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CIVE1400: An Introduction to Fluid Mechanics
Dr P A Sleigh
Dr CJ Noakes
January 2009
Module Material on the Web:
Use the VLE
Also: www.efm.leeds.ac.uk/CIVE/FluidsLevel
Unit 1: Fluid Mechanics Basics 3 lectures
Flow
Pressure
Properties of Fluids
Fluids vs. Solids
Viscosity
Unit 2: Statics 3 lectures
Hydrostatic pressure
Manometry/Pressure measurement
Hydrostatic forces on submerged surfaces
Unit 3: Dynamics 7 lectures
The continuity equation.
The Bernoulli Equation.
Application of Bernoulli equation.
The momentum equation.
Application of momentum equation.
Unit 4: Effect of the boundary on flow 4 lectures
Laminar and turbulent flow
Boundary layer theory
An Intro to Dimensional analysis
Similarity
Notes For the First Year Lecture Course:
An Introduction to Fluid Mechanics
School of Civil Engineering, University of Leeds. CIVE1400 FLUID MECHANICS Dr Andrew Sleigh January 2009
Contents of the Course
Objectives:
The course will introduce fluid mechanics and establish its relevance in civil engineering. Develop the fundamental principles underlying the subject. Demonstrate how these are used for the design of simple hydraulic components.
Civil Engineering Fluid Mechanics
Why are we studying fluid mechanics on a Civil Engineering course? The provision of adequate water services such as the supply of potable water, drainage, sewerage is essential for the development of industrial society. It is these services which civil engineers provide.
Fluid mechanics is involved in nearly all areas of Civil Engineering either directly or indirectly. Some examples of direct involvement are those where we are concerned with manipulating the fluid:
Sea and river (flood) defences; Water distribution / sewerage (sanitation) networks; Hydraulic design of water/sewage treatment works; Dams; Irrigation; Pumps and Turbines; Water retaining structures.
And some examples where the primary object is construction - yet analysis of the fluid mechanics is essential:
Flow of air in buildings; Flow of air around buildings; Bridge piers in rivers; Ground-water flow – much larger scale in time and space.
Notice how nearly all of these involve water. The following course, although introducing general fluid flow ideas and principles, the course will demonstrate many of these principles through examples where the fluid is water.
Schedule:
Lecture Month Date Week Day Time Unit
1 January 20 0 Tues 3.00 pm Unit 1: Fluid Mechanic Basics Pressure, density 2 21 0 Wed 9.00 am Viscosity, Flow Extra 27 1 Tues 3.00 pm Presentation of Case Studies double lecture 3 28 1 Wed 9.00 am Flow calculations 4 3 2 Tues 3.00 pm Unit 2: Fluid Statics Pressure 5 4 2 Wed 9.00 am Plane surfaces 6 February 10 3 Tues 3.00 pm Curved surfaces 7 11 3 Wed 9.00 am Design study 01 - Centre vale park 8 17 4 Tues 3.00 pm Unit 3: Fluid Dynamics General Descrip. MCQ 4.00 pm MCQ 9 18 4 Wed 9.00 am Bernoulli 10 24 5 Tues 3.00 pm Flow measurment 11 25 5 Wed 9.00 am Weir 12 March 3 6 Tues 3.00 pm Momentum 13 surveying 4 6 Wed 9.00 am Design study 02 - Gaunless + Millwood 12 10 7 Tues 3.00 pm Momentum 13 11 7 Wed 9.00 am Design study 02 - Gaunless + Millwood 14 17 8 Tues 3.00 pm Applications 15 18 8 Wed 9.00 am problem sheet given out Calculation Vacation 16 April 21 9 Tues 3.00 pm Unit 4: Effects of the Boundary on Flow Boundary Layer 17 22 9 Wed 9.00 am Laminar flow 18 28 10 Tues 3.00 pm Dim. Analysis 19 29 10 Wed 9.00 am (^) problem sheet handed in Dim. Analysis 20 May 5 11 Tues 3.00 pm Boundary layers MCQ 4.00 pm MCQ 21 6 11 Wed 9.00 am Revision
Books:
Any of the books listed below are more than adequate for this module. (You will probably not need any more fluid mechanics books on the rest of the Civil Engineering course)
Mechanics of Fluids, Massey B S., Van Nostrand Reinhold.
Fluid Mechanics, Douglas J F, Gasiorek J M, and Swaffield J A, Longman.
Civil Engineering Hydraulics, Featherstone R E and Nalluri C, Blackwell Science.
Hydraulics in Civil and Environmental Engineering, Chadwick A, and Morfett J., E & FN Spon - Chapman & Hall.
Online Lecture Notes:
http://www.efm.leeds.ac.uk/cive/FluidsLevel
There is a lot of extra teaching material on this site: Example sheets, Solutions, Exams, Detailed lecture notes, Online video lectures, MCQ tests, Images etc. This site DOES NOT REPLACE LECTURES or BOOKS.
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/s ms-1^ LT- acceleration m/s 2 ms-2^ LT- force N kg m/s^2 kg ms-2^ M LT- energy (or work) Joule J N m, kg m^2 /s^2 kg m 2 s-2^ ML^2 T- power Watt W N m/s kg m 2 /s^3
Nms - kg m 2 s-3^ ML^2 T- pressure ( or stress) Pascal P, N/m 2 , kg/m/s^2
Nm - kg m -1^ s-2^ ML-1^ T-
density kg/m^3 kg m-3^ ML- specific weight N/m 3 kg/m 2 /s^2 kg m -2^ s-2^ ML-2^ T- relative density a ratio no units
no dimension viscosity N s/m 2 kg/m s
N sm - kg m -1^ s-1^ M L-1^ T- surface tension N/m kg /s^2
Nm - kg s-2^ MT-
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.
Properties of Fluids: Density
There are three ways of expressing density:
1. Mass density:
ρ
ρ
mass per unit volume
mass of fluid
volume of fluid
(units: kg/m3)
2. Specific Weight:
(also known as specific gravity)
ω
ω ρ
weight per unit volume
g
(units: N/m
or kg/m
/s
)
3. Relative Density:
σ
σ
ρ
ρ
ratio of mass density to
a standard mass density
subs ce
H O at c
tan
2 (^4 )
o
For solids and liquids this standard mass density is
the maximum mass density for water (which occurs
at^4
o
c) at atmospheric pressure.
(units: none, as it is a ratio)
Pascal’s Law: pressure acts equally in all
directions.
A
C
E^ D
F
B
ps
py
px
δ z
δ y
δ x
δ s
B
θ
No shearing forces :
All forces at right angles to the surfaces
Summing forces in the x-direction:
Force in the x-direction due to px ,
F (^) x p (^) x Area (^) ABFE p (^) x x y
x
= × = δ δ
Force in the x-direction due to ps ,
F p Area
p s z
y
s
p y z
x s ABCD
s
s
s
= − × ×
= −
= −
sin θ
δ δ
δ
δ
δ δ
( sin θ
δ
δ
=
y
s
)
Force in x-direction due to py ,
Fx
y
To be at rest (in equilibrium) sum of forces is zero
F F F
p x y p y z
p p
x x x s x y
x s
x s
Summing forces in the y-direction.
Force due to py ,
F y p Area p x z
y
= y × EFCD = y δ δ
Component of force due to ps ,
F p Area
p s z
x
s
p x z
y
s
s ABCD
s
s
= − × ×
cos θ
( cos θ
x
s
Component of force due to px ,
Fy
x
Force due to gravity,
Fluid density ρ (^) z 2
p1, A z 1
p2, A Area A
Cylindrical element of fluid, area = A, density = ρ
The forces involved are:
Force due to p 1 on A (upward) = p 1 A
Force due to p 2 on A (downward) = p 2 A
Force due to weight of element (downward)
= mg= density × volume × g
= ρ g A(z 2 - z 1 )
Taking upward as positive, we have
p A 1 − p A 2 − ρ gA z ( (^) 2 − z 1 ) = 0
p 2 (^) − p 1 (^) = − ρ g z ( 2 (^) − z 1 )
In a fluid pressure decreases linearly with
increase in height
p 2 (^) − p 1 (^) = − ρ g z ( 2 (^) − z 1 )
This is the hydrostatic pressure change.
With liquids we normally measure from the
surface.
Measuring h down from the
free surface so that h = -z
x
y
z
h
giving p 2 − p 1 =^ ρ gh
Surface pressure is atmospheric, p atmospheric.
p = ρ gh + p atmospheri c
Pressure density relationship
Boyle’s Law
pV = constant
Ideal gas law
pV = nRT
where
p (^) is the absolute pressure, N/m 2 , Pa
V (^) is the volume of the vessel, m
3
n (^) is the amount of substance of gas, moles
R (^) is the ideal gas constant,
T (^) is the absolute temperature. K
In SI units, R = 8.314472 J mol
- K -
(or equivalently m
3 Pa K
− 1 mol
− 1 ).
Lecture 2: Fluids vs Solids, Flow
What makes fluid mechanics different
to solid mechanics?
Fluids are clearly different to solids.
But we must be specific.
Need definable basic physical
difference.
Fluids flow under the action of a force,
and the solids don’t - but solids do
deform.
- fluids lack the ability of solids to
resist deformation.
- fluids change shape as long as a
force acts.
Take a rectangular element
Fluids in motion
Consider a fluid flowing near a wall.
- in a pipe for example -
Fluid next to the wall will have zero velocity.
The fluid “ sticks” to the wall.
Moving away from the wall velocity increases
to a maximum.
v
Plotting the velocity across the section gives
“velocity profile”
Change in velocity with distance is
“velocity gradient” =
du
dy
As fluids are usually near surfaces
there is usually a velocity gradient.
Under normal conditions one fluid
particle has a velocity different to its
neighbour.
Particles next to each other with different
velocities exert forces on each other
(due to intermolecular action ) ……
i.e. shear forces exist in a fluid moving
close to a wall.
What if not near a wall?
v
No velocity gradient, no shear forces.
