diversion)

The pumped storage plant as the name implies are those plants whose inflow for power

generation is augmented through a system of pumping unit.

Regulating development is proposed at Ero-omola Fall, while Owu Fall is suitable for Runoff

River plant. The proposed typical schematic design diagram for the two sites is as shown in

Figure 2.1 and 2.2: The major components in the scheme are:

a) Gross head (H). The gross head is the difference of the water level in the head race and the

water level in the tail race.( for a run-off river plant)

b) Net Head (h). The net head (or effective head) is the head available for the turbine. It is equal

to the difference of total head at the point of entry and at the point of exit of the turbine.


Page 12

i. For a pelton wheel or impulse turbine,

h=H –Z –hf (2.7)

Where:

H =gross head (m)

Z= is the height of the pelton wheel exit above the tail race level and hf= is the loss of

head in the penstock.

ii. For a reaction turbine. h=H-(Vd)2

- hf(2.8)

2g-

Where Vd = is the exit velocity and other terms are as defined above.

c) Operating Head. The operating head is equal to the difference of the

water level in the forebay (or foreway) and that in the tail race.

FIGURE 2.1: OWU FALL


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FIGURE 2.2: ERO-OMOLA FALL


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CHAPTER THREE

3.0 STUDY APPROACH AND METHODOLOGY

3.1 Data Collection

Topographical map, Stream flow, hydraulic head and pipeline length must be estimated or

measured, before one can calculate the power that could be developed from a stream. Stream

flow is the most difficult to measure or estimate. Understanding of its sources, its fluctuations

and flow measurements is important.

3.2 Determination of Energy Demand

A constant monthly energy demand is defined from an assumed installed capacity and chosen

plant factor. The monthly energy demand as follows:

FE (t) = IC * n hours * PF(t) (3.1)

Where FE (t) is the target monthly firm energy demand (MWh) and other variables are

previously defined.

IC=installed capacity MW

N =no of operating hours

PF=Plant factor

Monthly firm energy demand was computed from the above equation: Owu Fall with installed

capacity of 8.81MW over assumed 8 hours of operation and plant factor of 0.25 is estimated

at 17.62MWh or 211.14MWh/annum, while Ero-omola Fall with installed capacity of

19.93MW over an assumed 8 hours of operations and plant factor of 0.25 is estimated at

39.86MWh or 478.32MWh/annum.

a) Population Estimate

Population is a major driver of energy demand. From the demographic data, the projected

population figure was deployed in the estimation of energy demand of the communities.

The project catchment areas comprises of about five local government areas namely;

Ekiti,Oke-ero, Isin, Irepodun, and Ifelodun LGAs with a combined population of 526,859

by the 2006 population census. This is projected to 2036 at a National population growth

rate of 2.83% and in consideration of 25 years life span of the proposed project. The

projection was achieved with the relation:

Pn =Po (1 + r)n (3.2)

526,859 X (1.0283)25

= 1,058,499


Page 15

b.) Electricity Demand per Capital

The electricity demand per capital of 321.59Kwh published by Energy Commission

of Nigeria (2006) was adopted for this study.

c.) Peak Domestic Electric Load demand

Using the annual electric energy demand, load factor of 0.75, transmission and

distribution losses; approximate estimates of the peak load demand was obtained. The

highest growth scenarios gives a peak demand 0f 3157MW.(NERC, 2009)

d.) Projected Electricity Demand

In accordance with the National Energy Policy (2003), access to electricity by

household is expected to increase to 75% by year 2020 for urban centre while that of

rural was put at 55%. This study assumed an average projected electricity demand of

the community to grow by about 55% due to development of many small agro

businesses within the project area.

3.3 River Stage Measurement

The river stage is the height of the water surface above the mean sea level (msl). For

convenience, the datum was arbitrarily selected at the lowest point on the river bed. The river

stage was measured to compute the cross-sectional area of the river so that the discharge can

be determined using the OTT current metre obtained from Lower Niger River basin

Development Authority.

3.4 Measurement of Discharge

A river discharge is the rate at which water flows through a cross section and is expressed as

volume per unit time.

The following methods are commonly used for the measurement of discharge in a river.

1. Area-velocity method 2. Slope-area method

3. Salt-concentration 4. Moving-boat method

5. Electromagnetic and ultrasonic 6. Indirect methods

A relationship between stage and discharge is required to convert stage measurements to flow

rates. Measurements of head were converted to flow rates. In this report the velocity-area

method was used for measuring the discharge of both sites.

3.4.1 In this method, the discharge is determined from the area of cross section and the mean

velocity. The area of cross section of the stream is determined from the profile of the stream

bed obtained by survey.(Appendix 1) The river cross section was divided in to a suitable

number of vertical segments (or strips).About 10 segments were taken in the case of Owu,

while Ero-omola had about 15 segments. The total discharge in the river is the total sum of


Page 16

various segments. The discharge in each segment is equal to the area of the segment

multiplied by the mean velocity of flow. The mean section method was used to estimate the

discharge, in this method; the segment is taken between two vertical lines on which the

velocity and depth are measured. The velocity in the segment is taken as the average of the

mean velocities V1and V2 determined at the two adjacent verticals. Similarly the depth is also

taken as the average of two depth d1and d2. Thus the discharge in the segment is given by

∆𝑄 = 𝑏 𝑑1+ 𝑑2

2

𝑉1+ 𝑉2

2 (3.3)

𝑇𝑜𝑡𝑎𝑙𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 𝑄 = 𝑄 (3.4)

3.4.2 Determination of Velocity (V): For the measurement of discharge, the mean velocity (V) is

required at various vertical lines as stated above. The following methods were used for the

sites.

1. Floats Method

2. Current Meter Method

both float and current metre method was undertaken on the field for accuracy checks.

a.) Floats method: In this method, a straight and uniform reach of the river was selected for the

float to travel. The time t taken by a float to travel a certain distance L is measured. There are three types of floats commonly used in practice. (i) Surface floats, (ii) Double floats (iii) Velocity rods. The

study adopted surface floats. The surface floats are generally made of wood (or any other light

material) so that they can float. Wooden discs of 7 – 15 cm diameters were used. As the surface floats travel at the water surface, they give the surface velocity. The mean velocity is usually taken as 0.85

times the surface velocity.

b.) Current Meter

A current meter is generally used for the measurement of velocity in a river. The current

meters are basically of two types.

(ii). Cup-type current meter (iii). Propeller-type current meter.

The accuracy of the cup-type current meter is about 0.3% for the velocity greater than 1 m/s. The

main disadvantage of a cup-type current meter is that its accuracy is low when there is an

appreciable vertical component of the velocity.

The basic principle of both types of current meters is the same; namely, when a current meter is

inserted in flowing water, there is an unbalanced drag on the rotating element (cup or propeller) which

starts rotating. As the velocity increases, the speed of rotation increases. The current meter is calibrated to give the velocity corresponding to different speeds of rotation. Manufacturers also

provide the calibration chart which gives the relationship between the velocity and the number of

revolutions per second. Generally, it follows a linear relationship,

𝑣 = 𝑎𝑁 + 𝑏 (3.5)

where v is the velocity at the instrument location, N is the number of revolutions per second, and a

and b are the constants of meter obtained by calibration. These constants are determined by towing the

instrument in a towing tank in the laboratory. The current meter gives the velocity (v) at a point. For

determination of the discharge in the river, the mean velocity (V) along a vertical line is required.


Page 17

CHAPTER FOUR

4.0 FIELD WORK OUTPUT AND DATA ANALYSIS

4.1 Introduction

Several visits were undertaken by the research team to Ero-omola and Owu Falls project

between September 2009 and March 2011. The purpose of the visit was to obtain stage-

discharge relation and preliminary peak discharge data for the two sites. Stream flow

measurement were undertaken to determine the extent and dependability of the flow. 2 Nos.

metric steel gauges were installed at the bottom of Fall at Owu and Ero-omola site as well.

Table 4.1: Details of Gauge at Owu and Ero-omola Falls

1. Item Owu Fall Ero-omola Fall

2. Purpose River Stage River Stage

3. Type Self illuminated steel gauge Self illuminated steel gauge

4. Station Bench

Mark

+455.51m +451.60m

5. Datum Nigeria Ordinance Datum/Universal Traverse

Mercator (UTM)

Nigeria Ordinance Datum/Universal Traverse

Mercator (UTM)

6. Gauge

Elevation(m)

+480.7m +449.996m

7. Water level

(m)

+426.2m +449.8m

8. Gauge Height

(m)

3 4

9. Location N080 20’ 40’’ and E05

0 08’ 56’’ N08

0 09’ 48’’ and E05

0 13’ 09’’

10 Date

Established

12th September 2009 11

th September 2009

4.2 Instrumentation Details

An OTT current metre obtained from the Lower Niger River Basin Development Authority

was deployed for the streamflow measurement. The instrument specification is as indicated

below:

Type: Propeller Current Metres (OTT-C31-BAREL 17929)

Propeller Diameter: 125mm

Impulse: 1

Error: +/- 0.25

The calibration equation of the instrument is given as;

V = 0.2483 n +0.011 for n=< 0.59 where n revolution per seconds

V = 0.2619 n + 0.003 for n= < 9.21

Discharge measurement trials were carried out with the instrument on both sites to determine its level

of accuracy. The float method was equally carried out as a check on the calibrated instrument. The


Page 18

float method involves the use of floating material moving under the drag of the river flow, so as to

evaluate or compute the speed or velocity of the river-flow. The float method trials result at Ero-

Omola Fall is as indicated in Table 4.2.The float method was carried out over a uniform distance of

5m along the stream. Stop watch was used to determine the time of travel of the float along the

stream. The computation of the discharge is as follows:

T=Time lapse (in seconds)

Velocity =Distance (L)/Time

Discharge=Area x Velocity

Table 4.2: Discharge computation of float method Trials at Ero-omola Fall from 21-26th October

2009

Distance(m) 5 5 5 5 5 5

Segment Area

(m2)

4.75 4.25 4.75 4.3 4.8 4.75

T(Time)(S) 8.43 3.55 3.38 3.67 3.85 3.29

V(m/s) 0.59 1.41 1.48 1.36 1.29 1.52

Q(m3/s=VA 2.802 5.992 7.030 5.848 6.192 7.22 35.084

The time travel by the float along subdivision of 5m segment on the stream was determined with a

stop watch. The total discharge of 35.084m3/s was obtained during the trials. Similar trials were also

carried out with the current metre. The trials result is as indicated in Table 4.3

Table 4.3: Result of Current Metre Trials at Ero-omola Fall

Date 18/10/2009 19/10/2009 20/10/2009 21/10/2009 22/10/2009

Water level(m) 1.98 1.98 1.95 1.89 1.87

Discharge 48.79 48.60 47.31 41.75 35.4

Similar trials carried out at Owu Fall are indicated in Table 4.4 and 4.5 respectively.

Table 4.4: Results of trial of float method at Owu Fall from11

th-15

th November 2009

Distance(m) 3 3 3 3 3 3

Segment Area

(m2)

6.8 6.8 6.4 5.35 6.8 6.5

T(Time)(S) 12.13 11.97 7.60 5.53 12.00 24.9

V(m/s) 0.25 0.25 0.39 0.54 0.25 0.12

Q(m3/s 1.70 1.70 2.50 2.89 1.70 0.78 11.27

Total Discharge = 11.27m3/s (November Peak)

Table 4.5Result of Current Metre Trials at Owu Fall

Date 11/9/2009 12/9/2009 13/9/2009 14/9/2009 15/9/2009

Water level(m) 0.98 0.97 0.95 0.92 0.89

Discharge 11.02 10.88 10.58 10.14 9.703


Page 19

Subsequent discharge measurements were carried out each month in order to have a relatively spread

of the flood discharge throughout the year. The rating curve equations were developed from the discharge so obtained each month.

4.3 Stream Discharge

Subsequent discharge measurement at Ero-Omola and Owu Falls were computed on the bases of

arithmetic method using the current meter measurements provided. The horizontal distance across the

stream was measured from the edge of the water at one bank. Depths were measured from the water surface.

The cross-section at Owu Fallis shown in Figure 4.1, with the location of each of the current meter measurements of point velocity. The Qi for each of the ten 1.0-m wide flow subareas are estimated

and summed to obtain the total flow. The cross-section area Ai for each subarea is estimated as depth

multiplied by 1-m width. The mean velocity in each subarea is estimated as the average of the flows at measured depth. The measured value is as indicated in Table 4.6

Table 4.6: Result of discharge measurement carried out at Owu Fall

Ai m2 0.5 2.2 3.7 4.3 3.7 2.8 2.4 1.8 1.1 0.7

Vi (m/s) 0.030 0.044 0.070 0.070 0.065 0.060 0.054 0.049 0.041 0.035

Qi=m3/s 0.0150 0.0968 0.3010 0.3010 0.2405 0.1680 0.1296 0.0882 0.0451 0.0245

Q = 0.0150 + 0.0968 + 0.2294 + 0.3010 + 0.2405 + 0.2405 + 0.1680 + 0.1296 + 0.0882 + 0.0451 +

0.0245

Q = 1.34 m3/s (January, 2010)

Distance across Owu stream in meters

Figure 4.1: Owu-Fall Stream Cross-section (Ero-Omola Fall cross section is presented in Appendix 1)

Similar stream flow measurements were carried out at Ero-Omola Fall. The stream cross-section or

profile is shown in Appendix 1. The details computation is as indicated in Appendix 2. The total

discharge of 5.40m3/s (January, 2010) were obtained from 15Nos. sub-divided segment of the profile.

4.4 Development of a monthly flood Rating Curve

4.4.1 A staff gage is the simplest device for measuring river stage or water surface

elevation. The staff gauge is a graduated self illuminated strip of metal marked in metres and

fractions thereof. Water levels were read daily, recorded and collated on monthly basis by the

observer employed. Streamflow discharge measurement normally involves:

(1) establishing the relationship (rating curve) between water surface elevation or height above a

reference datum (stage) and discharge (flow rate) at a gauging station.

1 2 3 4 5 6 7 8 9 10


Page 20

(2) continuously or periodically measuring stage at the gauging station

(3) transforming the record of stage into a record of discharge by applying the rating curve.

Limited numbers of discharge measurements (10Nos.) were undertaken each month for a range of

stage to define a relationship between stage and discharge at the two gauging station. The stage-

discharge relation, which is the rating curve, is then combined with continuous periodic stage

measurements to record discharge as well as stage simultaneously. The rating curve was converted to

discharge by Excel software and was subsequently extended for about 25 years. The extension

became necessary so as to ascertain the viability of the two sites for hydropower development.

For a gauge height H (m) at point of zero flow Ho ; the Discharge Q (m3/s) is related to height

H(m) as follows:

Q =K (H - Ho) n (4.1)

The rating equations (Sharma, 1979) relation is giving as:

Q = K H n (when Ho=0) (4.2)

Where

Q = Discharge (m3/s)

H = Gauge Height (m)

Ho = Zero Gauge Height (m)

n & k = Constants

This is a parabolic equation which plots as a straight line on double logarithmic graph sheet. K &n are determined using the least square method

The procedure for estimating discharge from the gauge height measurements is the Least Square Method.

4.4.2 Let Q = KHn (since Ho =0 from installation) be the function to be fitted to the given data.

Taking logarithms of both sides, we obtain the relation

log Q = log K + n log H (4.3)

which is of the form Q = a0 + a1, where Q = log Q, a0 = log K, a1 = n log H. Then k and n can be

calculated from the formulae a0 = log K and n = a1.

∑Log Q =NLog K + n∑Log H (4.4)

∑Log Q Log H = Log K ∑Log H + n ∑(Log H)2 (4.5)

Where: N = Numbers of pairs of observation

These two equations are solved simultaneously to determine constant k & n respectively for each

rating equation of each month.

The computation for January rating curve is as indicated in Table 4.7 while February to December is

presented in Appendix 3. While Owu Fall Least Square (LSM) Computation for November rating

curve is shown in Table 4.8.


Page 21

Table 4.7:Ero-omola January Flood Rating Curve (LSM)

S/n H (m) Q(m3/s) LogH Log Q (Log H)2 Log Qlog H

1 0.47 6.5 -0.327902142 0.812913 0.107519815 0.266556031

2 0.47 6.5 -0.327902142 0.812913 0.107519815 0.266556031

3 0.47 5.5 -0.327902142 0.740363 0.107519815 0.242766512

4 0.46 6.4 -0.337242168 0.80618 0.11373228 0.271877882

5 0.46 6.4 -0.337242168 0.80618 0.11373228 0.271877882

6 0.45 6.3 -0.346787486 0.799341 0.120261561 -0.2772013

7 0.45 6.3 -0.346787486 0.799341 0.120261561 -0.2772013

8 0.45 6.3 -0.346787486 0.799341 0.120261561 -0.2772013

9 0.45 6.3 -0.346787486 0.799341 0.120261561 -0.2772013

10 0.45 6.3 -0.346787486 0.799341 0.120261561 -0.2772013

SUM

-3.392128194 7.975252 1.151331808 2.705640838

∑Log Q =NLog K + n∑Log H-----------------------------------------------1

∑Log Q Log H = Log K ∑Log H +n ∑(Log H)2 ----------------------2

7.975252 = 10 log K + n (-3.392128194)1

2.705640838 = (-3.392128194) log K + n (1.151331808) 2

By solving these equations simultaneously k & n are estimated thus:

K = 9.206

n = 0.491

Q = K Hn

Q = 9.206 H 0.491

(4.6)

The twelve rating equations obtained from Ero-omla records was utilized to convert the gauge

readings to streamflow data (Appendix 4). The streamflow data generated by the Owu Fall rating

equations is indicated in Appendix 5. The January rating curve is shown in Figure 4.2. While that of

Owu Fall is shown in Figure 4.3.The summary of rating curve coefficient is presented in Table 4.9


Page 22

Figure 4.2:Ero-omola January Flood Rating Curve

Table 4.8: Owu Fall November Flood rating Curve

H(m) Q(m3/s) log Q log H (log H)2 logQlogH

0.27 1.986 0.298 0.103 0.011 0.0307

0.29 2.184 0.339 0.11 0.012 0.0373

0.24 1.698 0.229 0.093 0.009 0.0214

0.22 1.512 0.179 0.086 0.007 0.0154

0.21 1.42 0.152 0.083 0.007 0.0126

0.98 11.02 1.042 0.297 0.088 0.3095

0.97 10.88 1.037 0.294 0.086 0.3049

0.95 10.58 1.024 0.29 0.084 0.297

0.92 10.14 1.006 0.283 0.08 0.2847

0.89 9.703 0.987 0.276 0.076 0.2724

Total

6.293 1.915 0.46 1.5859

1.586=1.915 log k + 0.46n--------------------------------------------1

6.294=10log k +1.915n -----------------------------------------------2

by resolving above equation simultaneously we have

k=11.33

n=1.33

Ho=0

Which gives the rating equations as :

Q=11.33*H^1.33 for H> 0.20

y = -0.02ln(x) + 0.286R² = 0.997

0.325

0.33

0.335

0.34

0.345

0.35

0 0.05 0.1 0.15 0.2

GA

UG

E H

EIG

HT

LOG

H (

m)

LOG Q (m3/S)

JANUARY FLOOD RATING CURVE


Page 23

Figure 4.3: Owu Flow Duration Curve

Table 4.9: Summary of Coefficient of Rating Equations.(Ero-omola)

Months K N Coefficient of

Determinant *(R2)

January 9.206 0.491 0.0463

February 9.253 0.765 0.815

March 9.089 0.934 0.9857

April 10.496 1.049 0.8318

May 10.229 1.455 0.9954

June 8.539 2.258 0.9727

July 0.610 7.789 0.9834

August 12.65 1.517 0.941

September 25.308 0.400 0.8949

0ctober 1.166 5.505 0.9285

November 17.167 2.753 0.9471

December 1.617 5.977 0.8902

*R2=This is a measure of the strength of relationship between the predictive and response variables

4.5 Extension of Streamflow Data at Ero-omola Fall

One year stream flow data generated by the rating equation at Ero-omola has to be extended in order

to fulfill other hydrological analysis requirement. In order to achieve this, the Model proposed by

Thomas and Fierring in 1962 according to McMachon and Mein (1978) was adopted. The model

utilized Markov model to represent actual stream flow when the monthly stream flow, qi, are

normally distributed and follow a first – order auto regressive model. The algorithm for the Thomas

and Fierring model is giving as:

𝑞𝑖+1 = 𝑞 𝑗+1 + 𝑏𝑗 ,𝑗+1 𝑞1𝑞 𝑗 + 𝑍𝑖+1𝑆𝑗+1 1 𝑟𝑗 ,𝑗+12

1/2 (4.7)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.2 0.4 0.6 0.8 1 1.2

GA

UG

E H

EIG

TH (

m)

DISCHRGE Qm3/s

OWU NOVEMBER FLOOD RATING CURVE


Page 24

where qi+1, qi = monthly flows during (i + 1)th, i

th from the start of the synthesized

sequences,

𝑞 𝑗+1, 𝑞 𝑗 = mean monthly flows during (j + 1)th, j

th ( j =1,2,--- 12 ),

𝑏𝑗 ,𝑗+1 =least squares regression coefficient for estimating (j+1)th flow the j

th flow

𝑏𝑗 ,𝑗+1 = 𝑟𝑗 ,𝑗+1𝑆𝑗+1

𝑆𝑗÷÷ (4.8)

Zi+1 = normal random number with mean of zero and variance of unity

Sj+1, Sj = standard deviations of flows during the (j+1)th, j

th seasons, and

rj,j+1 = correlation coefficient between flows in , jth and (j+1)

th seasons.

If N years of data is available, the calculation for the terms in the Thomas – Fierring model for each

month, j = 1, 2, 3 ……………………… 12 in accordance to McMahon and Mein (1978) include:

(a) The mean flow

𝑞 𝑗 = 𝑞𝑗𝑖

𝑁 ÷÷ (4.9)

(b) The standard deviation

𝑆𝑗 = 𝑖 𝑞𝑗𝑖 𝑞 𝑗

2

(𝑁 1) (4.10)

(c) The correlation coefficient with flow in the preceding month

𝑟𝑗 ,𝑗+1 = 𝑖 𝑞𝑗𝑖 𝑞 𝑗 (𝑞𝑗+𝑖,𝑖𝑞 𝑗+1)

𝑖 𝑞𝑗𝑖𝑞 𝑗 2

𝑖(𝑞𝑗+𝑖,𝑖𝑞 𝑗+1)2

(4.11)

To use the model to generate monthly flows at a site, the monthly means, standard deviations and lag

one serial correlations are required and these parameters were obtained from analysis of monthly

historical flows of River Akamo and River Oshin. In order to run the model, q1 is set as: 𝑞1 = 𝑞 𝐽𝐴𝑁

and the synthetic flow q1, q2, q3, q4, ……… was computed successively. The model is restricted to

normally distributed flows, that is Zi is considered to be a Normal random number and is the only

unknown in the model and for each step it can be calculated as a pseudo-random normal number.

The model is the set of twelve regression equations following the pattern of equation (4.7) and

presented in equations 4.12(a) – 4.12(l).

𝑞1 = 𝑞 𝐽𝐴𝑁 (4.12a)

𝑞2 = 𝑞 𝐹𝐸𝐵 + 𝑏𝐽𝑎𝑛 /𝐹𝑒𝑏 (𝑞1𝑞 𝐽𝑎𝑛 ) + 𝑍2𝑆𝐹𝑒𝑏 1 𝑟𝐽𝑎𝑛 /𝐹𝑒𝑏2

1/2 (4.12b)

𝑞3 = 𝑞 𝑀𝑎𝑟 + 𝑏𝐹𝑒𝑏 /𝑀𝑎𝑟 (𝑞2𝑞 𝐹𝑒𝑏 ) + 𝑍3𝑆𝑀𝑎𝑟 1 𝑟𝐹𝑒𝑏 /𝑀𝑎𝑟2

1/2 (4.12c)

𝑞4 = 𝑞 𝐴𝑝𝑟 + 𝑏𝑀𝑎𝑟 /𝐴𝑝𝑟 (𝑞3𝑞 𝑀𝑎𝑟 ) + 𝑍4𝑆𝐴𝑝𝑟 1 𝑟𝑀𝑎𝑟 /𝐴𝑝𝑟2

1/2 (4.12d)


Page 25

𝑞5 = 𝑞 𝑀𝑎𝑦 + 𝑏𝐴𝑝𝑟 /𝑀𝑎𝑦 (𝑞4𝑞 𝐴𝑝𝑟 ) + 𝑍5𝑆𝑀𝑎𝑦 1 𝑟𝐴𝑝𝑟 /𝑀𝑎𝑦2

1/2 (4.12e)

𝑞6 = 𝑞 𝐽𝑢𝑚 + 𝑏𝑀𝑎𝑦 /𝐽𝑢𝑛 (𝑞5𝑞 𝑀𝑎𝑦 ) + 𝑍6𝑆𝐽𝑢𝑛 1 𝑟𝑀𝑎𝑦 /𝐽𝑢𝑛2

1/2 (4.12f)

𝑞7 = 𝑞 𝐽𝑢𝑙 + 𝑏𝐽𝑢𝑛 /𝐽𝑢𝑙 (𝑞6𝑞 𝐽𝑢𝑛 ) + 𝑍7𝑆𝐽𝑢𝑙 1 𝑟𝐽𝑢𝑛 /𝐽𝑢𝑙2

1/2 (4.12g)

𝑞8 = 𝑞 𝐴𝑢𝑔 + 𝑏𝐽𝑢𝑙 /𝐴𝑢𝑔 (𝑞7𝑞 𝐽𝑢𝑙 ) + 𝑍8𝑆𝐴𝑢𝑔 1 𝑟𝐽𝑢𝑙 /𝐴𝑢𝑔2

1/2 (4.12h)

𝑞9 = 𝑞 𝑆𝑒𝑝 + 𝑏𝐴𝑢𝑔/𝑆𝑒𝑝 (𝑞8𝑞 𝐴𝑢𝑔 ) + 𝑍9𝑆𝑆𝑒𝑝 1 𝑟𝐴𝑢𝑔 /𝑆𝑒𝑝2

1/2 (4.12i)

𝑞10 = 𝑞 𝑂𝑐𝑡 + 𝑏𝑆𝑒𝑝 /𝑂𝑐𝑡 (𝑞9𝑞 𝑆𝑒𝑝 ) + 𝑍10𝑆𝑂𝑐𝑡 1 𝑟𝑆𝑒𝑝 /𝑂𝑐𝑡2

1/2 (4.12j)

𝑞11 = 𝑞 𝑁𝑜𝑣 + 𝑏𝑂𝑐𝑡 /𝑁𝑜𝑣 (𝑞10𝑞 𝑂𝑐𝑡 ) + 𝑍11𝑆𝑁𝑜𝑣 1 𝑟𝑂𝑐𝑡 /𝑁𝑜𝑣2

1/2 (4.12k)

𝑞12 = 𝑞 𝐷𝑒𝑐 + 𝑏𝑁𝑜𝑣/𝐷𝑒𝑐 (𝑞11𝑞 𝑁𝑜𝑣 ) + 𝑍12𝑆𝐷𝑒𝑐 1 𝑟𝑁𝑜𝑣/𝐷𝑒𝑐2

1/2 (4.12l)

Z is calculated for each step as a pseudo – random normal variate.

4.6 Model Development

The multiple linear regression theory is based on the assumed distribution of all variables in

accordance with the Gaussian normal distribution. Therefore, mathematical integrity requires that

each variable be transformed to a normal distribution. It has been established that logarithms of

streamflow are approximately normally distributed in most cases, however for computational

efficiency, it is convenient to establish the model from a transform logarithms of streamflow data.

The data from the two synoptic stations (Oro and Omu Aran) were converted to natural logarithms

before the data was analyzed for the determination of various model coefficient variables. The data

for Ero-omola were extended for 25 years based on the twelve model equations generated from the

analysis.

In accordance with the above basic procedure, historical streamflow data with relatively long years

of records obtained from the Lower Niger River Basin Development Authority was utilized in

extending the short data from Ero-omola. The data was obtained from the 1982 Hydrological Year

Book published by the hydrology department. The raw data and the flood hydrograph is attached in

Appendix 10 of this report.

The method of Least Square method was used to obtain the Regression Coefficient and other

statistical parameters between the short streamflow data from Ero-omola and the long historical

streamflow data from River Oshin and River Akamo. These two rivers are located between Oro and

Omuaran a similar catchment characteristics to Ero-omola. The monthly streamflow parameters

between historical streamflow and Ero-omola are shown in Table 4.9 while the equivalent

transformed data to natural logarithm is shown in Table 4.10.

In modeling the monthly streamflow data the Thomas and Fierring model based on a first order

Markov model is used and the synthetic streamflow series were calculated in Table 4.9 using

historical flow data from River Akamo and Oshin. The series of equation derived from the model is

presented in equations 4.13(a)-4.13(l) as follows:


Page 26

Table 4.10: Monthly Streamflow Parameters for River Oshin (1979)

Month Mean STD Corr. Coeff. Coeff. Of Lag One

qj Sj Cv Skewness Corr.Coeff.rj

JANUARY 6.4706 0.0662 -0.169 -1.984 0.075

FEBRUARY 4.2696 0.1794 -0.28 -0.686 0.359

MARCH 0.9294 0.4885 0.3568 -0.235 -0.425

APRIL 10.386 0.0855 -0.265 2.1991 0.1358

MAY 15.422 0.1533 -0.438 1.8573 -0.243

JUNE 18.662 0.2224 0.1695 -1.339 -0.249

JULY 14.463 0.3254 0.0137 0.3426 0.142

AUGUST 15.398 0.2634 -0.391 0.4197 0.2095

SEPTEMBER 21.499 0.2634 -0.187 0.465 0.2487

OCTOBER 18.527 0.2598 0.1096 -0.42 0.0951

NOVEMBER 13.415 0.3264 0.5877 0.1667 0.1198

DECEMBER 7.7923 0.0677 0.5371 -0.032 -0.525

q1 = 6.470645 + 0.39210 (q122.89452) + 2.13421z1 (4.13a)

q2 = 4.269643 + 0.52523 (q,1 7.792258) + 4.199054z2 (4.13b)

q3 = 0.929355 + 0.169519 (q2 6.470645) + 2.166747z3 (4.13c)

q4 = 10.38645 + 0.095148 (q3 0.929355) + 0.259820z4 (4.13d)

q5 = 15.42161 + 0.222417 (q4 10.38645) + 3. 537140z5 (4.13e)

q6 = 18.66167 + 0.013661 (q5 15.42161) + 3.326388z6 (4.13f)

q7 = 14.46258 + 0.325371 (q6 18.66167) + 5.420320z7 (4.13g)

q8 = 15.39839 + 0.095148 (q7 14.46258) + 4. 259820z8 (4.13h)

q9 = 21.49900 + 0.179392 (q8 15.39839) + 6.067661z9 (4.13i)

q10 = 18.52742 + 0.03172 (q9 21.499) + 8.98356 z10 (4.13j)

q11 = 13.41467 + 0.587739 (q10 18.52742) + 5.074972z11 (4.13k)

q12 = 7.792258 + 0.525230 (q11 13.41467) + 4.325371z12(4.13l)

Table 4.10 :Transformed Natural Logarithmic Monthly Streamflow Parameters for River Oshin

(1979)

Mean

STD

Corr.Coff.

Coeff.of

Lag one Corr

qj

Sj

Cv

Skewness

rj

JANUARY

1.867276

-2.7154

-0.12691

0.108505

By setting q1= 6.470645

The historical streamflow data from only Oshin River, which was found to give a reliable statistical

parameter similar to Ero-omola was used to run the model. The above set of equations was used to

extend the streamflow flow data in an excel programme to 25 years. (2009-2034) The extended

streamflow data generated by the excel programme is giving in Appendix 6. Similarly historical

streamflow data from River Oshin and Akamo is shown in Appendix 7. The equivalent transform to

natural logarithm is shown in Appendix 8.


Page 27

Table 4.11 Transformed Natural Logarithmic Monthly Streamflow

Parameters for River Oshin (1979)


qj Sj Cv Skewness Corr.Coeff.rj

JANUARY 1.8673 2.715 -0.127 0.1085 0.2384

FEBRUARY 1.4515 1.718 -0.104 0.132 0.2434

MARCH -0.073 0.716 -0.107 0.1298 0.2277

APRIL 2.3405 2.459 -0.109 0.1287 0.2428

MAY 2.7358 1.875 -0.11 0.1293 0.239

JUNE 2.9265 1.503 -0.11 0.1287 0.2346

JULY 2.6716 1.123 -0.111 0.132 0.2379

AUGUST 2.7343 1.334 -0.112 0.1262 0.2394

SEPTEMBER 3.068 1.334 -0.112 0.1262 0.2403

OCTOBER 2.9193 1.348 -0.112 0.129 0.2319

NOVEMBER 2.5963 -1.12 -0.113 0.1267 0.2399

DECEMBER 2.0531 2.693 -0.114 0.1228 0.2298

Table 4.12: Monthly Streamflow Parameters for River Akamo (1981)


qj Sj Cv Skewness Corr. Coeff.rj

JANUARY 5.5168 0.3138 -0.209578889 -1.092 0.166323484

FEBRUARY 7.2808 0.1876 -0.174896707 -5.231 -0.174896707

MARCH 3.4519 0.4144 1 1.0393 0.761907351

APRIL 12.342 0.4144 0.761907351 1.0393 0.747056989

MAY 18.467 0.8012 1 0.2401 0.770461678

JUNE 22.246 0.7847 0.753907959 0.2265 0.655500363

JULY 16.596 0.4229 0.622736154 0.9587 0.229111101

AUGUST 20.552 1.0804 0.543791067 -0.346 0.675861256

SEPTEMBER 25.802 0.7272 0.554306075 -0.048 0.559931888

OCTOBER 22.35 0.9066 0.669627026 0.4298 0.736537432

NOVEMBER 18.52 1.0366 0.983150118 0.9183 -0.157603747

DECEMBER 12.635 1.178 -0.07175952 0.0267 -0.115143984

Table 4.13: Natural Logarithmic Transformed Monthly Streamflow Parameters for Akamo


Page 28

River(1981)


qj Sj Cv Skewness Corr. Coeff.rj

JANUARY 1.7078 -1.159 0.094296843 0.2336 0.338208832

FEBRUARY 1.9852 -1.674 0.080529482 0.2256 0.333803756

MARCH 1.2389 -0.881 0.102455523 0.2386 0.342761931

APRIL 2.513 -0.881 0.100029495 0.2372 0.342858112

MAY 2.916 -0.222 0.0827014 0.2269 0.353779166

JUNE 3.1021 -0.242 0.068728441 0.2188 0.34791206

JULY 2.8092 -0.861 0.075363026 0.2227 0.351357211

AUGUST 3.0229 0.0773 0.120742773 0.2317 0.351461525

SEPTEMBER 3.2504 -0.319 0.095364927 0.2348 0.34791206

OCTOBER 3.1068 -0.098 0.159226005 0.2744 0.360897776

NOVEMBER 2.9188 0.0359 0.116877947 0.248 0.354409363

DECEMBER 2.5365 0.1638 0.147501602 0.2671 0.349307898

4.7Determination Of The Required Reservoir Capacity

It is imperative to make provision for compensation reservoir due to 3 months break of runoff at Ero-

omola. The regulated reservoir will then provide the needed flow of to the turbines uninterrupted

through out the year. The capacity required for a reservoir depends upon the inflow available and the

demand. If the available inflow in the river is always greater than the demand, there is no storage

required. On the other hand, if the inflow in the river is small but the demand is high, a large

reservoir capacity is required. The required capacity for the reservoir at Ero-omola was evaluated or

determined by the following methods:

1. Graphical method, using mass curves and

2.Flow-duration curves method

4.7.1 Determination of Ero-omola Reservoir Capacity

The yield from a reservoir of a given capacity can be determined by the use of the mass inflow curve.

The following procedure was used.

Table 4.14: Mass Inflow Curve Computation for Ero-omola Fall using average monthly discharge data.

Month Average Monthly Discharge Cumulative Volume

(m3/s)

(m3/s)

JAN.

6.04984

6.04984 FEB.

4.939395

10.98924

MAR.

3.755002

14.74424 APR.

12.84037

27.58461

MAY

19.64738

47.23199 JUNE

21.39122

68.62321

JULY

24.09706

92.72027 AUG.

36.95531

129.6756

SEPT.

49.07125

178.7468


Page 29

OCT.

39.91781

218.6646

NOV.

32.30785

250.9725

DEC.

19.97958

270.9521

Sum 1316.955

Figure 4.4: Ero-omola Inflow Mass Curve

The maximum storage capacity computed from the mass inflow curve above is 60m3/s. The reservoir

is expected to fill up in the middle of September. Further computation is needed to convert the discharge into an inflow volume:

1 m3/ year = 1 x 365 x 24 x 60 x 60 = 31.536 x 10

6m

3

Reservoir Capacity = 31.536mcm x 60 = 1892.16mcm

Inflow volume in 2009 = 13I6.955 x 31.536mcm = 41531.49mcm

4.8 Evaluation of Sediment Load or Sediment Transport

In order to established the sediment load into the reservoir. It assumed that the reservoir capacity will

terminate when 80% of initial capacity is filled with sediment.

Average sediment inflow to River Ero is giving as 36000 tonnes (LNRBDA, 2003)

Specific weight of sediment taken from laboratory =1200kg/m3(LNRBDA, 2003)

Reservoir Capacity = 1892.16mcm

Annual Inflow = 41531.49mcm

Trap Efficiency = Sediment Deposited x 100% (US Bureau of Reclamation, 1987)

Sediment Inflow

y = 18.96xR² = 0.848

0

50

100

150

200

250

300

JAN. FEB. MAR. APR. MAY JUNE JULY AUG. SEPT. OCT. NOV. DEC.

Cu

mm

ula

tive

flo

w (

M3

/s)

Months

ERO-OMOLA INFLOW MASS CURVE


Page 30

Trap Efficiency = Reservoir Capacity/Mean Annual Inflow

Trap Efficiency = 1892.16/41531.49 =0.045

Annual sediment inflow = 36000 𝑡𝑜𝑛𝑛𝑒𝑠 = 3.6 × 106 𝑘𝑔. (LNRBDA, 1999)

Volume of sediment inflow = 3.6 ×106

1200= 3000 𝑚3

Annual Sediment Deposited = Trap Efficiency x Sediment inflow

=0.045 x 3000 = 135m3

Therefore, in 25years the sediment deposited will amount to 3,375m3which suggest the need

to provide sluice gate at the headworks for sediment discharge. This is to avoid a situation

where the reservoir is filled up before the expected project life of 25 years. Nevertheless, a

more details assessment is required to ascertain the useful life of the reservoir.


Page 31

CHAPTER FIVE

5.0 POTENTIAL ENERGY ASSESSMENT

5.1 Potential Energy Assessment of Ero-OmolaFall

In order to evaluate potential energy at Ero-omola. Twenty years ofstreamflow record

(2009-2034) was utilised from the projected 25 years records in Appendix 6. The streamflow

data was arranged in ascending order. The percentage of exceedence and annual projected

hydropower generation potential was computed in Table 5.1. The Flow Duration Curve as well

as the Power Duration Curve plotted is shown in Figure 5.1 and 5.2

Table 5.1:Computation of Flow Duration Curve using the projected 20 years figures

No. Year Flow(m3/s) Flow in Ascending Order

P{ower=9.8 x 59.4 x F(kw)

% of time of availability

N +1 -n

%

N

1 2009 22.57 21.97

12789.18 100

2 2010 22.82 21.98

12795 95

3 2011 23.14 22.03

12824.1 90

4 2012 22.99 22.57

13138.45 85

5 2013 23.71 22.79

13266.51 80

6 2014 24.39 22.82

13283.98 75

7 2015 23.34 22.99

13382.94 70

8 2016 21.98 23.14

13470.26 65

9 2017 21.97 23.34

13586.68 60

10 2018 22.03 23.61

13743.85 55

11 2019 22.79 23.71

13802.07 50

12 2020 23.61 24.34

14168.8 45

13 2021 24.49 24.39

14197.91 40

14 2022 24.94 24.49

14256.12 35

15 2023 24.8 24.8

14436.58 30

16 2024 24.34 24.83

14454.04 25

17 2025 24.83 24.94

14518.07 20

18 2026 26.06 25.39

14780.03 15

19 2027 25.39 26.06

15170.05 10

20 2028 26.07 26.07

15175.87 5


Page 32

Figure 5.1: Ero-omola Flow Duration Curve

Figure 5.2: Ero-omola Power Duration Curve

The minimum flow available for 100% of the time is estimated at 21.8m3/sfrom the flow duration

curve over an hydraulic head of 59.4m. Generator and Turbine Efficiency is assumed at 85% and 80%

Plant Efficiency = 0.85 x 0.80 = 0.68

From Equation (2.1) PE= 9.81QHe

Hydropower of Ero –Omola = 59.4 m x 21.8 m3/sx 9.81 x0.68 =8638.15kw or 8.64MW

FIRM ENERGY = Pdesign x 24 x 365 kWh (Equation 2.6)

21

22

23

24

25

26

27

0 20 40 60 80 100 120

Flo

w (

m3

/s)

Percentage of Exceedence

ERO-OMOLA FLOW DURATION CURVE

12789.176412794.9976

12824.103613138.448413266.514813283.978413382.938813470.256813586.6808

13743.853213802.0652

14168.800814197.906814256.118814436.57614454.039614518.0728

14780.0268

15170.047215175.8684

12500

13000

13500

14000

14500

15000

15500

0 20 40 60 80 100 120

Po

wer

(kw

)

Percentage of Exceedence

ERO-OMOLA POWER DURATION CURVE


Page 33

Annual Firm Energy = 8.64 x 24 x 365x 0.2 = 15137.28MWh (Analytical)

Also from the Power Duration Curve in Figure 5.2 the firm energy or plant capacity at 100% of time

is computed as 12794.9976kw or 12.794MW

Annual Firm Energy =12.794 x 0.68 x 24 x 365 x 0.2=15242.26MWh.(Graphical)

Using the new NIPP, Multi Year Tariff Order (MYTO) of Nigeria Regulatory Energy Commission

(Appendix 9) of N14.00/kWh. The total cost of bulk energy, excluding other charges is estimated at

15137280Kwh x N14.00/kWh = N211,921,920/Annum

5.2 Potential Energy Assessment of Owu Fall

The streamflow discharge data (Appendix 5) generated from the rating equation at owu was utilized to

develop the Flow Duration Curve (FDC) as well as Power Duration Curve (PDC). The minimum flow

available for 100% of the time from the FDC/PDC curve(Figure 5.3 and 5.4) amount to 9.9m3/s over

an hydraulic head of 95.5m. The computational procedures is shown in Table 5.2

Hydropower potentials for Owu Fall= 95.5m x 9.9m3/s x 9.81 x 0.95 = 8,811.12 kW or 8.81 MW

(with 95% efficiency plans).

Annual Firm Energy =8.81MW x 24 x 365 x 0.2 = 15435.12MWh

Using the NIPP tariff order of N14.00/Kwh. Annual energy generated is estimated at

N216,091,680.00/Annum.

Table 5.2 : Owu FDC/PDC Computation

No. Year Flow(m3/s

Flow in Ascending Order

Power=9.8 x 59.4 x F(kw)

% of time of availability

N +1 -n %

N

1 JANUARY 4.1856 10.955

3917.3133 100

2 FEBRUARY

0 91.667

3 MARCH

3.6371 10.342

3403.958 83.333

4 APRIL

3.6414 10.237

3407.9883

5 MAY

3.8497 4.1856

3602.9737 66.667 6 JUNE

3.5605 4.1856

3332.2596 58.333

7 JULY

0

8 AUGUST 10.237 3.8497

9580.4755 41.667 9 SEPTEMBER 4.1856 3.6414

3917.3133 33.333

10 OCTOBER

0

11 NOVEMBER 10.955 3.6371

10252.694 16.667

12 DECEMBER 10.342 3.5605

9679.3501 8.3333


Page 34

Figure 5.3: Owu Flow Duration Curve

Figure 5.4:Owu Fall Power Duration Curve

5.3 Hydropower Water Demand

From the flow duration curve(Ero-omola) the peak hydropower demand was estimated at 21.80m3/s,

hence 7m3/s is expected to be drafted by draft tube into bifurcated penstocks making a total of 7 x 24

x 3600 x 365 =220.752 MCM or 662.256mcm for the three turbines annually.

The storage capacity required to meet the peak hydropower demand of 21.80m3/s throughout the year

is given thus;

Yearly demand = 31.536 x 21.80 = 687.48mcm

0

2

4

6

8

10

12

14

0 20 40 60 80 100 120

FLO

W (

Qm

3/S)

PERCENTAGE OF EXCEDENCE

OWU FLOW DURATION CURVE

0

2000

4000

6000

8000

10000

12000

0 20 40 60 80 100 120

PO

WER

(kw

)

PERCENTAGE OF EXCEEDENCE

OWU POWER DURATION CURVE


Page 35

CHAPTER SIX

6.0 FINANCIAL JUSTIFICATION

6.1 Introduction

Economic feasibility and optimality represent just one of many considerations in the decision-

making process. However, economic analysis does play an important central role in decision-

making at many levels, in various settings. Economic evaluation of hydropower development

plans combines basic methods of engineering economics with benefit estimation procedures.

Analyses of economic costs and benefits provide important information for use, along with

various other forms of information, in making a myriad of decisions in planning, design,

operations, and other water resources engineering activities. (Printinger, 1972)

The economic objectives for comparing alternative plans may be in either of the following alternative forms:

Maximize net benefits, which are benefits less costs

Minimize cost required to provide a specified level of service

Maximize benefits derived from fixed resources.

In this study, both benefits and costs are relevant and are included in the analysis.

6.2 Engineering Economics

Engineering economics is a set of principles applied in comparing alternative plans to

determine the economically optimal design. Equivalence of kind and equivalence of time are

required so that all relevant costs and benefits of each alternative are comparable.

Equivalence of kind is achieved by expressing all benefits and costs included in the analysis

in both local and foreign currencies. Equivalence of time is achieved through discounting

techniques using compound interest formulas. Having a Naira today is worth more than

obtaining a Naira at some future time, because the Naira in hand today can be invested to

accrue interest.

6.3 Economic Analysis

Benefits and costs associated with water projects occur at various times, Initial investment

costs occurring at the beginning of the project life are associated with construction or

implementation. Operation and maintenance costs continue throughout the life of the project.

Major replacement and rehabilitation costs may occur periodically. Benefits typically accrue

over long periods of time. Time streams of benefits and costs may be converted to other

equivalent cash flows for purposes of comparison using discounting formulas, with a special

fixed discount rate. The discount rate is often linked to the concept of marginal internal rate of

return in National Integrated Power Project or National Independent Power Project industry.

If funds were committed to the project yielding the highest return first, and then to subsequent

projects in order of rate of return, the rate of return of the last project selected before funds


Page 36

ran out would be the marginal internal rate of return. The discount rate used by the National

Economic Planning Department is based on the market interest rate for risk free investment,

with the limitation that the rate may not be changed too rapidly. The financial analysis in this

study shall be limited to only Ero Omola project due to its obvious advantage of Owu Fall

Project.

6.4 Hydro Power Generation Benefit

The entire benefit envisaged from this project is generation of Hydro-power electricity. The

peak power generation contemplated of the project is 8638.15kw or 8.64 MW. This power

would be utilized for electrifying five LGAs town and neighboring villages.

The total capability of hydropower generation (number of Kilowatt hour units) in a year of

90% dependability would be 15137.28MWh. With 70% load factor, the total units generated

would be 0.7 x 15137.28 = 10596.096MWh.

6.5 Cost of generation per Kilowatt

The total cost of the project, except for the equivalent cost of 48 Km. long 133 KVA High Tension

Transmission line, equipments & distribution system, which is entirely for power generation works

out to 1809 million Naira. (Abstractive Cost) With the above investment, the installed capacity to be

provided is 8638.15kw; hence the cost per kW installed capacity works out to N209,419.84\kW

6.6 Internal Rate Return.

Internal rate of return is that discount rate that makes the net present value of a net benefit or

cash flow equal zero or is the maximum interest rate that a project could pay on invested

capital, if the project is to recover its investments and operating costs and still break even. It

could also be defined as the rate of return on capital outstanding per period while it is invested

in the project.

6.6.1 Assumptions:

Reservoir capital costs are given as input data and their operation and maintenance costs are

expressed as a fraction of their capital costs. Power house, penstock and forebay costs are

based on maximum draft tubes flow. Operation and maintenance costs are a fraction of this

value. Power and imported turbines spare parts costs are determined from abstractive market

value. Present worth is obtained from the actual cost (sum of the costs of actual Capital,

operation and maintenance, power, imported turbines parts, and deficit minus the

hydroelectric power benefits). The cost abstract is presented in Table 6.1.


Page 37

TABLE – 6.1: Consolidated Abstract of Cost

S.No Unit Description Cost in Millions(N)

1. Unit – I Civil Works 109

2. Unit – II Electrical Works 483

3. Unit – III Compensation and Honourariums 450

4. Unit – IV Design and Construction 568

5. Unit-V Operation and Maintenance 199

Total 1809

The preliminary cost of development of Ero-omola Fall is estimated at N1,809,000,000.00 which

include the Headworks, Civil, Electrical and the mechanical component. Using the current Central

Bank of Nigeria annual interest rate of 21% at a repayment period of 25years. The Internal Rate of

Return was interpolated between 16% and 20% to guess the true Rate of Return. The details

computational procedure is indicated in Table 6.2.

𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝐹𝑎𝑐𝑡𝑜𝑟 = (1+𝑖)𝑁− 1

𝑖(1+𝑖)𝑁 = =

(1+0.16)− 1

0.16(1+0.16) =0.8620 (i=16%)

= (1+0.20)− 1

0.20(1+0.20) =0.833 (i=20%) =

(1+0.21)− 1

0.21(1+0.21) =0.8264 (i=21%)


Page 38

TABLE 6.2: COMPUTATION OF INTERNAL RATE OF RETURN FROM CASH FLOW (ABSTRACTIVE COST)

METHOD:INTERPOLATION METHOD

YEAR CAPITAL O & M (N)*M GROSS(N)M VALUE OF INCREMENTAL 16%D.F 16% PW 20% D.F 20% PW

COMPONENT(N)M

INCREMENTAL NET

GROSS BENEFIT

BENEFIT(N)M CASH

FLOW(N)M

1 1.09

0

1.09

-1.09

0.862 -0.94 0.833 -0.91

2 4.83

0

4.83

-4.83

0.743 -3.59 0.694 -3.35

3 5.68

0

5.68

-5.68

0.641 -3.64 0.579 -3.29

4 4.5

0

4.5

-4.5

0.552 -2.48 0.482 -2.17

5 1.99

0

1.99

-1.99

0.476 -0.95 0.402 -0.8

6 0

0.67

0.67

1

0.41 0.41 0.335 0.34

7 0

0.97

0.97

2.37

0.354 0.84 0.279 0.66

8 0

1.3

1.3

3.7

0.305 1.13 0.233 0.86

9 0

1.62

1.62

5.06

0.263 1.33 0.194 0.98

10 0

1.95

1.95

6.43

1.57 10.1 0.948 6.1

TOTAL 18.09 6.51 24.6 0.47 6.176 2.21 4.979 -1.58

(*M=million)

Interpolation Procedures: Internal Rate of Return= Lower Discount rate +Difference Between the Discount rate x Ratio of Present Worth of Incremental benefit cash flow at Lower Discount Rate

and Sum of the Incremental Net Benefit Stream Cash flow of the two Discount rate (when the signs are ignored)

Present Worth of Benefit @ 16% = 2.21 Million Present Worth of Benefit @ 20% = 1.58 Million

The Sum of the Streams at the two Discount rates Ignoring the signs=2.21+1.58=3.79

INTERNAL RATE OF RETURN =16 (4)2.21/3.79=16 + 4(0.58) = 18.62 OR 18%


Page 39

The internal rate return of 18% with an abstractive cash flow analysis suggests a promising profit

outlook. Accurate Internal Rate of Return will be achieved when both structural and non-structural

design of all hydropower components is completed and the true Bill of Engineering Measurement and

Evaluation is incorporated in the Economic Analysis. The amortization of various hydropower

components at the prevailing interest rate of 21% is computed below:

6.7 Amortization Analysis

The projected hydropower cash flow is presented in Appendix 11. The cash flow indicates that Ero-

omola project is expected to grow by 5% profit beginning from year 2015. The total Kilo Watt Hour

units available annually at 90% dependability excluding Power-Station requirement is 15137.28

MWh. Taking the estimated life span of electrical works (generation), civil, operation and

maintenance and other works as 25 years. Amortization of various component of hydropower project

outlined above was computed in consideration of prevailing interest rate of 21%. The discount factor

computed at 21% interest rate is presented thus:

𝐴 = 𝐹 𝑖

(1+𝑖)𝑁− 1 = 𝐴 = 𝐹

0.21

(1+0.21)25− 1 =0.0018 (when n=25years)

1. Amortization Cost Amount(N)

(a) Electrical Works (21% Interest, 25 yrs. life)

a) (b) Civil Works. (21% Interest, 25 yrs. life)

(c) Design and Construction

(d) Compensation and Honourariums

(a) (e)Operation and Maintenance(1.5% of Total Cost)

Total

= 0.0018 x 1090000 = N1,962.00

= 0.0018 x 4830000 = N8,694.00

= 0.0018 x 5680000 =N10,224.00

= 0.0018 x 4500000 =N8,100.00

= 0.015 x 1990000 =N29,850.00

= N58,830.00


Page 40

APPENDIX 1:

CROSS-SECTION OF

ERO-OMOLA STREAM


Page 41

APPENDIX 2


Page 42

Streamflow Discharge Computation with Current Metre (Arithmetic Method)

The calibration equation of the instrument is given as;

V = 0.2483 n +0.011 for n=< 0.59 where n revolution per seconds

V = 0.2619 n + 0.003 for n= < 9.21

Segment 1

𝑛 = 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛

𝑡𝑖𝑚𝑒

= 5

40 = 0.125

𝑣1 = 0.2483 × 𝑛 + 0.011

= 0.2483 × 0.125 + 0.011 = 0.034𝑚𝑙𝑠.

𝐴1 = 12 𝑏𝑑

= 12 × 3 × 0.95

= 1.43𝑚3

𝑞1 = 𝑣1𝐴1

= 0.03 × 1.43

= 0.049𝑚3/𝑠

Segment 2

𝑛 = 7

43 = 0.163

𝑉2 = 0248 × 0.163 + 0.011

= 0.043𝑚/𝑠

𝐴2 = 𝑄2 + 𝑄3

2 𝑏

= 0.095 + 1.4

2 3

= 3.53𝑚2

𝑞2 = 𝑉2𝐴2

= 0.043 × 3.53

= 0.152𝑚2/𝑠

Segment 3

𝑛 = 7

52 = 0.135

𝑣3 = 0.2483 × 0.135 + 0.011


Page 43

= 0.036𝑚/𝑠

𝐴3 = (𝑄3 + 𝑄4)

2 𝑏

= (1.4 + 2.0)

2

= 5.0𝑚2

𝑞3 = 𝑉3𝐴3 = 0.184𝑚3/𝑠

𝑞3 = 0.184𝑚3/𝑠

Segment 4

𝑛 = 7

40 = 0.175

𝑣4 = 0.2483 × 0.175 + 0.011

= 0.046𝑚/𝑠

𝐴4 = (2.0 + 2.1)3

2

= 6.15𝑚2

𝑞4 = 𝑉4𝐴4

= 0.046 × 6.15

= 0.283𝑚3/𝑠

Segment 5

𝑛 = 10

55 = 0.182

𝑣5 = 0.2483 × 0.182 + 0.011

= 0.048𝑚/𝑠

𝐴5 = (2.1 + 2.3)3

2

= 6.6𝑚2

𝑞5 = 𝑉5𝐴5

= 0.048 × 6.6

= 0.317𝑚3/𝑠

Segment 6

𝑛 = 10

53 = 0.189

𝑣6 = 0.2483 × 0.189 + 0.011


Page 44

= 0.049𝑚/𝑠

𝐴6 = (2.3 + 2.25)3

2

= 6.83𝑚2

𝑞6 = 𝑉6𝐴6

= 0.049 × 6.83

= 0.334𝑚3/𝑠

Segment 7

𝑛 = 10

48 = 0.208

𝑣7 = 0.2483 × 0.208 + 0.011

= 0.054𝑚/𝑠

𝐴7 = (2.25 + 2.2)3

2

= 6.68𝑚2

𝑞7 = 𝑉7𝐴7

= 0.054 × 6.68

= 0.360𝑚3/𝑠

Segment 8

𝑛1 = 15

50 = 0.3 𝑉81 = 0.2483 × 0.3 + 0.011

= 0.077𝑚/𝑠

𝑛2 = 10

50 = 0.2 𝑉82 = 0.2483 × 0.2 + 0.011

= 0.0524𝑚/𝑠

𝑉8𝑎𝑣𝑔 = 0.065𝑚/𝑠

𝐴8 = (2.2 + 2.5)3

2

= 7.05𝑚2

𝑞8 = 𝑉8𝐴8

= 0.065 × 7.0

= 0.458𝑚3/𝑠

Segment 9


Page 45

𝑛1 = 15

45 = 0.33 𝑉91 = 0.2483 × 0.33 + 0.011

= 0.085𝑚/𝑠

𝑛2 = 10

48 = 0.2 𝑉92 = 0.2483 × 0.21 + 0.011

= 0.054𝑚/𝑠

𝑉9𝑎𝑣𝑔 = 0.069

𝐴9 = (09 + 010 )

2𝑏 𝐴9 =

(2.5 + 2.8)

22

= 5.3𝑚2

𝑞9 = 𝑉9𝐴9

= 0.069 × 5.3

= 0.366𝑚3/𝑠

Segment 10

𝑛1 = 15

43 = 0.35 𝑉101 = 0.2483 × 0.35 + 0.011

= 0.089𝑚/𝑠

𝑛2 = 10

46 = 0.22 𝑉102 = 0.2483 × 0.22 + 0.011

= 0.057𝑚/𝑠

𝑉10𝑎𝑣𝑔 = 0.073𝑚/𝑠

𝐴10 = (010 + 04)

2𝑏 𝐴10 =

(2.8 + 3.0)

22

= 5.8𝑚2

𝑞10 = 𝑉10𝐴10

= 0.073 × 5.8

= 0.423𝑚3/𝑠

Segment 11

𝑛1 = 20

52 = 0.38 𝑉111 = 0.2483 × 0.38 + 0.011

= 0.098𝑚/𝑠

𝑛2 = 10

40 = 0.25 𝑉111 = 0.2483 × 0.25 + 0.011

= 0.065𝑚/𝑠

𝑉11𝑎𝑣𝑔 = 0.081𝑚/𝑠

𝐴11 = (011 + 012 )

2𝑏 𝐴11 =

(3.0 + 2.95

22


Page 46

= 5.95𝑚2

𝑞11 = 𝑉11𝐴1

= 0.081 × 5.95

= 0.482𝑚3/𝑠

Segment 12

𝑛1 = 20

50 = 0.40 𝑉121 = 0.2483 × 0.40 + 0.011

= 0.102𝑚/𝑠

𝑛2 = 10

42 = 0.24 𝑉122 = 0.2483 × 0.24 + 0.011

= 0.062𝑚/𝑠

𝑉12𝑎𝑣𝑔 = 0.082𝑚/𝑠

𝐴12 = (012 + 013 )

2𝑏 𝐴12 =

(2.95 + 3.1

22

= 6.05𝑚2

𝑞12 = 𝑉12𝐴12

= 0.082 × 6.05

= 0.496𝑚3/𝑠

Segment 13

𝑛1 = 20

48 = 0.42 𝑉131 = 0.2483 × 0.42 + 0.011

= 0.106𝑚/𝑠

𝑛2 = 10

46 = 0.22 𝑉132 = 0.2483 × 0.22 + 0.011

= 0.057𝑚/𝑠

𝑉13𝑎𝑣𝑔 = 0.081𝑚/𝑠

𝐴13 = (013 + 014 )

2𝑏 𝐴13 =

(3.1 + 3.2 )

22

= 6.3𝑚2

𝑞13 = 𝑉13𝐴13

= 0.081 × 6.3

= 0.51𝑚3/𝑠

Segment 14

𝑛1 = 20

52 = 0.38 𝑉141 = 0.2483 × 0.38 + 0.011


Page 47

= 0.098𝑚/𝑠

𝑛2 = 15

55 = 0.27 𝑉142 = 0.2483 × 0.27 + 0.011

= 0.07𝑚/𝑠

𝑉14𝑎𝑣𝑔 = 0.084𝑚/𝑠

𝐴14 = (014 + 015 )

2𝑏

= 6.25𝑚2

𝑞13 = 𝑉14𝐴14

= 0.084 × 6.25

= 0.525𝑚3/𝑠

Segment 15

𝑛1 = 15

42 = 0.36 𝑉151 = 0.2483 × 0.36 + 0.011

= 0.091𝑚/𝑠

𝑛2 = 10

46 = 0.22 𝑉152 = 0.2483 × 0.22 + 0.011

= 0.057𝑚/𝑠

𝑉15𝑎𝑣𝑔 = 0.074𝑚/𝑠

𝐴15 = (015 + 016 )

2𝑏 𝐴9 =

(3.05 + 3.1)

22

= 6.15𝑚2

𝑞15 = 𝑉15𝐴15

= 0.074 × 6.15

= 0.46𝑚3/𝑠

Total Discharge Q

Q = 0.049 + 0.152 + 0.184 + 0.283 + 0.317 + 0.334 + 0.360 + 0.458 + 0.366 + 0.423 +

0.482 + 0.496 + -.510 + 0.525 + 0.460 = 5.40m3/s.


Page 48

APPENDIX 3


Page 49

APPENDIX 4


Page 50

APPENDIX 4a: ERO-OMOLA DAILY GAUGE RECORDS

JA FE MA AP MA JN JL AU SE OC NO DE

1. 0.470 0.710 0.610 0.520 0.560 1.350 1.36 0.840 0.980 1.370 1.360 1.260

2. 0.470 0.690 1.360 0.520 1.320 1.320 1.340 0.810 0.970 1.350 1.350 1.240 3. 0.470 0.680 1.330 0.510 1.290 1.260 1.310 1.780 1.420 1.320 1.310 1.210

4. 0.460 1.270 1.310 0.50 1.260 1.210 1.280 1.760 1.380 1.280 1.270 1.190

5. 0.460 1.250 1.280 0.690 1.180 1.120 1.250 1.760 1.360 1.240 1.240 1.170

6. 0.460 1.230 1.250 0.670 1.130 0.940 1.210 1.710 1.320 1.460 1.210 1.140 7. 0.460 1.220 1.210 0.640 0.970 0.890 1.170 1.650 1.190 1.430 1.170 1.110

8. 0.460 1.210 1.180 0.630 0.960 0.850 1.120 1.620 1.190 1.390 1.165 0.970

9. 0.460 1.190 1.140 0.630 0.950 0.810 1.240 1.530 1.370 1.350 1.140 0.940 10. 0.460 1.430 1.110 0.620 0.980 0.780 1.210 1.480 1.340 1.310 1.120 0.910

11. 0.460 1.410 0.950 0.60 0.940 1.240 1.150 1.440 1.310 1.260 0.960 0.860

12. 0.460 1.380 0.890 0.590 0.910 1.220 1.110 1.410 1.290 1.225 0.930 0.830

13. 0.460 1.350 0.830 0.580 0.880 1.180 0.940 1.320 1.230 1.180 0.880 0.790 14. 0.460 1.330 0.780 0.560 0.870 1.130 0.920 1.170 1.890 1.130 0.880 0.750

15. 0.450 1.290 1.150 0.530 0.840 1.10 0.920 1.140 1.860 1.110 0.870 0.730

16. 0.450 1.260 1.140 0.510 0.810 0.890 0.790 0.970 1.810 0.960 0.850 0.710 17. 0.450 1.180 1.120 0.740 0.980 0.850 0.750 0.930 1.640 0.950 1.230 0.670

18. 0.450 1.120 0.880 0.710 0.960 0.970 1.560 1.590 0.930 1.190 0.630

19. 0.450 0.940 0.940 0.620 0.940 0.920 1.470 1.530 0.880 1.160 1.160 20. 0.450 0.860 0.890 0.610 0.910 0.8750 1.430 0.840 1.480 0.840 1.110 1.120

21. 0.450 0.770 0.850 0.80 0.870 1.460 1.350 0.790 1.480 1.260 0.970 0.980

22. 0.450 0.690 0.810 0.780 0.860 1.410 1.310 0.780 1.560 1.240 0.940 0.960

23. 0.450 0.650 0.760 0.940 0.840 1.380 1.260 0.780 1.510 1.210 0.910 0.940 24. 0.450 0.630 0.730 0.890 0.830 1.340 1.190 0.760 1.490 1.180 0.870

25. 0.450 0.610 0.650 0.840 0.810 1.290 1.130 1.540 1.440 1.160 0.830

26. 0.450 0.630 0.820 0.8150 1.230 1.110 1.510 1.30 1.130 27. 0.50 0.940 0.80 1.170 0.980 1.430 1.280 1.130

28. 0.580 0.780 1.140 0.970 1.370 1.250 1.110

29. 0.580 1.10 0.940 1.280 1.220 1.350 30. 0.950 0.880 1.220 1.180 1.330

31. 0.850 1.280


Page 51

APPENDIX 4b: ERO-OMOLA DAILY DISCHARGE DATA GENERATED FROM

RATING EQUATIONS

JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV. DEC.

6.177174 4.908227 3.220095 5.285807 4.39994 16.81515 6.69059 9.710066 25.10431 6.596982 40.0246 6.436129

6.177174 4.866968 3.580008 5.285807 15.32033 15.98317 5.961412 9.188874 25.00153 6.083954 39.21961 5.849132

6.177174 4.846234 3.526813 5.179227 14.81635 14.38943 4.997536 30.33735 29.11878 5.375985 36.10292 5.052638

6.143801 4.977332 3.491306 5.072749 14.31767 13.13217 4.172423 29.82176 28.78787 4.538261 33.14867 4.573558

6.143801 4.941396 3.437978 7.111751 13.01432 11.02913 3.468662 29.82176 28.62025 3.810526 31.03733 4.132919

6.143801 4.905325 3.384568 6.895667 12.21975 7.425568 2.692434 28.54602 28.28052 9.363992 29.01366 3.538591

6.143801 4.887238 3.313222 6.572137 9.785568 6.563412 2.07219 27.04043 27.13168 8.352634 26.44905 3.017209

6.143801 4.869116 3.25961 6.464457 9.63913 5.916092 1.47465 26.29813 27.13168 7.144881 26.13904 1.34786

6.143801 4.832767 3.187988 6.464457 9.493383 5.305987 3.258302 24.1139 28.70424 6.083954 24.62371 1.117108

6.143801 4.260239 3.134162 6.356861 9.932695 4.872554 2.692434 22.9286 28.45114 5.155574 23.45263 0.920239

6.143801 4.225299 3.845396 6.141925 9.348334 13.87884 1.811779 21.99512 28.19463 4.16139 15.34218 0.656458

6.143801 4.17267 3.736305 6.034587 8.917403 13.3785 1.375151 21.30374 28.02165 3.56359 14.05814 0.530933

6.143801 4.119771 3.626727 5.927339 8.492889 12.40842 0.376723 19.2753 27.49286 2.900073 12.07411 0.395209

6.143801 4.084351 3.535013 5.713116 8.352831 11.25274 0.31862 16.05198 32.64694 2.285048 12.07411 0.289702

6.110057 4.013134 3.205908 5.392488 7.937058 10.58941 0.31862 15.43175 32.43867 2.071102 11.70014 0.246485

6.110057 4.959381 3.187988 5.179227 7.527987 6.563412 0.097263 12.07878 32.08701 0.931326 10.9745 0.208776

6.110057 4.814538 3.152114 7.653285 9.932695 5.916092 0.064891 11.33128 30.84575 0.879158 30.35311 0.147625

6.110057 4.704389 3.718077 7.328141 9.63913 7.971455 19.47948 0 30.46609 0.781983 27.71247 0.102181

6.110057 4.365158 3.827246 6.356861 9.348334 7.073591 12.26209 0 30.00091 0.576867 25.83136 3.926227

6.110057 4.209575 3.736305 6.24935 8.917403 6.316277 9.891046 9.710066 29.60483 0.446536 22.88066 3.183363

6.110057 4.030405 3.663309 8.305489 8.352831 20.06854 6.316835 8.846894 29.60483 4.16139 15.78618 1.433073

6.110057 4.866968 3.590086 8.087812 8.213503 18.54999 4.997536 8.677568 30.23484 3.810526 14.47823 1.266908

6.110057 4.783594 3.49822 9.836372 7.937058 17.67071 3.690762 8.677568 29.84342 3.329906 13.24144 1.117108

6.110057 4.741457 3.44291 9.288251 7.79995 16.53521 2.36464 8.34228 29.68468 2.900073 11.70014 0

6.110057 4.699005 3.294663 8.741637 7.527987 15.17465 1.580367 24.35339 29.28214 2.63961 10.27818 0


Page 52

SUM 78.32396 64.08454 48.59602 166.9248 241.1845 284.7805 102.4264 423.8826 726.7812 97.94532 557.6962 49.48943

MEAN 6.02492 4.92958 3.738155 12.84037 9.647381 11.39122 4.097057 16.95531 29.07125 3.917813 22.30785 1.979577

MIN 3.110057 1.699005 1.220095 5.072749 4.39994 4.872554 0.064891 0 25.00153 0.446536 10.27818 1.793888

MAX 3.177174 3.260239 2.580008 9.836372 15.32033 20.06854 19.47948 30.33735 32.64694 97.94532 40.0246 5.849132

APPENDIX 5a: OWU FALL DAILY GAUGE

READINGS

JA FE MA AP MA JN JL AU SE OC NO DE

1. 0.48 0.42 0.43 0.42 0.43 0.88 0.48 0.88

2. 0.48 0.42 0.43 0.44 0.43 0.87 0.48 0.87

3. 0.48 0.42 0.43 0.44 0.43 0.87 0.48 0.87

4. 0.48 0.42 0.43 0.44 0.43 0.89 0.48 0.89

5. 0.48 0.42 0.43 0.44 0.42 0.88 0.48 0.88

6. 0.48 0.42 0.43 0.44 0.42 0.87 0.48 0.87

7. 0.48 0.42 0.43 0.45 0.42 0.86 0.48 0.86

8. 0.48 0.42 0.43 0.45 0.42 0.86 0.48 0.865

9. 0.47 0.42 0.43 0.44 0.42 0.85 0.47 0.85

10. 0.47 0.42 0.42 0.44 0.42 0.84 0.47 0.84

11. 0.47 0.42 0.43 0.44 0.42 0.84 0.47 0.84

12. 0.47 0.42 0.43 0.44 0.42 0.63 0.47 0.83

13. 0.47 0.43 0.43 0.44 0.43 1.52 0.47 1.52

14. 0.47 0.43 0.43 0.44 0.42 1.49 0.47 1.49

15. 0.47 0.43 0.43 0.43 0.42 1.42 0.47 1.42

16. 0.47 0.43 0.42 0.43 0.42 1.3 0.47 1.3

17. 0.47 0.43 0.42 0.44 0.42 1.11 0.47 1.11

18. 0.47 0.43 0.41 0.44 0.42 0.95 0.47 0.95

19. 0.47 0.43 0.43 0.48 0.43 0.92 0.47 0.92

20. 0.47 0.43 0.41 0.48 0.43 0.83 0.47 0.83


Page 53

21. 0.47 0.43 0.42 0.46 0.43 0.79 0.47 0.79

22. 0.47 0.43 0.42 0.44 0.48 0.76 0.47 0.76

23. 0.47 0.43 0.42 0.44 0.46 0.76 0.47 0.76

24. 0.47 0.43 0.44 0.44 0.46 0.74 0.47 0.74

25. 0.47 0.43 0.43 0.44 0.45 0.69 0.47 0.69

26. 0.47 0.43 0.42 0.47 0.45 0.67 0.47 0.98 0.67

27. 0.47 0.43 0.42 0.44 0.67 0.47 0.97 0.675

MEAN

NO OF

DAYS=217

APPENDIX 5b: OWU STREAMFLOW DISCHARGE DATA GENERATED FROM THE RATING

EQUATIONS

JANUARY FEBRURY MARH APRIL MAY JUNE JULY AUGUST SEPTEMBER

4.268554

3.573975 3.687593 3.573975 3.687593

9.558547 4.268554

4.268554

3.573975 3.687593 3.802086 3.687593

9.414354 4.268554

4.268554

3.573975 3.687593 3.802086 3.687593

9.414354 4.268554

4.268554

3.573975 3.687593 3.802086 3.687593

9.703281 4.268554

4.268554

3.573975 3.687593 3.802086 3.573975

9.558547 4.268554

4.268554

3.573975 3.687593 3.802086 3.573975

9.414354 4.268554

4.268554

3.573975 3.687593 3.917442 3.573975

9.270707 4.268554

4.268554

3.573975 3.687593 3.917442 3.573975

9.270707 4.268554

4.150688

3.573975 3.687593 3.802086 3.573975

9.12761 4.150688

4.150688

3.573975 3.573975 3.802086 3.573975

8.985068 4.150688

4.150688

3.573975 3.687593 3.802086 3.573975

8.985068 4.150688

4.150688

3.573975 3.687593 3.802086 3.573975

6.128481 4.150688

4.150688

3.687593 3.687593 3.802086 3.687593

19.77342 4.150688

4.150688

3.687593 3.687593 3.802086 3.573975

19.25607 4.150688

4.150688

3.687593 3.687593 3.687593 3.573975

18.06231 4.150688


Page 54

4.150688

3.687593 3.573975 3.687593 3.573975

16.06107 4.150688

4.150688

3.687593 3.573975 3.802086 3.573975

13.01696 4.150688

4.150688

3.687593 3.461246 3.802086 3.573975

10.58284 4.150688

4.150688

3.687593 3.687593 4.268554 3.687593

10.14069 4.150688

4.150688

3.687593 3.461246 4.268554 3.687593

8.843084 4.150688

4.150688

3.687593 3.573975 4.033646 3.687593

8.280831 4.150688

4.150688

3.687593 3.573975 3.802086 4.268554

7.86524 4.150688

4.150688

3.687593 3.573975 3.802086 4.033646

7.86524 4.150688

4.150688

3.687593 3.802086 3.802086 4.033646

7.591159 4.150688

4.150688

3.687593 3.687593 3.802086 3.917442

6.916704 4.150688

4.150688

3.687593 3.573975 4.150688 3.917442

6.651344 4.150688

4.150688

3.687593 3.573975 3.802086 0

6.651344 4.150688

4.185611

3.637096 3.641402 3.849742 3.560487

10.23664 4.185611


Page 55

APPENDIX 5:

OWU FALL STREAM FLOW DATA


Page 56

APPENDIX 6:

EXTENDED STREAMFLOW DATA

(2009-2034) AT ERO-OMOLA


Page 57

APPENDIX 7:

STAGE DISCHARGE RECORDS OF

RIVER AKAMO AND OSHIN


Page 58

APPENDIX 8:

STREAMFLOW DATA TRANSFORM

TO NATURAL LOGARITHM


Page 59

APPENDIX 9:

PHCN TARIFFS


Page 60

APPENDIX 10:

SCANED COPY OF HYDROGRAPH OF

RIVER OSIN AND AKAMO INCLUDING

THE RAW DATA AS OBTAINED FROM

THE LOWER NIGER RIVER BASIN

AUTHORITY


Page 61

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