1 Introduction

This section of the Module Consists of:

Lectures:

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    In-person classes and pre-recording over 3 weeks presenting the concepts, theory and application.

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    In-person classes will be predominantly worked examples to demonstrate how the theory is applied. You should do the pre-work as asked and in the class you will be doing some calculations - so bring a calculator.

Assessment (of the whole module):

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    1 Online Exam (OTLA) of 5 hours (plus 1 hour to submit), worth 80% of the module credits.
    This consists of questions on Materials, Water (Fluids) and Soils.

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    1 Assessed laboratory (Materials), worth 5% of the module credits.

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    3 Formative laboratories (2 for Water and 1 for Soils), these have no module credits attached but are essential to help your understanding of the theory covered in lectures.

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    2 Marked problem sheet, each worth 5% of the module credits. One on Water one on Soils

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    1 Multiple choice question (MCQ) paper (combined Water& Soils), worth 5% of the module credits.
    This will be given in class towards the end of the second semester, once you have done sufficient soils mechanics.

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    Resit
    In the case of a resit, the exam is worth 100% of the module credits i.e. any marks from the MCQs and problem sheets do not count toward the resit mark.

Water Engineering Laboratories:

There are two laboratories offered which are designed to allow you to examine how well the theoretical analysis of fluid dynamics describes what we observe in practice. During the laboratory you will take measurements and draw various graphs according to the details on the laboratory sheets. These graphs can be compared with those obtained from theoretical analysis. You will be expected to draw conclusions regarding the validity of the theory based on the results you have obtained and the experimental procedure. After you have completed the laboratory you should have obtained a greater understanding as to how the theory relates to practice, what parameters are important in analysis of fluid and where theoretical predictions and experimental measurements may differ.

The two laboratories are:

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    Impact of jets on various shaped surfaces - a jet of water is fired at a target and is deflected in various directions. This is an example of the application of the momentum equation.

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    The rectangular weir - the weir is used as a flow measuring device. Its accuracy is investigated. This is an example of how the Bernoulli (energy) equation is applied to analyses fluid flow. [As you know, these laboratory sessions are compulsory course-work. You must attend them. if you fail to attend either one you will be asked to complete some extra work. This will involve a detailed report and further questions. The simplest strategy is to do the lab.]

Example sheets:

These will be provided throughout the course. Doing these will greatly improve your exam mark. They are course work but do not have credits toward the module. Lecture notes: These should be studied but explain only the basic outline of the necessary concepts and ideas.

Books:

It is very important do some extra reading in this subject. To do the examples you will definitely need a textbook. Any one of those identified below is adequate and will also be useful for the fluids (and other) modules in higher years - and in work.

There are a number of copies of each of these in the library

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    Fluid Mechanics, Douglas J F, Gasiorek J M, and Swaffield J A, Longman.

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    Civil Engineering Hydraulics, Featherstone R E and Nalluri C, Blackwell Science.

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    Hydraulics in Civil and Environmental Engineering, Chadwick A, and Morfett J., E & FN Spon - Chapman & Hall.

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    Mechanics of Fluids, Massey B S., Van Nostrand Reinhold.

Online (Free) Books

Online Lecture Notes: All lectures / notes / examples will be on the Minerva

An additional (unmaintained but pre-dominantly up-to-date) site:

There is a lot of extra teaching material on this site: Example sheets, Solutions, (very old) past exams papers.

1.1 Units - Take care with the System of Units

As any quantity can be expressed in whatever way you like it is sometimes easy to become confused as to what exactly or how much is being referred to. This is particularly true in the field of fluid mechanics. Over the years many different ways have been used to express the various quantities involved. Even today different countries use different terminology as well as different units for the same thing - they even use the same name for different things e.g. an American pint is 4/5 of a British (Imperial) pint!
[There are 20 fl.oz. in a British pint, but only 16 in a American one. Both systems have 8 pints to a gallon, so the gallon also has the same volume difference ratio.]

To avoid any confusion on this course we will always use the SI (metric) system - which you will already be familiar with. It is essential that all quantities are expressed in the same system or the wrong solutions will result.

Despite this warning you will still find that this is the most common mistake when you attempt example questions.

1.1.1 The SI System of units

The SI system consists of six primary units, from which all quantities may be described. For convenience secondary units are used in general practice which are made from combinations of these primary units.

Primary Units

The six primary units of the SI system are shown in the table below:

Quantity SI Unit Dimension
Length metre, m L
Mass kilogram, kg M
Time second, s T
Temperature Kelvin, K θ\theta
Current ampere, A I
Luminosity candela Cd
Table 1: SI Primary Units and their Dimensions

In fluid mechanics we are generally only interested in the top four units from this table. Notice how the term Dimension of a unit has been introduced in this table. This is not a property of the individual units, rather it tells what the unit represents. For example a metre is a length which has a dimension L but also, an inch, a mile or a kilometre are all lengths so have dimension of L. (The above notation uses the MLT system of dimensions, there are other ways of writing dimensions - we will see more about this in the section of the course on dimensional analysis.)

Derived Units

There are many derived units all obtained from combination of the above primary units. Those most used are shown in the table below:

Quantity SI Unit Dimension
velocity m/sm/s m⁢s−1ms^{-1} L⁢T−1LT^{-1}
acceleration m/s2m/s^{2} m⁢s−2ms^{-2} L⁢T−2LT^{-2}
force N
k⁢g⁢m/s2kg\;m/s^{2} k⁢g⁢m⁢s−2kg\;ms^{-2} M⁢L⁢T−2MLT^{-2}
energy (or work) Joule JJ
N⁢mNm,
k⁢g⁢m2/s2kg\;m^{2}/s^{2} k⁢g⁢m2⁢s−2kg\;m^{2}s^{-2} M⁢L2⁢T−2ML^{2}T^{-2}
power Watt W
N⁢m/sNm/s N⁢m⁢s−1Nms^{-1}
k⁢g⁢m2/s3kg\;m^{2}/s^{3} k⁢g⁢m2⁢s−3kg\;m^{2}s^{-3} M⁢L2⁢T−3ML^{2}T^{-3}
pressure ( or stress) Pascal P,
N/m2N/m^{2}, N⁢m−2Nm^{-2}
k⁢g/m/s2kg/m/s^{2} k⁢g⁢m−1⁢s−2kg\;m^{-1}s^{-2} M⁢L−1⁢T−2ML^{-1}T^{-2}
density k⁢g/m3kg/m^{3} k⁢g⁢m−3kg\;m^{-3} M⁢L−3ML^{-3}
specific weight N/m3N/m^{3}
k⁢g/(m2⁢s2)kg/(m^{2}s^{2}) k⁢g⁢m−2⁢s−2kg\;m^{-2}s^{-2} M⁢L−2⁢T−2ML^{-2}T^{-2}
relative density a ratio 1
no units no dimension
viscosity N⁢s/m2Ns/m^{2} N⁢s⁢m−2Nsm^{-2}
k⁢g/(m⁢s)kg/(ms) k⁢g⁢m−1⁢s−1kg\;m^{-1}s^{-1} M⁢L−1⁢T−1ML^{-1}T^{-1}
surface tension N/mN/m N⁢m−1Nm^{-1}
k⁢g/s2kg/s^{2} k⁢g⁢s−2kg\;s^{-2} M⁢T−2MT^{-2}
Table 2: Some SI Secondary Units and their Dimensions

The above units should be used at all times. Values in other units should NOT be used without first converting them into the appropriate SI unit. If you do not know what a particular unit means - find out, else your guess will probably be wrong. More on this subject will be seen later in the section on dimensional analysis and similarity.

Common physical measures

We will use these common physical measures throughout this module:

Acceleration due to gravity 9.8⁢m/s29.8\;m/s^{2}
Density of water 1000⁢k⁢g/m31000\;kg/m^{3}
Density of Air 1.2⁢k⁢g/m31.2\;kg/m^{3}

Calculations & Significant figures

In fluid mechanics we quite often find ourselves using numbers up to 10 orders of magnitude different. This causes a lot of students to ask questions about accuracy. A simple answer is to stick with a fixed number of significant figures (sf). 3 sf will usually be fine, 4 sf will almost always give same answer as using more than this for the examples you see in water engineering.