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The University of Southampton

CENV3063 Applied Hydraulics

Module Overview

This module aims to cover topics of hydraulics that, due to time constraints, cannot be covered in Part 2 Hydraulics (CENV2008) but still find important applications in water engineering. The course can be divided into 4 main parts: • Techniques solving hydraulic problems. The course demonstrates the use of numerical techniques as powerful tools to solve a range of problems in hydraulic engineering. This part presents both generic theoretical concepts on PDEs and solution methods as well as practical tools to solve problems involving unsteady flow in open-channels. • Hydraulic Machinery. This part of the course is devoted to introduce the operating principles governing the functioning of pumps and turbines. Furthermore, the course looks into details at the problem of unsteady flows generated by hydraulic machines and introduces theoretical tools required to design: pumping stations, structures for surge protection (surge towers and air chambers) and hydropower plants. • Hydraulic structures. The student will learn how to use the theory of hydraulic jumps and open channel flows to design important hydraulic structures such as culverts, stilling basins and drop structures. • Coursework on numerical techniques: The students will implement a numerical code to solve a series of simple hydrodynamic equations.

Aims and Objectives

Learning Outcomes

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

  • Classification of partial differential equations and the type of physical problems they model.
  • Governing equations for shallow water flows in open-channels in one and two dimensions.
  • Fundamental concepts of the numerical solution of partial differential equations.
  • The strengths and limitations of some numerical methods usually used in hydraulics to solve open-channel flow equations.
  • Practical aspects of modelling open-channel flows.
  • Unsteady flows in pipes due to switch on/off of pumps/turbines.
  • Working principles of pumping and hydropower stations.
  • Issues associated with the design of culverts, stilling basins and drop structures.
Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

  • Recognise problems in hydraulic engineering that may be solved numerically.
  • Select the appropriate numerical solution technique to solve a given problem.
  • Understand important numerical issues leading to inaccurate or unstable solutions.
  • Understand and apply the Bernoulli theorem for a range of unsteady flow problems encountered in pipe systems connected to hydraulic machines (pumps and turbines).
  • Understand the working principles of different types of turbines and pumps.
  • Use open channel flows theory to design inlet-outlet controlled culverts.
  • Use the theory of hydraulic jumps to design and stilling basins and drop structures.
Transferable and Generic Skills

Having successfully completed this module you will be able to:

  • Ability to learn.
  • Critical analysis and judgment as to the quality of computer analysis output.
  • Time management and independent learning.
  • Problem analysis and problem solving.
  • Information handling.
  • Decision Making.
  • Technical decision making.
  • Data analysis.
  • Logical thinking and conceptualisation of a problem for solution by computer algorithm.
  • Ability to use the MATLAB programming platform including built-in functions.
  • Presentation of data and analysis results.
Subject Specific Practical Skills

Having successfully completed this module you will be able to:

  • Write, execute and test MATLAB programs to solve selected PDEs numerically.
  • Critically evaluate the results of numerical simulations in open-channel flow.
  • Design the storage volume of pumping stations and the necessary number of pumps for a given discharge.
  • Design, from a hydraulic point of view, structures for surge protection (surge towers and air chambers).
  • Design and control, from a hydraulic point of view, low- and high-head hydropower plants.
  • Design structures for hydraulic jump control.
  • Design inlet and outlet controlled culverts of different shape.


• Introduction (total: 1 lecture): Course overview: general introduction to the relevance of the topics addressed in the course. • Hydraulic machinery (total: 8 lectures) - Pumps: types of pumps, pump performance characteristics curves, pumps in series and parallel. - Pumping stations: sumps; design criteria based on switch-on/switch off procedures - Turbines and Hydropower : Introduction to hydropower – turbine types – the Pelton turbine, theory of turbine, start-up and shut down, unsteady flow, low-head hydropower • Hydraulic structures (total: 9 lectures) - Culverts: flow conditions, inlet control, outlet control outlet velocity, road overtopping - Stilling basins: types of hydraulic jumps, hydraulic jump formation, jump position,tailwater conditions; control of hydraulic jumps, length of hydraulic jumps in horizontalchannels - Vertical drop structures, Inclined drop structures, Baffled drop structures • Numerical methods in open-channel flow (total: 16 lectures) - Introduction: classification of PDEs, characteristic paths, range of influence, domains of dependence, advection-diffusion equation, initial values and boundary conditions, well posed problems. - Parabolic and hyperbolic linear PDEs: general features of parabolic and hyperbolic PDEs, explicit and implicit finite-difference schemes, consistency, order, stability and convergence, nonlinear equations, multidimensional problems. - The Saint Venant equations (1D): Basic hypothesis, integral and differential forms, supplementary terms, use of approximate forms, characteristics and Riemann Invariants, numerical solution by the method of characteristics, boundary and initial conditions, Finite Difference schemes, stability, modified equations, non-linear hyperbolic systems and the formation of shocks, other practical stability issues . - Modelling open-channel flow in 2D (shallow-water equations): Integral and differential form of the SWE, Finite Difference methods, discretization with structured and unstructured meshes, limitations, mesh resolution and computational cost, introduction to Finite Volume method. • Revision (total: 2 lectures)

Learning and Teaching

Teaching and learning methods

• Lectures and tutorials • Computer lab supervisions/Computer lab classes • Tutorials and worked examples • Problem assignments • Private study

Completion of assessment task40
Practical classes and workshops5
Wider reading or practice74
Total study time150

Resources & Reading list

Hoffman, J. D. (2001). Numerical methods. 

Cunge, J. A., Holly, F. M. and A. Verwey (1980). Practical Aspects of Computational River Hydraulics.. 



MethodPercentage contribution
Assignment 15%
Assignment 15%
Examination  (120 minutes) 70%


MethodPercentage contribution
Examination  (120 minutes) 100%


MethodPercentage contribution
Examination  (120 minutes) 100%

Repeat Information

Repeat type: Internal & External

Linked modules

Pre-requisite: CENV2008

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