University of Benin (UNIBEN) Water Resources and Petroleum Engineering Courses from 1st year to final year. Course Content and Structure to guide UNIBEN Students, Aspirants, Jamb Candidates and the General Public.
Watch Free UNIBEN Tutorial Videos here, Click Here for UNIBEN 100 Level Engineering Courses or Continue reading for the University of Benin Faculty of Engineering, Department of Water Resources and Petroleum Engineering Courses for First and Second Semester.
Recommended: Uniben courses for all departments
UNIBEN Water Resources and Petroleum Engineering Courses
First Semester 100 Level
S/N  Course Code  Course Title  LT  Lab  Credit Units  Course Status 

1  MATH 101  Set Theory and Number System  2  2  Cognate Course  
2  MATH 103  Trigonometry and Coordinate Geometry  2  2  Cognate Course  
3  MATH 105  Differential and Integral Calculus  2  2  Cognate Course  
4  COSC 101  Programming in Basic  2  2  Cognate Course  
5  PHYS 111  Mechanics  2  2  Cognate Course  
6  PHYS 161  General Physics Practical I  3  Cognate Course  
7  CHEM 101  Introduction to General Chemistry  2  2  Cognate Course  
8  CHEM 121  Introduction to Inorganic Chemistry  2  2  Elective  
9  CHEM 191  Introduction to Practical Chemistry I  2  1  Cognate Course  
10  ENGG 101  Introduction to Engineering  1  1  Cognate Course  
11  GENS 101  Nationalism  1  1  General Studies  
12  GENS 103  English for Communication Skills  2  2  General Studies  
13  GENS 107  History of Scientific Ideas  1  1  General Studies  
14  PHYS 131  Heat and Properties of Matter  2  2  Cognate Course 
Second Semester
S/N  Course Code  Course Title  LT  Lab  Credit Units  Course Status 

1  CHEM 122  Introduction to Physical Chemistry II  2  2  Cognate Course  
2  MATH 102  Algebra  2  2  Cognate Course  
3  MATH 104  Comic Sections and Application of Calculus  2  2  Cognate Course  
4  MATH 106  Vector and Dynamics  2  2  Cognate Course  
5  STAT 102  Introductory Statistics  2  2  Cognate Course  
6  PHYS 122  Electricity, Modular and Magnetic Physics  3  Cognate Course  
7  PHYSC 124  Geometric and Wave Optics  2  2  Cognate Course  
8  GENS 102  Environmental Health  2  2  Cognate Course  
9  CHEM 132  Introduction to Organic Chemistry  2  1  Elective  
10  CHEM 192  Introductory Practical Chemistry II  2  2  Elective 
First and Second Semesters 200 Level Courses
First Semester
S/N  Course Code  Course Title  LT  Lab  Credit Units  Course Status 

1  MATH 241  Calculus I  2  2  Cognate Course  
2  MATH 243  Methods of Linear Algebra  2  2  Cognate Course  
3  EEEN203  Electrical Machine, Power and Installation  2  2  Cognate Course  
4  CVEN 201  Introduction to Structural Analysis  2  2  Cognate Course  
5  EEEN203  Electrical Machine, Power and Installation  2  2  Cognate Course  
6  MEEN 201  Engineering Graphics  1  Cognate Course  
7  MTEN 201  Material Science  1  2  Cognate Course  
8  WREN 201  Fluid Mechanics I  1  2  Core Course  
9  GENS 201  Moral Philosophy  1  1  General Studies  
10  ARCH 101  Graphic Communications I  1  1  Non Compulsory Elective  
11  URPL 205  Urban Land Use Components  1  1  Non Compulsory Elective 
Second Semester
S/N  Course Code  Course Title  LT  Lab  Credit Units  Course Status 

1  CHEM 202  Introduction to Engineering Management  1  1  Cognate Course  
2  MEEN 202  Engineering Drawing  2  2  Cognate Course  
3  MEEN 204  Strength of Materials I  2  2  Cognate Course  
4  MEEN 206  Fundamental of Dynamics  2  2  Cognate Course  
5  MEEN 208  Basic Thermodynamics  2  2  Cognate Course  
6  MEEN 202  Electronics Measurement and Transducers  1  Cognate Course  
7  MATH 242  Calculus II  2  2  Cognate Course  
8  MATH 244  Methods of Linear Algebra II  3  3  Cognate Course  
9  GENS 202  Entrepreneurship and Innovations  2  1  Cognate Course 
First and Second Semesters 300 Level Courses
First Semester 1
S/N  Course Code  Course Title  LT  Lab  Credit Units  Course Status 

1  MATH341  Differential Equation and Transforms  3  3  Cognate Course  
2  STAT343  Statistics  2  2  Cognate Course  
3  WREN301  Fluid Mechanics II  1  2  Core Course  
4  WREN303  Engineering Soil Science I  1  1  Core Course  
5  CVEN 301  Theory of Structures I  2  2  Cognate Course  
6  CVEN 303  Reinforced Concrete Fundamentals  3  Cognate Course  
7  CVEN305  Mechanics of Materials  2  2  Cognate Course  
8  CVEN321  Soil Mechanics  2  2  Cognate Course  
9  CVEN331  Civil Engineering Materials 1  2  2  Cognate Course  
10  LNSV331  Surveying for Professionals  1  1  Cognate Course  
11  QTYS309  Development Economics  3  3  Cognate Course  
12  ARCH203  Architectural Graphics 1  2  2  Non Compulsory Elective  
13  MICR281  Introduction to Microbiology  1  1  Non Compulsory Elective  
14  URPL303  Transport Planning  2  2  Non Compulsory Elective  
15  WREN305  Water Resources for Quantity Surveyors  2  2  
16  WREN307  Aspect of Water Resources to Land Surveying  2  2 
Second Semester 3
S/N  Course Code  Course Title  LT  Lab  Credit Units  Course Status 

1  MATH 342  Functions of Several Variables  2  2  Cognate Course  
2  COSC 344  Basic Computer Knowledge and Fortran Programming  3  3  Cognate Course  
3  WREN 302  Fluid Mechanics III  2  2  Core Course  
4  WREN 304  Engineering Soil Science II  2  2  Core Course  
5  CVEN 302  Theory of Structures II  2  2  Cognate Course  
6  CVEN 304  Design of Structural Elements  3  Cognate Course  
7  CVEN 322  Geology For Engineers  2  2  Cognate Course  
8  CVEN 332  Civil Engineering Materials II  2  2  Cognate Course  
9  LNSV 332  Surveying for Professionals  2  2  Cognate Course  
10  ARCH 204  Architectural Graphics II  2  2  Non Compulsory Elective  
11  URPL 208  Urban Economics  2  2  Non Compulsory Elective  
12  URPL 206  Site Planning  2  2  Non Compulsory Elective  
13  MICR 282  General Microbiology  2  2  Non Compulsory Elective  
14  GEOL 301  Geophysics  1  1  Non Compulsory Elective 
First and Second Semesters 400 Level Courses
S/N  Course Code  Course Title  LT  Lab  Credit Units  Course Status 

1  COSC 441  Numerical Analysis  3  3  Cognate Course  
2  STAT 443  Experimental Design and Control  2  2  Cognate Course  
3  WREN 401  Hydraulics and Hydrology  3  3  Core Course  
4  WREN 403  Design of Hydraulic Structures  3  3  Core Course  
5  WREN 405  Soil and Water Conservation  1  1  Core Course  
6  WREN 407  Chemistry and Microbiology of Water and Wastewater  1  Core Course  
7  CVEN 407  Design of Structural Elements  2  2  Cognate Course  
8  WREN 409  Computer Methods  2  2  Core Course  
9  CVEN 421  Geotechnics and Design of Foundations  2  1  Cognate Course  
10  QTYS 421  Law for Engineers  1  1  Cognate Course  
11  GEOL 405  Hydrogeology  3  3  Elective  
12  MATH 441  Complex Analysis  2  2  Elective 
Second Semester
SIWES 499: Students Industrial Works Experience Scheme II (SIWES II) FOR 22 WEEKS. 6 Credit Unit. PREREQUISITE not less than 72 TCUE
First Semester 500 Level
S/N  Course Code  Course Title  LT  Lab  Credit Units  Course Status 

1  WREN 501  Hydraulics  2  2  Core Course  
2  WREN 503  Engineering Hydrology  2  2  Core Course  
3  WREN 505  Unit Operations and Processes in Water Treatment  2  2  Core Course  
4  WREN 507  Water and Waste Water Engineering  2  2  Core Course  
5  WREN 509  Irrigation  2  2  Core Course  
6  WREN 515  Engineering Design I  1  Core Course  
7  WREN 511  Environmental Pollution and Control  2  2  Core Course  
8  WREN 597  Final Year Project I  3  Core Course  
9  QTYS 503  Civil Engineering Measurement I  2  2  Cognate Course  
10  URPL 309  Rural Settlement Planning  2  2  Non Compulsory Elective  
11  URPL 311  Resources Planning  2  2  Non Compulsory Elective 
Second Semester 500 Level
S/N  Course Code  Course Title  LT  Lab  Credit Units  Course Status 

1  WREN 502  Water Power Systems Engineering  2  2  Core Course  
2  WREN 504  Rural Water Supply and Sanitation  2  2  Core Course  
3  WREN 506  Elements of Public Health  2  2  Core Course  
4  WREN 508  Drainage Engineering  2  2  Core Course  
5  WREN 512  Unit Operations and Processes in Wastewater Treatment  2  2  Core Course  
6  WREN 510  Engineering Design II  1  Core Course  
7  WREN 516  Environmental Impact Assessment  2  2  Core Course  
8  QTYS 508  Civil Measurement II  2  2  Conate Course  
9  WREN 598  Final Year Project II  3  Core Course  
10  WREN 514  Environmental Engineering for Civil Engineers  2  2  
11  CHEN 409  Financial Management  2  2  Non Compulsory Elective  
12  GEOL 402  Geophysics  2  2  Non Compulsory Elective 
100 Level Courses
ENGG 101: ENGINEERING PROFESSION AND INSTITUTION (1 CREDITS) 

Development of professional engineering history of technology and its effect on society, the engineering institutions, their objectives and functions. Data measurement, representation and interpretation, report writing and oral presentation of information 
GENS 102: ENVIRONMENTAL HEALTH 
Introduction to Engineering Health: Concept of environment: Concept of health: Concept of environmental health. Relationship between environmental hazards and their effects on health. Environmental hazards and examples. Sources of environmental hazards. Effects on Human health. Control of environmental hazard. ACCIDENT Definition, Distribution, types, human factor, causes, control of Accident, prevention should focus on, first Aid, contributions of students to environmental protection. The need, their contributions leadership. Violence at Home and society, Definition of Violence. Type of violence. Cause of violence. Cultural values that constitute violence in the family. Prevention and control of violence. Conservation of Natural resources. Soil Air Water relationship. Soil Water plant relationship. Plant Animal Man relationship. Environmental friendly situation. Conservation of renewable and nonrenewable natural resources. Need for environmental impact assessment studies. 
200 Level Courses
CVEN 201: FUNDAMENTALS OF STRUCTURAL ANALYSIS (2 CREDITS) 

Concept of Structural analysis, Stability and determinacy of frameworks. Analysis of statistically determinate structures. Bending moment and shear force diagrams for determinate beams. Beam deflection. Framework deflections and strain energy in frames. Suspension cables. Determinate arches, stability of gravity sections. 
WREN 201: FLUID MECHANICS I (2 CREDITS) 
Properties of Fluids: Pressure, viscosity, surface tension, compressibility etc. Hhydrostatics: Variation of pressure with position in a fluid, equilibrium of a fluid of constant density, measurement of pressure, barometer, manometer, the Bourdon gauge, thrust on plane and curved surfaces, buoyancy, stability of floating and submerged bodies. Principles of Fluid Motion: Continuity, Bernoulli’s equation, energy transformation in a constant density fluid, energy correction factor, streamlines, pressure variation perpendicular to streamlines, flow through a sharp edged orifice, pilot tube, venturi meter, nozzle and orifice meter, notches and sharp crested weirs. Momentum Equation: Momentum equation for steady flow, momentum correction factor, application of the momentum equation, force caused by a jet striking a surface, force caused by flow round pipe bend, force at a surface, force at a nozzle and reaction of a jet under short wheel as an example of a simple hydraulic machine. 
MEEN 201: ENGINEERING GRAPHICS (2 CREDITS) 
The principles of engineering drawing, engineering lettering, figures and types of lines (BS 308 – 1972, Part 1, 2, 3), dimensioning, useful geometrical constructions, principles of tangency, lociconk sections (ellipse, hyperbola, parabola); cycloids, epicycloids, hypocycloids, involutes, helices, orthographic project (1st and 3rd angle orthographic projection). 
MEEN 202: ENGINEERING DRAWING (2 CREDITS) 
Isometric projection; free hand sketching, sections and sectional views, auxiliary projections, interpretation of surfaces, development of surfaces, screw threaded and threaded screwed fastenings, conventional representation on the threaded elements on drawing. 
MEEN 204: STRENGTH OF MATERIALS (2 CREDITS) 
Direct stress and stain: tension, compression. Hook’s law elastic constants, strain energy, impact load, thermal stress. Geometrical properties of areas: centroid, first and second moments of area, parallel axis theorem, product moment of area, cross sections having and not having axes of symmetry. Simple theory of bending : Classification, bending moment and shear force diagrams, relations between bending moment, shear force and load, bending stress section modulus, strength requirements, combined bending and tension/compression, eccentric loading, unsymmetrical bending, compound bars deflection of beams. Simple shear force: Shear stress, shear strain, Hooke’s law technical shear. Torsion of circular crosssections: Torque diagram angle of twist, shear stress due to torsion, transmission to power by shafts, helical springs. Special problems statistically indeterminate problems, thin cylinders and spheres under pressure. 
MEEN 206: FUNDAMENTALS OF DYNAMICS (2 CREDITS) 
Kinematics of particles: rectilinear motion, plane curvilinear motion, appropriate choice of reference frame in solving problems. Relative motion, translating axes. Kinetics of particles: Newton’s second Law of Motion, Work and Kinetic energy method for deriving equations of motion, Impulse and momentum. Kinetics of systems of particles: Defining equations, Steady mass flows, Variable mass problems. Plane kinematics of rigid bodies; Absolute motion, Relative Velocity, Instantaneous center of zero velocity, Relative acceleration. Plane kinetics of rigid bodies: General equation of motion, Translation, Fixedaxis rotation. General plane motion, Work energy relations, Impulse and momentum equations for rigid bodies. 
MEEN 208: BASIC THERMODYNAMICS (2 CREDITS) 
Dimensions and Units: (S.I. Units to be Introduced): Fundamental concepts: Energy i.e. Potential, Kinetic, internal; property, state, process and cycle system and surroundings; pressure; temperature, Zeroth law, arbitrary nature of temperature, scales; equilibrium reversibility, heat and work. First Law of Thermodynamics: As applied to closed and flow systems, and in the cyclic and concyclic (process) forms, as well as in the differential form; Application to particular processes of constant volume; constant pressure, Isothermal, adiabatic, polytropic and throttling; the flow energy equation and its application to turbines, compressors, nozzles, boilers, condensers, heat exchangers (treated as black boxes only). , Second Law of Thermodynamics: Definition of heat engines, Cannot cycles, thermodynamic temperature scale, entropy (as a property) Properties of Pure Substances: Condensible fluids: TP diagram, PV diagram, the twophase mixture, TS diagram, hs diagram, the use of property tables and diagrams Perfect Gases: Properties of perfect gas; entropy changes in perfect gases. 
MTEN 201 – MATERIALS SCIENCE (2 CREDITS) 
Physical properties of materials: structure of atoms, bonding forces, structure of matter, including mention of wood, cement and plastics. Electrical properties of materials: electrical properties, conductors, electronic properties, semi and superconductors, magnetic properties, dielectric properties. Mechanical properties: Elastic –plastic deformation of materials, Temperature effects n mechanical properties, Fatique, Creep, Hardness, Mechanical working. Thermal properties: Thermal capacity, thermal expansion, thermal conductivity, thermocouple phenomenon, temperature consideration in the choice of materials. Chemical properties of materials: corrosion phenomenon and its prevention. Metallurgy; structure of crystalline materials, solidification, mechanical working, liquid and solid solutions, introduction to the concepts of phase and solid solutions, introduction to the concepts of phase equilibrium, micro and macrostructure of materials. Nonmetallic materials: Cement, concrete, wood, Ceramics (Glass, ceramic ware), Plastic (Wood, Rubber etc) and resin. 
MATH 241: CALCULUS I (3 CREDITS) 
Sequences and Functions: Infinite sequences and their limits, a short recollection of elementary functions and their properties, limits and continuity of functions of a single independent variable. Differential Calculus: Definition of thee derivative. Differentiability of a function of one independent variable; geometrical and physical interpretation of the derivative, techniques of differentiation, Rolle’s theorem and the meanvalue theorem, Taylor and Maclaurin’s series expansion, application of differentiations maxima and minima of function of a single differentiations maxima and minima of function of a single independent variable, curve sketching in Cartesian rectangular coordinates, L’Hospital rule for evaluation of limits of functions in the indeterminate forms, tangents and normals, curvatures and evolutes of plane curves, Laibnitz’s formula, for finding the nth differential coefficient of a product of two functions. Integral calculus: indefinite integral, techniques of integration – change of variable, integration by parts and reduction formulae, integration of rational functions (standard integral and methods of partial fractions), the definite integral interpretation and properties; applications of integration, average value of a function, finding lengths of areas, plane areas, volumes of solids of revolution area of surface of revolution, pressure, etc. 
MATH 242: CALCULUS II (3 CREDITS) 
Infinite number series and their properties, tests of convergence complex number series. Improper integral: Improper integral of types I, II and III. Evaluation of improper integral, convergence of improper integral, Convergence in the Cauchy Principal value, tests of convergence. Partial differentiation: partial derivatives of functions of two or three variables, total differentials and applications. Ordinary differential equations: First order differential equations with variables separable, exact equations and integrating factors; linear first order equations and those reducible to linear form. The Bernouli equation, applications (geometrical and physical situations). 
MATH 243: METHODS OF LINEAR ALGEBRA I (2 CREDITS) 
Complex numbers: addition, multiplication, division, argand diagram, polar representation, DeMoivre’s theorem. Vector Algebra: Definition of Vector and Physical examples, addition, multiplication by scalar, scalar and vector products, triple products, components, applications in geometry. Vector Analysis: Cartesian and polar coordinates in two and three dimensions. Vector functions of a real variable, continuity and differentiation, application to curves and surfaces in 3 space equation of straight lines, plane and sphere, tangent and normals to a curve, tangent plant and normal to a surface. 
MATH 244: METHODS OF LINEAR ALGEBRA II (3 CREDITS) 
Determinants and matrices: definition and properties of the determinant, its evaluation, matrices addition, multiplication by scalar, adjugate, inverse of nonsingular matrix, rank and its evaluation. Simultaneous linear equations, consistency, linear dependence, solution (including Cramer’s rule) eight values and eigenvectors, special matrices, symmetric, skew symmetric orthogonal etc. 
ENGG 101: ENGINEERING PROFESSION AND INSTITUTION (1 CREDIT) 
Development of professional engineering: history of technology and its effect on society, the engineering institutions, their objectives and functions. Data measurement, representation and interpretation, report writing and oral presentation of information. 
CHEN 202: INTRODUCTION TO MANAGEMENT (1 CREDIT) 
Introduction (definition, uses and types of organization, need for management, the manager and his functions), planning, decision making, organizing, directing and leadership (motivation, communication and leadership), control. 
EEEN 201: ELECTRICAL CIRCUITS AND FIELD THEORY (2 CREDIT) 
CIRCUIT ELEMENTS: Basic circuit elements and their analogues in mechanical systems. Energy storage and energy conversion by means of these basic elements: D.C. CIRCUIT: Linearing and methods of analysis. Basic circuit theorems. D.C. steady state circuit response. Transients in 1st order circuits. A.C. CIRCUIT: Representation of A.C. variables; time domain; Power in A.C. Circuits. Balanced three phase systems ; voltage ,current and power relationships. Rectification principles ,simple derivation for S/ phase types and descriptive treatment for 3 phase . Field Theory: Electric: Electric charges, Coulomb’s Law, Gauss’ Law. Electric field. Electric dipoles, potentials, capacitance, work energy. Magnetic: Magnetic forces between current elements, BiotSavart Law. Ampere’s Law. Lenz’s law, Lorentz Law. Motor Principle. Generator principle. Work Energy. 
EEEN 203: ELECTRICAL MACHINE, POWER AND INSTALLATION (2 CREDIT) 
Transformers and Rotating Machines: Basic Principles: Induction (Faradays Law), interation (BiotSavats Law), and alignment. Generalized Basic Units: Magnetic, electrical, mechanical and thermal. Qualitative analysis of the production of torque and rotation of electric machines. Generalized torque equation of electric machines and simple calculations. Transformer; Constructional features, types, connections (including 3phase tpe) and application of various types. DC Machines: Constructional features, types (separately excited, shunt, series and compound), and application. Induction Machines: Constructional features, types (single –phase and 3phase), types of rotor (squirrel cage and wound or slipring) and application. Synchronous Machines: Constructional features, types (salient or nonsalient poles types), and application. Brief Introduction and Application of Special Machines: A.C. commutator machines, general purpose machines, repulsion machine, linear motors, etc. Electric Power Generation, Transmission and Distribution Types of Power stations. Power generation and transmission problems (Flow diagram representation from generator to consumer terminals). The synchronous generation and its importance in power generation (from small types) in motor cars to huge types in power stations. Transmission of electric power; The H.T. overhead lines and stepup power transformers in overhead lines (330 K V lines). Distribution of electric power using overhead lines and underground cables (show typical underground cables). The distribution transformers in power distribution and their use in the design of estates a.c. and d.c supplies. The use of a.c. in preference to d.c., stressing the importance of the transformer. Single and three phase supplies; (delta and star connections); typical 3phase, 4wire distribution systems. Two wire services and typical consumer circuits. The meaning of impedance (X), volts (V), power ohms and power factor (PF) in a.c. supply systems. Wiring System Supply, control and distribution in buildings including; intakes, diversity, wiring circuits for lighting using loop methods, number of points on one circuit, wiring socket outlets. Conductors and cables including; main parts of cables, types of insulators and the choice of cable sizes in various types of installation. Wiring systems including: Conduct systems, rubber and PVC soothed systems; components and accessories used in wiring systems, ceiling roses, lamp holders, switches etc. Safety precaution including, the need for safety, the use of circuit breakers and fuses, and the importance of earthling. Illumination: Principle of illumination, definition of terms and the inverse square law. Glare and its effects. Types of lamps and lamp fittings. Principle of lighting design and illumination requirement for various types of usual tasks. 
300 Level Courses
WREN 301: FLUID MECHANICS II (2 CREDITS) 

Types of Flows: Turbulent and laminar flows; Reynolds number, transitional flows. Laminar Flow: Laminar flow between narrow plates, laminar flow between two parallel plates, laminar flow over a flat surface, velocity distribution and average velocity, friction factor etc. Open Channel Flow: Types of flow in open cannel (uniform, nonuniform, turbulent, laminar, steady, unsteady, critical, subcritical and super critical etc). Steady uniform, Chezy’s and Manning’s equations, DarcyWeisbach equation, hydraulically efficient sections, flow in circular conduit with free surface. Specific energy, critical, subcritical and super critical flows, Froude number, local smooth flow transitions, Venturi flume and broad crested weir. Application of momentum principles, hydraulic jump, energy dissipated in hydraulic jump, use of hydraulic jump as energy dissipator in stilling basins, baffle piers for fixing position of hydraulic jump in stilling basins. Flow in Pipes: Head lost in friction, coefficient of friction, equations for friction coefficient, Moody’s diagram, minor (local) head losses in pipes. Hydraulic energy gradients. Simple pipe problems. Pumps: Centrifugal pumps, Specific speed and characteristics. Use of characteristics in selecting pumps, operating points and system equation, specific speed, multistage pumps etc. Pipeline with pumps. 
WREN 302: FLUID MECHANICS III (2 CREDITS) 
Laminar flow: Laminar flow between narrow plates, Laminar flow between two parallel plates, Laminar flow over a flat surface, Velocity distribution and average velocity, friction factor etc. Laminar flow in pipes, velocity distribution, some types of viscometers: Turbulent Flow of Pipes: phenomenological theory of turbulent flow, mixing length etc., logarithmic law of velocity distribution, laminar boundaries layer and its thickness, surface roughness, smooth and rough turbulent flows and logarithmic velocity distribution laws for these flows Pipes in parallel and series, branched pipes, simple pipe networks, use of the Hardy Cross methods, networks connecting reservoirs. Unsteady flow in pipes, water hammer, rapid and slow closure of valves, surge analysis in surge tanks. Dimensional Analysis and Hydraulic Modelling: Dimensional homogeneity, grouping variables in dimensional relation using power method, Pitheorem, dimensionless groups, significance of dimensionless numbers, and use of dimensional considerations in extrapolating data. Hydrodynamics: Ideal fluid, unsteady differential equation of compressible fluids, continuity equation for incompressible three, two and onedimensional flows cases. Circulation and vorticity, potential flow (irrotational), rotational flow, stream function, Laplace equation for potentials flow, CauchyRiemann equation. Euler’s equations of motion, effect of viscosity modification of Euler’s equations to Navier – stokes equations, Bernoulli equation for ideal fluids. Standard cases of potential flow e.g. uniform flow, line source and sink, irrotational vortex, combination of flow patterns, flow around a circular cylinder, etc. Hydraulic Machines: Application of momentum principles to simple cases (revision of work done in Part I), Pelton wheel, limitations of Pelton wheels, reaction turbines, draft tubes etc. 
WREN 303: ENGINEERING SOIL SCIENCE I (1 CREDIT) 
Definition and uses of soils, soil formation, soil development, classification of soils, structure of layersilicate minerals, laterites and lateritic soils. 
WREN 304: ENGINEERING SOIL SCIENCE II (1 CREDIT) 
Physical chemistry of soils; cation and anion exchange phenomena; salinity and alkalinity of soils, quality of irrigation waters, soil waterair relationship; infiltration, evaporation, consumptive use, and movement of soil water. 
CVEN 301: THEORY OF STRUCTURES I (3 CREDITS) 
PREREQUISITE: CVEN 201 Review of Bending Moment and Shear forces in determinate beams, Frames and Trusses. Principles of Indeterminacy and Static stability of Plane Frames and Trusses. Moment Area Method. Force (Flexibility) Method. Applications to indeterminate beams and simple frames. Flexibility coefficients – practical interpretation. Compatibility equations. Virtual work method principles of virtual displacements. Applications to beams, trusses and plane frames. Use of 1st and 2nd theorems of castigliano in Structural Analysis. 
CVEN 302: THEORY OF STRUCTURES II (3 CREDITS) 
PREREQUISITE: CVEN 201 Influence lines for reactions, shears and bending moment in determinate beams, lattice girders and three hinged arches. Maximum moments and shear envelopes slope deflection method. Moment distribution method. Analysis of indeterminate beams and frames. Analysis of two hinged tied and fixed arches including numerical methods. Introduction to Plastic Analysis. Estimation of yield and collapse loads for simple beams and plane frames using virtual work methods. 
CVEN 303: REINFORCED CONCRETE FUNDAMENTALS (2 CREDITS) 
PREREQUISITE: CVEN 201 Concept of reinforced concrete and historical development of its theory and practice. An introduction to different methods of analysis. Limit states. Review of physical and mechanical properties of concrete and reinforcement. Safety factors. Ultimate limit state of bending. Analysis and design of singly reinforced cores sections. Doubly reinforced crosssections. Flanged crosssections. bond and anchorage. shear and punching shear. 
CVEN 304: DESIGN OF STRUCTURAL ELEMENTS (3 CREDITS) 
PREREQUISITE: CVEN 201 Curtailment (development) of bars (simplified and precise). One way spanning and twoway spanning solid slabs. columns, axially, eccentrically, biaxially loaded, short and slender. Torsion in RC. Deep beams, short cantilevers. Detailing and drawings of RC structures. General characteristics of steel and other metals: classification of metal structures, skeleton and shell system. Production of steel and other metals. Advantages and disadvantages of metal products. Loading of structural steel systems. Method of analysis and design of structural elements. Structural steel connections. 
CVEN 305: MECHANICS OF MATERIALS (2 CREDITS) 
PREREQUISITE: CVEN 201 Analysis of three – dimensional state of stress in structural systems. Principal stresses and maximum shear stresses. Analysis of three – dimensional state of strain; experimental stress analysis; strain gauges and applications. Energy theorems and applications for response of statically indeterminate structural systems. Strength theories applied to failure of structural elements. Analysis/design of compound and composite structural elements. Theory and design of slender members. Critical load and stresses. Euler’s theory and its limitations. Bending of curved bars and springs. 
CVEN 321: SOIL MECHANICS (3 CREDITS) 
Lectures: Soil classification for engineering purpose. Soil as a multiphase system. Seepage analysis in one and two dimensions. The principle of effective stress. Shear strength. Laboratory: Soil classification on the basis of index properties. Particle size analysis. Soil compaction. Constanthead falling head permeability test. Direct shear on sand. Triaxial testing of Soil compressibility. 
CVEN 322: GEOLOGY FOR ENGINEERS (3 CREDITS) 
Classification of minerals and rocks. Geological structures. Maps. Surface and sedimentary processes. The collection and interpretation of geological data for engineering use. Engineering properties of intact rocks. Influence of discontinuities on rock mass behaviour. 
CVEN 331: CIVIL ENGINEERING MATERIALS I (3 CREDITS) 
Production, use and properties of cements. Production, use and properties of bricks and blocks (ceramic and sandcrete). Insulation and finishing materials (oats, papers, rendering and plasters) for roofs, floors, underground water retaining structures and foundations. 
CVEN 332: CIVIL ENGINEERING MATERIALS II (2 CREDITS) 
Production, use and properties of aggregates: concrete – mix design, quality control, special concrete (admixtures); production, use and properties of concrete; timber, Reinforcing steel bars and steel profiles for structures. 
MATH 341: DIFFERENTIAL EQUATIONS AND TRANSFORM (3 CREDITS) 
Exact equations, linear equations of first and second order with variable coefficient, geometrical interpretation, isoclines, statement of existence theorem, series solution of differential equation with nonsingular points, definition of Bessel equation and Bessel function of the first kinds, definition of Legendre equation, Legendre polynomials, Fourier integral and transforms, Laplace transform and its applications to the solution of differential equations. 
STAT 343: STATISTICS (2 CREDITS) 
Axiomatic definition of probability, basic rules of probability, Bayes formula, Random variables, probability distributions (rectangular, hypergeometric, binomial multinomial, poisson, normal, geometric, exponential, beta and gamma), Mathematical expectation, Mean, variance and moments, Bivariant distributions, joint, marginal and conditional distributions, covariance. Correlation coefficient Bivariant normal distribution. Regression and correlation, method of least squares, regression curves. Random sampling, sampling distributions. Expected values, standard error, the central limit theorem. Student’s t test, X2 and F distributions, Estimates of parameters, maximum likelihood principle, confidence intervals for mean, proportion, variance, difference of means, difference of proportions and ratio of variances. Elements of tests of hypothesis, critical region significance level, type I and II errors, power functions, testing the mean of a normal population when variance is known, testing the difference of means of two normal populations having equal but unknown variances, testing the variance of a normal population, testing the ratio of variances of two normal populations, test of independence inn consistency tables, test of goodness of lift. 
COSC 344: BASIC COMPUTER KNOWLEDGE AND FORTRAN PROGRAMMING (3 CREDITS) 
Binary, octal and hexadecimal number series, conversion, complement of numbers, representations of negative numbers, digital computers, main functional elements of a computer (memory control and arithmetic units, inputoutput devices, backing storage) information in the core store, binary coded decimal fixed and floating point representations, programming languages (short summary of the machinecode, assembly, machine and problem oriented languages), the flow chart language, loops, iteration, the basic Fortran, Numerical data, Arithmetic, Arrays, Input Out control statement, segmentation of programmes, statement function, function and subroutine segments common, equivalence statements. 
QTYS 309: ECONOMIC ORGANISATION (1 CREDIT) 
Introduction to economics: Elementary concepts, evolution of economic activity, characteristics of modern economic concepts. Basic Economics; Economics of taxation and public expenditure, business organization, industrial concentration and government control. Location of west African industry and trade: Background of West African economy, economic planning, development problems. The banking system: Money and Capital Markets, inflation, costbenefit analysis. 
LNSV 331: SURVEYING FOR ENGINEERS I (2 CREDITS) 
Introduction Kinds and operations of surveying (land surveying, topographic surveying, cadastral Surveying, town surveying, photogrametries surveying, engineering surveying, imine surveying,, hydrographic surveying,, geodesy, cartography). Units of measurement (linear, angular, area, volumetric). Fundamental definitions. Requisites of a good surveying work. Principal surveying Instruments Levelling staffs, levelling instruments and its adjustment. Theodolite (Transit) and its adjustment. Different reading systems. Measurement of Small Areas. Steel linear networks. Ranging of lines. Distance measurement with a steel band. Corrections. Fields notes. Measurement of details by offsets. Check measures. Proper field sketching. Plotting of the measurements results. Completing plans of small estates and buildings. General: benchmarks, turning ponts, backsight, foresight, height of instrucment etc. Procedure in differential leveling. Differential leveling. Adjustment and computation of elevations. Profile leveling. Crosssections. Grade line. Cuts and fills. Volumes of earthwork. Area leveling for contouring: by square network and by spots. Plotting and interpolation of contour lines. Working Surveys Setting out of street line and building line. Staking our of sexcavation lines according to design sketch. Marking points on corner profile. Giving foundation level. Levelling Computations and Working Out the Results Given field books of profile and crosssection leveling. Students will make: computations of elevations, checking between benchmarks, simple adjustment, estimation of precision. Plotting profile and crosssections. Projecting grade line. Volumes computation of earthworks. Given leveling data of a square network. Students should make: Computation of elevations, plotting, interpolation of contours. Using Constructional Design for Working Surveys: Basic data necessary for setting out (location) of buildings. Preparing work sketches out of constructional design. Setting out of modular space grid of a modern construction. 
LNSV 332: SURVEYING FOR ENGINEERS II (2 CREDITS) 
Simple Traversing Closed and open traverse. Angle measurement. Field notes. Precision of angle measurement. Distant measurement (steel band, wooden rods, subsistence bars, wires, electronic distancers). Precision of distance measurements. Field notes. Computation and simple adjustment of coordinates. Compass traverses. Coordinates Computations: Given field data of traversing. Students will compute coordinates, make simple adjustments and determine precision of obtained results. Tacheometric Computations Use of principal formulae. Use of different kinds of Tacheometric tables. Tacheometric slide rule and its use. Circular Curves Computations Converting curvature data; degree of curve into radius and opposite. Computation of basic data; tangent distance, external distance, long chord, middle ordinates. Computation of necessary data for setting out intermediate points by different methods. Use of curve tables.

400 Level Courses
WREN 401: HYDRAULICS AND HYDROLOGY (3 CREDITS) 

Hydraulics Gradually varied flow, development of basic differential equation, flow profiles, numerical evaluation of flow profiles, simplified equation using Cheese’s and Manning’s equation in wide rectangular channels, algebraic solution (Bresse’s equations) etc. Surges in open channels, moving hydraulic jump, positive and negative waves, simple application to dam break problem. Monoclinal flood wave. Undistorted modelling; Criteria of geometric, kinematics and dynamic similarities, models and prototype, undistorted models using Reynolds and Froude number as modelling criteria, preliminary discussion on undistorted modelling. Hydrology Hydrological Cycle: Existence of water in various forms. Basic Analysis of major components of the hydrologic cycle. Meteorology PRECIPITATION: Rainfall and snow fall. Measurement of rainfall. Rain gauges – simple and recording. Rain gauge networks. Point rainfall and average areal rainfall e.g. simple arithmetic average of point rainfall, isohyetal method and the method of Thiessien’s Polygons. Air temperatures: Methods of determining average rainfall e.g. simple arithmetic average of point rainfall, isohyetal method and the method of Thiessien’s Polygons. Evaporation and evapotranspiration measurement. Hydrometry: Stage and Discharge Hydrographs. Analysis of hydrographs. Base flow and its separation from the main flow. Recession curves and empirical formulae. Use of statistics in hydrology. Frequency, probability and average return period with different probabilities of nonexceedence. Flood forecast and monitoring. Drought studies and low flows analysis. 
WREN 403: DESIGN OF HYDRAULIC STRUCTURES (3 CREDITS) 
Conveyance Structures; Pipe lines and pipe systems, siphons, draft tubes, canals, sewers, transitions, spillways, chutes, culverts, reservoir outlet, conduits. Energy Dissipating Structures: – Surge tanks, stilling basins, drop structures. Storage Structures: Dams, earth fill dams, site selection, types, seepage control, Reservoir design, Flow Measurement and Control Structures: Weirs, sluices, gates and valves turnouts. Collection and Diffusion Structures: Intake structures, infiltration galleries, drains, surface drainage inlets, perforated pipes. Water stabilization structures: Levees, cutoff, dikes, breakwaters and seawalls. Channel lining: Seepage from channels, Design, construction and maintenance of linings (vegetative, impervious soils, masonry, concrete, bituminous materials). COSC 441 – Numerical Analysis (2 credits) Accuracy in numerical calculations, errors, significant figures, calculation of sin, cos and exponential by Taylor expansion. Interpolation, Newton’s forward, backward and central differences formulae. Numerical differentiation, numerical integration, trapezoidal rule, simpson’s rule, automatic selection of interval size, NewtonCote formulae. Solution of algebraic and transcendental equations, graphical, bisection, interval, NewtonRaphson solution of simultaneous equations, (Gauss and GaussSiedel) eigenvalues and eigenvectors). Numerical solution of ordinary differential equations. Methods of Euler, Picard, Taylors ordinary differential equations. Methods of Euler, Picard, Taylors and RungeKutta predictorcorrector. Method for solving ordinary differential equations. Introduction to partial differentiation. 
STAT 443 – Experimental Design and Control (2 credits) 
Analysis of variance, randomised blocks, latin squares, simple factorial designs, statistical quality control, control charts for means, standard deviation,image, number of proportion of defective and defects. Acceptance sampling (sampling inspection plans – examples of single, double, multiple and sequential sampling, plants) the operating characteristics (OC) curve, producer’s and consumers, risks, average sample number (ASN) and average outgoing quality level (AOQL), Linear programming. 
CVEN 402: DESIGN OF HYDRAULIC STRUCTURES (2 CREDITS) 
PREREQUISITES: CVEN 302, 303 Eccentrically loaded structures. Limit state of cracking. Stress analysis for gravity, arch, earthfill, and rock fill dams, spillways and reservoirs. Design of water tanks and retaining walls. Criteria for stability. 
CVEN 421: GEOTECHNICAL DESIGN OF FOUNDATIONS (3 CREDITS) 
PREREQUISITE: CVEN 321 Compressibility consolidation and settlement. Induced stresses and displacements. Rigid retaining structures. Shallow footings. Compensated foundations. Deep foundations. Dewatering. 
CVEN 441: COMPUTER METHODS (2 CREDITS) 
PREREQUISITE: COSC 344 Review of computer programming languages; elements of operations research techniques – linear programming etc. Introduction to finite difference/finite element methods. Computer applications to water resources allocation, control theory, traffic analysis and structural analysis/design. Special computeraided design projects in specific fields (i.e., structural, transportation, geotechnical, water resources, and environmental engineering) of civil water engineering. 
500 Level Courses
WREN 501: ENGINEERING HYDRAULICS (2 CREDITS) 

Review of Hydraulics: Basic relationship. Flow equations. Fluid flow in pipes and open channels. Hydraulics and energy grade line and losses. Nonuniform flow, system head curves, pump performance and selection. Headcapacity relationship for multiple pump system demand. Siphon, equivalent pipes, pipes, in series and parallel, branching pipes. Methods of sections, Hardy cross method, balancing equivalent pipe lengths method, reservoir and pumping station. Hydrodynamics – some advanced topics. Harmonic water waves, DEEP WATER (short) and shallow water (Long ) waves, shape of orbits etc. Sediment transportation in open channels. Properties of sediments, threshold of particle movement, critical velocity and shear stress, shields diagram, Bed load movement; Du Boy’s bed load formula and brief discussion of other bed load formulae. Suspended sediment, one dimensional steady, equation of suspended sediment, evaluation of total suspended load etc. Empirical method of stable alluvial channels design. Local scour and channel erosion. Reservoir sedimentation. 
WREN 502 WATER POWER SYSTEMS ENGINEERING (3 CREDITS) 
Planning of a hydropower project. Demand for power, load and load fact, firm load etc. Supply of power. Relation between demand, supply and river runoff Types of plants. The forebay, intakes and relevant equipments. Penstocks and tunnels and their economic size. Substructure and superstructure. Components of a hydro powerhouse. Underground hydro powerhouse. Hydropower machinery. Water turbine e.g. Pelton wheels, Francis turbines, Kaplan and propeller turbines etc. Governing of water turbines. (General discussion and mechanics of flow through turbines is included in fluid mechanics Part II). Selection of turbine and pump capacities. Choice of speed of sets and physical arrangement of sets. Efficiency of pumped storage schemes. 
WREN 503 ENGINEERING HYDROLOGY (3 CREDITS) 
Surface Water Hydrology: Unit Hydrograph – concept and definition. Development of unit hydrograph for a given catchment. Scurve and converting unit hydrograph of a given duration to any other duration. Instantaneous Unit Hydrograph (IUH). Flood Routing. Routing through reservoir. Routing through river channels. Muskingum method. Sedimentation of reservoirs. Ground Water Hydrology: Hydraulics of wells. Single well in unconfined aquifer with full penetration. Single well in confined aquifer. More than one well in confined and unconfined aquifers. Effect of aquifer boundaries (steams and impervious barriers) on the well hydraulics, method of images. Unsteady flow in wells. Storage coefficient and transmissivity. Draw down and pumping tests. Analysis of pumping test data for evaluating storage and transmissivity coefficients. Recovery of wells. Use of complex variables in analysis of ground water flow. Brief description of drilling methods, Screens and other parts of a borehole. Different types of pumps used for pumping water from a borehole. Water prospecting methods, Geophysical prospecting etc. Recharge mechanisms and recharge estimation. 
WREN 504: RURAL WATER SUPPLY AND SANITATION (2 CREDITS) 
Sources and treatment methods for small water supply schemes. Appropriate technology in water lifting devices and water treatment for rural areas. Application and importance of small water works. Water borne, waterbased, and waterrelated diseases and their mode of transmission. Individual waste disposal systems, including aqua privies, pit latrines, septic tanks, soak ways and drain fields. Storage, collection, transport and disposal of agricultural and domestic solid waste. Planning water and sanitation programmes for rural communities and gradual upgrading of such programmes. 
WREN 505: UNIT OPERATIONS AND PROCESSES IN WATER TREATMENT (2 CREDITS) 
Theory and application of physical, chemical and biological operation and processes in water treatment. Sedimentation: Discrete and nondiscrete settling tanks, sedimentation theory, sizing of tanks, tanks, construction details and design example of sedimentation tank. Coagulation / Flocculation: Coagulant clarification processes, Chemical dosing. Rapid and slow mixing units design. Conventional Clarifiers, Inclined plate clarifiers, Combined clarifiers, Pulsators and super pulsators. Filtration: impurities removal mechanisms, Types: Slow sand Filters, Rapid Sand filtration, Down and Up flow Filtration. Aeration and Gas Transfer processes: Gravity aerators, inclined plates, aeration towers etc. Disinfections: Chlorination, Break point chlorination, Chemicals used for chlorination and design of chlorination installations. 
WREN 506: ELEMENTS OF PUBLIC HEALTH (2 CREDITS) 
Health and personal hygiene: Its definition, value and changing outlook towards it. Measurement of health. Individual health, maturity, parental care, family conditions etc. Epidemiology: The study of community diseases. Conditions giving rise to disease. Infection: Methods of spread, sources of spread and conditions affecting spread. Protection: Natural and artificial Methods. Epidemics: Their spread, How they can be controlled and their importance. Infectious diseases in the United Kingdom: Their cause, mode of spread, mortality and control methods. Infectious diseases in the Tropical Countries: Their cause, mode of spread, mortality and control methods. NonInfectious diseases: Influence on the environment, Bronchitis, lung cancer and various types of poisoning, Radiation. Accidents: Roads, Factory (Industrial) and Rehabilitation. Food Adulteration and Poisoning. Malnutrition – Causes, their recognition and control. Mental outlook Towards family work and community. Health and Community Hygiene: Historical surveys, World Health Organization, Its growth and adjustment. Local achievement. Local achievements in slum clearance, rodent control etc. Health education Its methods and opportunities. 
WREN 507 WATER AND WASTEWATER ENGINEERING (2 CREDITS) 
Sources of water and wastewater, Physical, chemical and biological characteristics of water and wastewater. Water quality standards. Volume and rate concepts. Design periods, population studies. Water consumption variation in demand. Fire demand, coincidental draft. Hydrant flow test and flow calculations. Sewage flow rates. Design principles of separate, combined and semiseparate sewerage systems, Estimation of dry weather flows and stormwater flows using different methods, Sizing and construction of sewer pipes. Manhole chambers and storm water overflows, Pumping systems and inverted siphons. Maintenance of sewers. Principles involved in the design, operation and maintenance of water and wastewater treatment facilities. 
WREN 508: DRAINAGE ENGINEERING (2 CREDITS) 
Sources of drainage problems; land (surface) drainage systems; Drainage structures; Highway drainage, Urban drainage, Drainage of airstrips, subsurface drainage systems; Drainage of tidal areas; Reclamation of tidal areas. 
WREN 509: IRRIGATION ENGINEERING (2 CREDITS) 
Introduction to irrigation practice in humid and arid regions, cropwater requirements; Infiltration and water holding capacities of soil; salinity and water quality; reclamation and management; irrigation water application (surface, sprinkler, and subirrigation) use and distribution water management and efficiency; Economic analysis; operation and management of irrigation schemes. Irrigation water scheduling, and costing. 
WREN 510: ENGINEERING DESIGN I (2 CREDITS) 
Application of basic engineering design concepts to analyse and solve a real life water resources or/and environmental engineering problem. 
WREN 511: ENVIRONMENTAL POLLUTION CONTROL (2 CREDITS) 
Water Pollution: Types and sources of water pollution, Selfpurification of streams. Analysis of the dispersal of pollutants in streams and estuaries, The effects of pollutants on the chemical quality and the ecology of receiving stream, Eutrophication, Control of water pollution, Stream and effluent standards. Determination of required degree of treatment. Site visits to water and wastewater treatment plants. Air Pollution: The theory, principles and practices related to engineering control of the particuate and gaseous emissions from natural, industrial, agricultural, commercial and municipal sources of atmospheric pollution: The effects of of atmospheric pollution on various forms of life including both direct and secondary effects. Control devices of air pollutions. Solid waste collection and management: Principles and practices of Storage, collection, transport and disposal of solid wastes from domestic, industrial and agricultural sources. Industrial Utilisation of solid waste. Refuse processing and recovery. Noise Control: Sound, sound pressure, weighting scales, Measurement, indexes, Definitions of Noise, human perception. Sources of Noise pollution: Vehicles, aircraft, industrial, domestic. Acoustic insulation. Standards. 
WREN 512: UNIT OPERATIONS AND PROCESSES IN WASTEWATER TREATMENT (2 CREDITS) 
Theory and application of physical, chemical and biological operation and processes in wastewater treatment. Kinetics of aerobic and anaerobic treatment of wastewater. Treatment studies; activated sludge process, biological filtrations, stabilization ponds, Anaerobic sludge digestion and thickening, vacuum filtration, air and sand bed drying of sludge, heat treatment, land disposal, incineration and wet oxidation. Tertiary treatment, nutrient removal, suspended solids removal, organic and inorganic removal. 
WREN 515: ENGINEERING DESIGN II (2 CREDITS) 
Application of basic engineering design concepts to analyse and solve a real life water resources or/and environmental engineering problem. 
WREN 516: ENVIRONMENTAL IMPACT ASSESSMENT (1 CREDIT) 
Method of impact analysis. Prediction and assessment of the physical, sociological, legal and economic effects of human activities on air, water, noise, biological, cultural and socioeconomic environment. Effects of the changed environment on man. Examples of environmental impact assessment with particular references to developing countries. Role of environmental engineering in prevention of environmental stress. Planning and policy, administration and organisation of natural resources development and public health. Land use planning and landscape design. 
CVEN 524: GEOTECHNICAL ENGINEERING (2 CREDITS) 
Prerequisite (CVEN 421) Site investigation methods. Ground improvement technical (special reference to Nyam). Foundation subjected to vibrations. Foundation in reclaimed lands and sanitary land fill areas. 
QTYS 407: CIVIL ENGINEERING MEASUREMENT I (2 CREDITS) 
Introduction to Civil/Water Engineering Standard Method of Measurement including: Definitions, General principles, Application of the classification coding and numbering of items, Preparation of Bill of Quantities: MethodRelated charges.
Insitu concrete and concrete ancillaries. Brickwork, block work and masonry, Simple bridges and Culverts, 
QTYS 508: CIVIL ENGINEERING MEASUREMENT II (2 CREDITS) 
Measurement of the following and their associated temporary works; Simple tunnelling, Large sewers and drains, water and gas pipelines, Seawalls, Wharves, jetties, Timber works, Structural metal works, Roads and pavements and simple bridges, Simple railway work and simple bridges. Other civil engineering constructions related to the above. 
Leave a Reply