Fluid mechanics engineering
Fluid mechanics
Fluid mechanics is an active field of research. A lot of
advancements are made in the field of fluid dynamics (study of fluid in motion)
and creating new facilities, advancements toward the new, efficient, and cheap
fuel which helps to increase the efficiency of the machines.
What is fluid mechanics?
Fluid mechanics: The branch of physics deals with the
mechanics of fluid (liquids, gases, and plasmas) at both the stationary (at
rest) and dynamics (in motion) state and the effect of force on them.
Fluid mechanics introduction:
Fluid mechanics has a vast application in every field such
as mechanical, civil, oceanography, meteorology, astrophysics, biology,
geography, etc.
Before going deep into concepts on fluid mechanics in its
branches we need to know some important terms and their branches and their
history.
It is divided into fluid two main branches
Fluid statics: The study of fluids at rest is called
fluid statics.
Fluid dynamics: The study of the effects of forces on
fluid motion is called fluid dynamics.
Computational fluid dynamics (CED): it is a modern
field that deals with an experimental method for visualizing and analyzing
fluid flow, and how to take advantage of the visual nature of the fluid flow.
History:
The study of fluid mechanics is started when Archimedes
investigated fluid statics and latterly buoyancy formulated his famous law
known as the Archimedes’ principle which is based on floating bodies. Few
scientists made advancements in the field of fluid mechanics are:
|
scientists |
Advancements/
works |
|
Leonardo da Vinci
|
Observation
and experiments on fluid mechanics |
|
Evangelista Torricelli |
Invented the barometer |
|
Issacs newton |
Investigated
viscosity |
|
Blaise pascal
|
Researched
hydrostatics, formulated pascal law |
|
Daniel Bernoulli |
Mathematics
fluid dynamics in hydrodynamic |
|
Jean le round’,
joseph Louis, prerecession Laplace, Denis’s poison |
Inviscid flow |
|
Leonard Marie
Inviscid flow Hagen |
Viscous flow |
|
Osborne
Reynold, Kolmogorov, Geoffrey Ingram Taylor |
Advanced of
the fluid Taylor |
What is fluid?
A fluid is a substance that continually deforms under the
application of shear stress.
What is stress? What are its types of uses in fluid
mechanics?
Stress: A stress is defined as a force per unit area,
the force acting on the surface of an element. Stress has both magnitude (force
per unit area) and direction (the direction is relative to the surface on which
the stress acts.
There are mainly two types of stress used in fluid dynamics:
Normal stresses: A stress which acts inward (toward
the surface) and perpendicular to the surface of the element. For example,
pressure
Shear stress: It is also called tangential stress. It
acts along the surface of the element (parallel to the surface) for example
friction due to fluid viscosity.
For visualization of fluid: A body diagram can be
used to visualize the effect of forces such as to visualize both shear and
normal stress acting on the body.
Free body diagram:
A free-body diagram is a vector diagram that is used to
represent the magnitude and direction of all the forces acting on the body.
Fluid mechanics is a subdiscipline of continuum mechanics
Continuum mechanics:
The study of the
physics of continuous material. It is subdivided into two branches
·
Solid mechanics
·
Fluid mechanics
Solid mechanics: The study of the physics of continuous
materials with a defined rest shape. It is further divided into two fields
·
Elasticity
·
plasticity
Elasticity: it describes the materials which are
return to their rest shape after applied stresses are removed.
Plasticity: it describes the materials which are
deformed after sufficient applied stress.
Fluid mechanics: The study of the physics of continuous
materials which deform when subjected to a force. It is further divided into
two fields
·
Non-Newtonian fluids
·
Newtonian fluids
Non- Newtonian fluids: The fluids which do not
undergo strain rate proportional to the applied shear stress.
Newtonian fluids: The fluids which undergo strain
rates proportional to the applied shear stress.
Rheology: The study of materials with both solid and
fluid characteristics.
What is the difference between Newtonian and
Non-Newtonian fluids?
Newtonian fluids: the fluids whose viscosity does not
change, no matter how much pressure is applied are called Newtonian fluids.
These fluids are continuous to flow and don’t compress. In the language of
material sciences, it could be said that a fluid whose shear stress is linearly
proportional to the velocity gradient in the direction perpendicular to the
plane of shear.
For example, water is Newtonian fluid because it
continues to display fluid properties no matter how much it is stirred. Water
does not change its viscosity no matter how much pressure is applied to them.
Other examples of Newtonian Fluids are oil, alcohol, and gasoline. The drag of
the object through the Newtonian fluids is proportional to the applied force.
Fluid mechanics formulas:
The equation for Newtonian fluid:
To describe the
incompressible Newtonian fluid the simple equation is
T= -muon dv/die
Were
T= the shear stress exerted by the fluid
U=is the fluid viscosity, a constant of proportionality
Viscosity: the constant of proportionality between the
viscous stress tensor and velocity gradient is known as viscosity. For a Newtonian
fluid, viscosity depends upon the pressure, temperature not on the forces
acting on it.
du/die =the velocity gradient perpendicular to the direction
of shear.
For incompressible fluids:
If the fluid is incompressible the equation for viscous
stress is
Where
Tij= is the shear stress on the itch face of the fluid
element in the jet direction
Vi= is the velocity in the itch direction
Xu= is the jet direction coordinate
For compressible fluids:
If the fluid is not compressible Newtonian fluid the general
equation for the viscous stress is
K = c p / c v
Where
K= is the second viscosity constant or bulk constant
If the fluid is not following these relations then it is
called a Non- Newtonian fluid
Non-Newtonian fluids: The fluids whose viscosity
changes, when force is applied to them are called Non-Newtonian fluids.
Stirring a non-Newtonian fluid can leave a hole behind, this will gradually
fill up over time. Stirring a non-Newtonian fluid causes the viscosity to
decrease, so the fluid appears thinner (this could be seen in non-drip paints).
In the language of material sciences, it could be said that the strain rate does
not proportional to the shear stress applied.
For example: pseudoplastic, dilatant, thixotropic,
viscoelastic, better, cream, plastic, etc. are examples of Non- Newtonian
fluid.
Branches of
Non-Newtonian fluid: Non- Newtonian fluid is further divided into four
branches.
·
Dilatants
·
Pseudoplastic
·
Rheopectic
·
Thixotropic
Dilatant fluid: The fluids whose viscosity become
increases when force is applied is called Dilatant fluids. For example, Colbeck
(which is a mixture of water and cornstarch), silly putty, etc.
Pseudoplastic fluid: The fluids whose viscosity
decreases when the force is applied is called pseudoplastic. For example,
blood, milk, wet send, etc.
Rheopectic fluid: the fluids which get thicker when
the pressure is applied to them are called Rheopectic fluid. For example,
cream, cream becomes thicker butter with time and pressure.
Thixotropic fluids:
The fluids which get thinner when the pressure is applied to them are
called Thixotropic fluids. For example, cosmetics asphalt, etc.
Branches of fluid
mechanics:
There are two branches of fluid mechanics:
·
Fluid
Statics
·
Fluid
Dynamics
Fluid Statics: It
is a branch of fluid mechanics that studies fluids at rest, which is due to a stable
equilibrium.
Explanation:
Consider a fluid element that is at rest (or moving at
constant speed in a straight line). A fluid at rest has only normal stresses
since at rest cannot resist shear stress. In this case, a condition of
hydrostatic is satisfied that, the sum of all the forces must balance the
weight of the fluid element. Pressure always acts inward, the pressure at the
bottom side is slightly larger than at the top to balance the total pressure
and weight of the system.
The same as the pressure on the right side is equal to the
pressure on the left side. The pressure on the front side is equal to the
pressure on the backside.
Applications:
Hydrostatics gives physical explanations for many phenomena
of everyday life such as
why oil float on water?
When oil is added to the surface of the water, the oil
floats to the surface of the water because oil is less dense than water and
therefore it floats to the surface.
Why does atmospheric pressure change with altitude?
Atmospheric pressure decreases with altitude because of two
reasons. Gravity and density. The gravity pulls the molecules or air so, the
pressure increases as the molecule close to the surface as possible.
Hydrostatics:
Hydrostatics is fundamental to hydraulics, which is the engineering
of equipment for storing, transporting, and using fluids. Hydrostatics has also
the application in many fields like geophysics, astrophysics, meteorology, medicine,
and many other fields.
Fluid dynamics:
Fluid dynamics deals with the fluid flow, the science of
liquid and gases in motion. The properties of fluid such as velocity, pressure,
temperature, density are necessary for the calculation of the hydrodynamic
problems.
Explanation:
Consider a fluid element that is moving around in some flow
field. The fluid is in motion, it has both the normal and shear stresses. It satisfies
the newton second law.
The vector sum of all
forces acting on the fluid element must be equal to the mass of the element
times it is acceleration.
F=ma
The net moment about the center of the body is obtained by
adding the forces sue to each shear stress tomes its moment sum.
Fluid mechanics applications:
Fluid dynamics has vast applications such as determining the
mass flow rate of petroleum through pipelines, predicting evolving weather
patterns, understanding nebulae in interstellar space and modeling explosions,
calculating forces and movements on aircraft, and also being used in traffic
and crowd dynamics.
What is the difference between inviscid and viscous
fluids?
Inviscid fluid: A fluid where is viscosity is not
important and there is no shear force between the adjusted layers of the fluid
is called inviscid fluid. It is considered an ideal fluid. It is determined
through the Reynolds number. If Re is greater than 1 the flow may be considered
inviscid fluid. If there are any boundaries in the flow, near any of those
boundaries a viscous boundary, which is considered as viscous flow. So, in
reality, the inviscid flow does not exist.
Viscous fluid: the fluid where viscosity is important
and there is shear stress between the adjusted layers of the fluid is called a
viscous fluid. It is easily determined by Reynolds number. If the Re is smaller
than 1 then the flow is considered to be the viscous fluid. For example, the
gases and liquid flow may be considered as the viscous flow.
Navier stokes equations:
The Navier stokes equations are differential equations that
describe the force balance at a given point within a fluid.
For an incompressible fluid with vector velocity u, the
Navier-stokes equations are
P= pressure
V= kinematic velocity
The momentum or force is due to the response of pressure and
viscosity, parameterized by the kinematic velocity. These differential
equations are analogs for deformable materials to Newton’s equation of motion
of particles.
In practice, only the simplest cases can be solved in this
way. These cases generally involve non-turbulent, steady flow in which the
Reynolds number is small.
For complex cases, in those involving turbulence, such as
hydrodynamics, aerodynamics, global weather system, and many others, the
solution of the Navier-stokes equations can currently only be found with the
help of computers.
Solutions of the Navier-stokes equations for a given
physical problem are sought out with the help of calculus.
Assumption:
There is the assumption that every mechanical system obeys
·
Conservation of mass
·
Conservation of energy
·
Conservation of momentum
·
The continuum assumption
The continuum assumption is an idealization of
continuum mechanics under which fluids can be treated as continuous. Under the
continuum assumption, macroscopic (measurable) properties such as density, volume,
pressure, temperature, bulk velocity are taken into account.
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