Lecture 1

Lecture 1
Ramiro Neves, 1397
• Ramiro Neves, ext. 1397, telem. 917224732
• Lígia Pinto
• Offices: Pavilhão de Mecânica I, 1º floor
Where to use Fluid Mechanics?
• About everywhere...
Boussinesq Model
Douro Estuary mouth:
West and SW Waves
Thessaloniki NATO ARW (19-24 April 2005)
Integrated Basin Modelling
1D Drainage
2D Overland flow
3D Porous
variable in time
& space
Dia mundial da água, Cascais, 2007
Integrated Basin Modeling
Flow Production:
2 Different Soils
Overland Flow
Rain Intensity
Integrated Basin Modeling
Sediment transport:
2 Catchments
1 Reservoir
Rain Intensity
Dia mundial da água, Cascais, 2007
Classical Problems
Reduction of air resistance
Flow in a artery
Flow around a leaf
Balloon fish
Low mobility high toxicity....
Even the bacteria know the
importance of fluids mechanics
• The formalism...
Difficulties are apparent because:
• Fluid Mechanics requires a limited number of
physical concepts;
• Mathematical operators are mostly derivatives,
gradients and divergences;
• This course is an excellent opportunity to
consolidate basic concepts of Engineering
Set of courses downstream MFA
Transferência de Energia e Massa
Hidráulica Ambiental
Hidrologia Ambiental e Recursos Hídricos
Física da Atmosfera e do Oceano
Modelação Ambiental
Gestão Integrada de Bacias Hidrográficas
• Physics: Forces, Newton law and acceleration,
kinetic energy, momentum, fluxes.
• Mathematics: derivative, integral, divergence,
gradient, vector internal and external products.
Knowledge to acquire
• Understanding of fluid mechanics equations and
processes that determine the fluid motion
• Control of the advection and diffusion concepts
and of the evolution equation concept essential
for the downstream courses
MFA practical part
• A computational component is added to the classical
exercises with 3 objectives:
To show that Fluid Mechanics goes much beyond simple
analytical solutions;
To help students to enhance their programing skills;
To replace the classical laboratory lectures (essential
before computational methods were available)
• This component will be consolidated with a group
home work programmed using (preferentially) VBA
– VBA is part of the MS Office, is object oriented and
useful for a wide range of engineering issues (database,
• Fluid Mechanics, Frank White, McGraw-Hill, (or
any other Fluid Mechanics Introduction book)
• Apontamentos de Mecânica dos Fluidos I
• Texts about specific subjects
• Lectures’ PPT
Students Knowledge Assessment
• Tests/Exam (75%)
• Computational exercise report (25%)
• Exams: (14 and 31 January 2015)
What is a fluid?
• Is formed by molecules...
– that move, as in any other type of matter, above 0 kelvin;
– the difference between a fluid and a solid is that in the
fluid the molecules can change their relative positions
allowing them to get the shape of the containers;
– fluids can be liquids or gases.
• In gases molecules have free relative movement
• In liquids molecules form groups with relative free
movement (allowing them to get the shape of the
container) which dimension depends on temperature
(influencing their viscosity)
Why is Fluid Mechanics distinct from
Solid Mechanics?
• In a fluid each molecule (or group of molecules) have
relative movement freedom and in solids not. The
consequence is that tangential stress deforms the fluids.
Or in other words, if there is tangential stress there is
• Normal stress compress the fluid, that can remain at
rest. Tangential shear moves the fluid in layers creating
velocity gradients.
Shear is proportional to the
rate of deformation
Elementary Volume
• Is large enough to include a large number of molecules and
small enough to have uniform properties.
• If the Elementary volume is of the order of the size of a molecule, the
density value is uncertain due to the number of molecules it contains. If it
is too large the density can change from one region to another.
Continuum Hypothesis
• The elementary volume is much larger than 10 nm
• Necessary because we cannot assess the movement of
individual molecules (too many and the Heisenberg
• But they move individually....
– The unknown molecule movement will be dealt as
diffusion in the equations.
• When do we have velocity in a fluid?
– When there is net mass transport across a surface.
What is the velocity?
• Velocity is the flux of volume per unit of area.
• The Velocity is defined at a point and thus is the flow per unit of
area, when the area tends to zero:
• A surface can have 3 orientations in a tridimensional space and thus
velocity can have up to 3 components.
• The velocity component in one direction is the internal product of
the velocity vector by the unitary vector along that direction. Using
the surface normal one can write :
Discharge / Advective Flux
Knowing the 3 velocity components and knowing that the velocity is the
discharge per unit of area when the area tends to zero ( the velocity is defined
at a point) we can compute the discharge across an area integrating the
velocity along the whole area:
Defining a specific property as its value per unit of volume
(when the volume tends to zero)
We can say that the flux of M
across an elementary surface
And the flux of M across a surface is:
If c is uniform along the surface then:
• We know what is fluid Mechanics and what is for;
• We know what is a fluid;
• We know what is velocity and the advective flux;
• We know that Fluid Mechanics aims to study flows and
thus to know the velocity distributions;
• To compute fluxes we also need to know specific
properties distributions….