Differential Analysis of Fluid Flow
Part II
Potential Flows
Irrotational Flow
Analysis of inviscid flow can be simplified by an assumption of irrotational flow. For
irrotational flow vorticity is zero
Condition of irrotationality imposes specific relation
Differential Analysis of Fluid Flow
Part III
Viscous Flow
Equations of Motion
The resultant force acting on a fluid element must equal the mass times the
acceleration of the element
Equations of motion
u
xx yx zx
u
u
u
gx
u
v w
x
y
z
x
y
z
t
xy
Flow Over Immersed Bodies
General External Flow
Characteristics
Flow Over Immersed Bodies
Learning objectives
After completing this chapter, you should be able to:
identify and discuss the features of external flow.
Explain the fundamental characteristics
Differential Analysis of Fluid Flow
Part I
Governing Equations
Chapter review
Fluid element kinematics
Velocity and acceleration fields
Linear and angular motion and deformation
Continuity equation
Stream function
Equation of motion
Inviscid flow
Euler
Fluid Mechanics I Review
Introduction
What is Fluid?
Dimensions and Units. Systems of Units
Mass, Density, Specific Weight, Specific Gravity
Viscosity
Compressibility of Fluids. Bulk Modulus.
Speed of Sound
Vapor Pressure
Surface Tension
Fluid Statics
Pre
FLUID STATICS
Introduction
In many fluid problems fluid is at rest or moves as a rigid body
When fluid is at rest (hydrostatic condition), the pressure variation is due only to
the weight of the fluid and may be calculated by integration. Important applic
FLUID STATICS
Introduction
In many fluid problems fluid is at rest or moves as a rigid body
When fluid is at rest (hydrostatic condition), the pressure variation is due only to
the weight of the fluid and may be calculated by integration. Important applic
INTRODUCTION
Characteristics of fluids
A fluid may be liquid, vapour or gas. It has no permanent
shape but takes up the shape of a containing vessel or
channel or is shaped by external forces (e.g. the atmosphere).
A fluid consists of atoms/molecules in
Fluid Kinematics
Velocity Field
Continuum hypothesis:
fluid is made up of fluid particles;
each particle contains numerous molecules;
infinitesimal particles of a fluid are tightly packed together
Thus, motion of a fluid is described in terms of fluid
Elementary Fluid Dynamics
The Bernoulli Equation
Newtons Second Law: F = ma
Consider inviscid, steady, two-dimensional flow in x-z plane
Define streamlines
Select coordinate systems based on streamlines
Define acceleration
Define forces
Apply Newtons sec
Viscous Flow in Pipes
Introduction
Flow of viscous, incompressible fluid in pipes and ducts will be considered.
Pipe is of round cross section, duct is not round.
Basic components of a typical pipe system include pipes, fittings, valves, pumps or
turbines
Finite Control Volume Analysis
Conservation of Mass Continuity Equation
Reynolds transport theorem establishes relation between system rates of change and
control-volume surface and volume integrals
DBsys
Dt
n
cv bdV cs b Vg dA
t
With B = mass and b = 1,
Dimensional Analysis and
Similarity
Dimensional Analysis
Consider steady flow of an incompressible Newtonian fluid through long, smooth-walled,
horizontal, circular pipe.
We are interested in the pressure drop per unit length that develops along the pipe
Elementary Fluid Dynamics
The Bernoulli Equation
Newtons Second Law: F = ma
Consider inviscid, steady, two-dimensional flow in x-z plane
Define streamlines
Select coordinate systems based on streamlines
Define acceleration
Define forces
Apply Newtons sec
Finite Control Volume Analysis
Conservation of Mass Continuity Equation
Conservation of Mass Continuity Equation
Reynolds transport theorem establishes relation between system rates of change and
control-volume surface and volume integrals
DBsys
Dt
n
cv b
Dimensional Analysis and
Similarity
Dimensional Analysis
Consider steady flow of an incompressible Newtonian fluid through long, smooth-walled,
horizontal, circular pipe.
Study pressure drop per unit length along the pipe as a result of friction
Analytica
Fluid Kinematics
Velocity Field
Continuum hypothesis:
fluid is made up of fluid particles;
each particle contains numerous molecules;
infinitesimal particles of a fluid are tightly packed together
Thus, motion of a fluid is described in terms of fluid
Viscous Flow in Pipes
Introduction
Flow of viscous, incompressible fluid in pipes and ducts will be considered.
Pipe is of round cross section, duct is not round.
Basic components of a typical pipe system include pipes, fittings, valves, pumps of
turbines
INTRODUCTION
Characteristics of fluids
For a solid, application of a shear stress causes a deformation
which, if modest, is not permanent and solid regains original
position.
Attached
plates
Solid
Characteristics of fluids
For a fluid, continuous deform
ME 321 Fluid Mechanics I
Lecturer
Dr. M. G. Bannikov,
Professor FME
Room No. G-03, FME Building
Ph. 2249 E-mail: [email protected]
Teaching assistant
Mr. Abdullah Khan
E-mail:
CLASSES
Monday
11:40 - 12:30
Wednesday
8:55 - 9:45
Thursday
9:50 - 10:40
FME L