Fluid Mechanics and Fluid Dynamics
Fluid mechanics is the branch of physics
that studies fluids (liquids, gases, and
plasmas) and the forces on them. Fluid
mechanics can be divided into fluid statics,
the study of fluids at rest; fluid kinematics,
the study of fluids in motion; and fluid
dynamics, the study of the effect of forces
on fluid motion. It is a branch of continuum
mechanics, a subject which models matter
without using the information that it is
made out of atoms,
Basic Equations
• Analysis of any problem in fluid mechanics
necessarily begins either directly or indirectly
with statements of basic laws governing the fluid
motion. The basic laws which applicable to any
field are,
• The conservation of mass
• Newton’s second law of motion
• Principal of angular momentum
• The first law of thermodynamics
• Second law of thermodynamics
Basic Flow Analysis Techniques
• Control Volume or Integral analysis
• Infinitesimal system or differential analysis
• Experimental Studies or dimensional analysis
A control volume is an arbitrary volume in space
through which the fluid flows. The geometric
boundary of the control volume called the
control surface. Control surfaces may be real
or imaginary.
Continuum Hypothesis
• Fluids are composed of molecules that collide with one
another and solid objects. The continuum assumption,
however, considers fluids to be continuous. That is,
properties such as density, pressure, temperature, and
velocity are taken to be well-defined at "infinitely"
small points, defining a REV (Reference Element of
Volume), at the geometric order of the distance
between two adjacent molecules of fluid. Properties
are assumed to vary continuously from one point to
another, and are averaged values in the REV. The fact
that the fluid is made up of discrete molecules is
ignored.
Flow Patterns
•
•
•
•
•
Fluid flow is characterized by a velocity vector field in three-dimensional space,
within the framework of continuum mechanics. Streamlines, streaklines and
pathlines are field lines resulting from this vector field description of the flow.
They differ only when the flow changes with time: that is, when the flow is not
steady.[1] [2]
Streamlines are a family of curves that are instantaneously tangent to the velocity
vector of the flow. These show the direction a fluid element will travel in at any
point in time.
Streaklines are the locus of points of all the fluid particles that have passed
continuously through a particular spatial point in the past. Dye steadily injected
into the fluid at a fixed point extends along a streakline.
Pathlines are the trajectories that individual fluid particles follow. These can be
thought of as a "recording" of the path a fluid element in the flow takes over a
certain period. The direction the path takes will be determined by the streamlines
of the fluid at each moment in time.
Timelines are the lines formed by a set of fluid particles that were marked at a
previous instant in time, creating a line or a curve that is displaced in time as the
particles move.
Equation of Streamtubes
Equation of Streamtubes
Let r =xi+yj+zk
Is the position
Vector of point
A point P on
A streamtube. Then
By definition of
Streamtube .
The tangent at P is
dr
 V
ds
P
r
V
dx
dy
dz
i
j
k   u i   v j   wk
ds
ds
ds
dx
dx
 u 
 ds
ds
u
dy
dy
 v 
 ds
ds
v
dz
dx
 w 
 ds
ds
w
dx
dy
dz


du
dv
dw
-Example
•
•
•
•
Find the equation of streamlines if
u=-2y, v=2x
Sol:
Applying the formula and integration we will
get
• x2+y2=c
• Which is a circle. How to find the direction of
flow.
Direction of Streamline
• Direction of streamline is the direction of velocity vector at each point.
If the vector is in first quadrant
The direction would be
-2,2
Calculated as:
1,1
Choose any point in first quad.
V
V
Say(1,1) then velocity will be
• V=-2yi+2xj
• At (1,1)
• V=-2i+2j, at (1,1). The position vector is
• Shown in figure. At (1,1)
Another way to find direction
• In first quadrant ,x and y is positive.
• Therefore, the velocity vectors in this quadrant will be
• X-component of V is negative
u
v
• y-component of V is positive
• Head to tail rule gives
V
v
u
Another Example
• V= Ax i- Ay j, A=0.3 S-1
• Find h the equation of streamline through
(2,8)
• Sol: xy=c;
• At (2,8) c=16. So
• xy=16.
• How to find direction
Home Exercise
• Find the equation of streamline
V=2yi+2xj
Viscosity
• Viscosity is a measure of the resistance of a fluid which is being deformed
by either shear stress or tensile stress. In everyday terms (and for fluids
only), viscosity is "thickness" or "internal friction". Thus, water is "thin",
having a lower viscosity, while honey is "thick", having a higher viscosity.
Put simply, the less viscous the fluid is, the greater its ease of movement
(fluidity).[1]
• The degree to which a fluid resist flow under an applied force called
coefficient of viscosity or dynamic viscosity. (mue). Kinematic viscosity is
the dynamics viscosity divided by density of the fluid (pa-s {N·s/m2},
poise(cgi)).
Rate of Deformation(share rate- strain
rate)
• Consider the behavior of a fluid element between two infinite plates
shown in fig.
Newton’s Law of Viscosity