Course program: VVR 120, Fluid mechanics for W3, 2010.
Course responsible: Ronny Berndtsson, room 5127 V-building, 5th floor, tel: 222 8986, email:
Ronny.Berndtsson@tvrl.lth.se.
Office hours: Teachers are usually available during normal office hours.
Course structure: Lectures 44 hours, tutorials 28 hours, self studies 123 hours.
Teachers: Ronny Berndtsson (RoB), Rolf Larsson (RL), room 5155 V-building, tel: 222 7398,
email: Rolf.Larsson@tvrl.lth.se, Hanna Modin (HM), room 5119 V-building, tel: 222 4487, email:
Hanna.Modin@tvrl.lth.se, Arun Rana (AR), room 5119 V-building, tel: 222 4487, email:
Arun.Rana@tvrl.lth.se
Course objectives are to give students basic knowledge in fluid mechanics required to analyze and
solve water related problems that environmental engineers may encounter. This means that after the
course the students should be able to apply their knowledge in fluid mechanics to solve problems
within water resources, water management, and water supply. Applications and examples from
nearby areas are also included such as environment and energy.
Contents include fluid fundamentals: density, viscosity, surface tension etc. Hydrostatics: relation
pressure/density/level, hydrostatic force. Fundamentals of flow: stationary and nonstationary flow,
stream lines, laminar/turbulent flow etc. Basic equations: continuity equation, energy equation,
momentum equation. Flow around bodies. Engineering applications: pipe flow, pumps, and
channels. Applications in natural systems: water courses. Measuring methods include pressure,
velocity, and flow.
Touching points with earlier courses: Technical modeling – force, movement, simple stationary
flow. Hydrology and aquatic ecology – water courses/channel flow, groundwater-flow.
Mathematics – integrals, ordinary and partial differential equations. Later courses: Mass transport –
advective and diffusive transport, turbulent diffusion, interaction particle/fluid, Stoke´s law. General
connection to advanced courses within water resources.
Fluid mechanics 2010
Student involvement: A course committee, with course responsible and student representatives,
will meet approximately every second week (if necessary more often) to discuss course results.
nd
Literature: 1) Hamill L., Understanding Hydraulics, 2 ed., Palgrave, 2001 (main text book).
2) Malm J. and Larsson R., Fluid mechanics for environmental engineering, examples.
3) Complementing material (lecture notes, etc).
Main course literature 1) and 2) is sold at KF.
Home page: On course home page lecture notes, dictionary, example exams, etc, can be found:
http://www.tvrl.lth.se/utbildning/undergraduate_courses/vvr120/.
Exam: Two alternatives are possible in connection to regular exam, 1) two written tests or 2)
written exam. Open book is allowed in tests and exam: Main text book, lecture handouts, and
individual notes in connection to lectures (example book is not allowed; solved examples from the
example book are not allowed, thus, separate your lecture notes from your example notes!).
1) The first of the two written tests gives maximum 24 credits and covers hydrostatics and basic
equations (lectures 1-11). Written test 1 is given 8:00-10:00, Monday 27 September in MA8.
Written test 2 gives maximum 36 credits and covers pipe flow, channel flow, and flow around
bodies (lectures 13-21). Written test 2 is given 8:00-11:00, Saturday 23 October in Eden 25-26.
Maximum credit sum for the two written tests is 60 credits (same as regular exam).
2) If result on the written test 1 was not so good it is possible to take the written exam. This is given
8:00-13:00, Saturday 23 October in Eden 25-26. The written exam covers all course contents. The
written exam also gives maximum 60 credits. Results from written exam are given priority over
results from written test 1.
NOTE!! Results/solutions to tests and exam that are not structured, not clear, or not readable will
result in point subtraction!!
Grading: Maximum credits on the two written tests/exam are 60 credits. To pass a minimum of 30
credits are necessary. 30 credits correspond to grade 3.0, 60 credits correspond to grade 6.0. Grades
are truncated (highest grade is 5.0). For students that failed during regular exam an extra exam is
given (pre-notification necessary) Monday 2 May, 8-13 in K:N. NOTE! Extra exam is not divided
into two written tests and results at previous written tests are not counted for the extra exam.
Course contents – lectures:
Lecture no. Title (corresponding to chapter in Hamill)
• Contents - lecture.
Exercise no. refers to the Exercise book. NOTE!! Small deviations during the course may appear in the
course program.
1. Introduction, Fluid properties (1.1, handouts)
 Introduction
 Course structure
 Fluid as continuous medium
 Density
 Compressibility
 Exercise: A1
2. Fluid properties cont. (2.8, 4.1, handouts)
 Viscosity
 Surface tension, capillarity
 Exercise: A2, A7, A9
3. Hydrostatics I (1.2-1.5)
 Hydrostatic pressure, pressure-densitylevel
 Pressure on plane surfaces
 Exercise: B15, B17
4. Hydrostatics II (1.6-1.7)
 Pressure on curved surfaces
 Buoyancy / Archimedes principle
 Exercise: B23, B27
5. Hydrostatics III (1.8, 2.1-2.7)
 Hydrostatic equation
 Pressure measurement, manometry
 Exercise: B1, B3, B4, (B10)
6. Fundamental properties of flow, basic
equations I (4.2-4.4)
 Stationary and nonstationary flow, stream
lines, stream tubes
 One-, two-, and three-dimensional flow
 Laminar and turbulent flow
 Reynolds number
 System and control volume
 Continuity equation
 Exercise: C1, C2, C4, C7
Fluid mechanics 2010
7. Basic equations II (4.7-4.8)
 Bernoulli equation
 Kinetic energy, potential energy, and
pressure energy for fluid in motion
 Energy level: velocity level, geometric
level, and pressure level
 Bernoulli equation, applications
 Exercise: C12, C14, C23
8. Basic equations III (5.1-5.4)
 Pitot tube
 Vapor pressure, cavitation
 Equation for parabolic trajectory
 Bernoulli equation, applications
 Exercise: C26, C33, C40
9. Basic equations IV (5.1-5.4)
 Energy equation
 Pumps and turbines
 Flow with energy loss
 Energy and pressure levels
 Flow measurements
 Exercise: C34-35, C41
10. Basic equations V (4.5-4.6)
 Momentum equation
 Applications - momentum equation
 Exercise: C43, C44
11. Basic equations VI (4.5-4.6)
 Applications - momentum equation
 Exercise: C54, C64
12. Repetition, Lec. 1-11
 Repetition
of
fluid
properties,
hydrostatics, and basic equations
 Solving typical exam problems at written
test 1 (problem 6, 9, 13, and 16 in exam
leaflet)
13. Pipe flow I (6.1-6.4, 6.6)
 Energy losses in pipe flow
 Local energy losses
 Pipes connected in series
 Exercise: D13, D14 (D15)
14. Pipe flow II (6.4, 7.1-7.4)
 Pipes connected in parallel
 Three reservoir problem
 Quasi-stationary pipe flow
 Exercise: D21, D26 (D27)
15. Pipe flow III (6.5)
 Laminar pipe flow
 Turbulence models
 Exercise: D1, D2, D4
16. Pipe flow IV (6.5)
 Smooth turbulent flow
 Rough turbulent flow
 Friction coefficient, Moody diagram
 Non-circular pipes
 Exercise: D8
17. Pipe flow V (11.5-11.7)
 Pump types
 Pump systems
 Pumps in series and in parallel
 Exercise: D35-36, D38
18. Flow around bodies (4.9)
 Introduction, basics
 Boundary layer theory, basics
 Boundary layer for a flat surface
 Separation and shape resistance
 Stokes´ law for spherical bodies
 Exercise: F1, F2, F7
19. Channel flow I (8.1-8.5)
 Introduction, definitions
 Laminar channel flow
 Uniform channel flow, Manning equation
 Exercise: E1-2
20. Channel flow II (8.6-8.9)
 Specific energy
 Critical depth
 Froude number
 Control section
 Exercise: E9, E12, E16, E21
21. Channel flow III (8.10-8.11)
 Weak non-uniform flow
 Step calculation water surface profile
 Hydraulic jump
 Flow measurements
 Exercise: E22, E24, E25
22. Summary – Written test 2
 Summary of course
 Solving typical written test 2 problems
Fluid mechanics 2010
SCHEDULE
Week
1
2
3
4
5
6
Date
Mon 30 Aug
Tues 31 Aug
-“-“Wed 1 Sep
Fri 3 Sep
-“-“Mon 6 Sep
Time
10-12
08-10
13-15
-“08-10
10-12
13-15
-“08-10
Room
K:F
K:G
K:H
K:I
K:G
DC:Shö
K:M
K:P
MHA
Teacher
RoB
RoB
HM
AR
RoB
RoB
HM
AR
RoB
Class
Lec 1
Lec 2
Ex 1-Grp 1
Ex 1-Grp 2
Lec 3
Lec 4
Ex 2–Grp1
Ex 2–Grp2
Lec 5
Tues 7 Sep
08-10
K:G
RoB
Lec 6
-“-
13-15
K:H
HM
Ex 3–Grp1
-“Wed 8 Sep
Fri 10 Sep
-“-
-“08-10
10-12
13-15
K:I
K:G
K:D
K:M
AR
RoB
RoB
HM
Ex 3–Grp2
Lec 7
Lec 8
Ex 4–Grp1
-“Mon 13 Sep
Tues 14 Sep
-“-
-“08-10
08-10
13-15
K:P
MHA
K:G
K:H
AR
RoB
RoB
HM
Ex 4–Grp2
Lec 9
Lec 10
Ex 5–Grp1
-“Wed 15 Sep
Fri 17 Sep
-“-
-“08-10
10-12
13-15
K:I
K:G
DC:Shö
K:M
AR
RoB
RoB
HM
Ex 5–Grp2
Lec 11
Lec 12
Ex 6–Grp1
-“Mon 20 Sep
Tues 21 Sep
-“-“Wed 22 Sep
Fri 24 Sep
-“-“Mon 27 Sep
-“08-10
08-10
13-15
-“08-10
10-12
13-15
-“08:0010:00
13-15
-“08-10
10-12
13-15
-“08-10
08-10
K:P
MHA
K:G
K:H
K:I
K:G
DC:Shö
K:M
K:P
MA8
AR
RoB
RoB
HM
AR
RoB
RoB
HM
AR
RoB
Ex 6–Grp2
Lec 13
Lec 14
Ex 7–Grp1
Ex7–Grp 2
Lec 15
Lec 16
Ex 8–Grp1
Ex 8–Grp2
K:H
K:I
K:G
DC:Shö
K:M
K:P
K:G
K:G
HM
AR
RoB
RL
HM
AR
RoB
RoB
Ex 9– Gr1
Ex 9– Gr2
Lec 17
Lec 18
Ex 10–Gr1
Ex 10–Gr2
Lec 19
Lec 20
Tues 28 Sep
-“Wed 29 Sep
Fri 1 Oct
-“-“Mon 4 Oct
Tues 5 Oct
WRITTEN
TEST 1
Fluid mechanics 2010
Content
Introduction, Fluid properties
Fluid properties, cont.
A3, A8, A10-11, (A4-6)
-“Hydrostatics I
Hydrostatics II
B16, B18, B20 (B19, B21-22)
-“Hydrostatics III
Fundamentals of flow and basic
equations I
B24-25, B6, B8, B14 (B26, B28, B5
B7, B9, B11-13, B2)
-“Basic equations II
Basic equations III
C3, C9-10, C15, C20, C22, C24 (C5-6,
C8, C11, C13, C16-19, C21)
-“Basic equations IV
Basic equations V
C25, C27, C32, C36, C38, C42
(C29-31, C37, C39, C46-49, C51-52)
-“Basic equations VI
Repetition Lec 1-11, Test 1 problems
C45, C50, C53, C56, C65 (C46-49, C5152, C55, C57-59, C60-63)
-“Pipe flow I
Pipe flow II
D12, D17, D18, D25 (D16, D22-24)
-“Pipe flow III
Pipe flow IV
Repetition + Test 1 problems
-“Fluid properties, Hydrostatics, Basic
equations (Lec 1-11)
D28, D33, D3, D29 (D7, D5-6)
-“Pipe flow V
Flow around bodies
D11, D19, D20,D39 (D10, D37, D40-41)
-“Channel flow I
Channel flow II
-“-“_
Wed 6 Oct
Fri 8 Oct
13-15
-“08-10
10-12
K:H
HM
K:I
AR
No teaching!
K:M
HM
Ö11 – Gr1
Ö11 – Gr2
F3, F4, F8 (F5-6)
-“-
Ö12 – Gr1
E3, E5, E7, E10, E11, E14 (E4, E6, E8,
E13, E15)
-”-
-“-“K:P
AR
Ö12 – Gr2
-“13-15 No teaching!
7
Mon 11 Oct
08-10
DC:Shö
RoB
Lec 21
Channel flow III
Tues 12 Oct
08-10 K:G
RoB
Lec 22
Summary course, Test 2 problems
Ö13 - Gr1
-“13-15 K:H
HM
E17, E23, E26, E20, E27 (E18-19)
-“-“K:I
AR
Ö13 - Gr2
-“Wed 13 Oct
08-10 Guest lecture, Patrik Nilsson and Anna Järvegren Meijer, VA SYD; DC:Shö
-“15-17 K:N
HM
Ö14 – Gr1
Repetition + Test 2 problems
-“-“K:P
AR
Ö14 – Gr2
-“Fri 15 Oct
10-12 Study visit, Höja pumping station, Hyllie water tower.
Test 2 and exam is given Saturday 23 October, 8:00, in Eden 25-26. Duration: 3 hrs (test 2), 5 hrs (exam).
Fluid mechanics 2010