Post on 30-Aug-2018
CH6050: Viscous Fluid Flows
Instructor's details:
Dr. Kirti Chandra Sahu
Department of Chemical Engineering
Room No: 04
Email: ksahu@iith.ac.in
Tel: 040 2301 6053
Attendance is compulsory in this course.
Student with below 80 % attendance will not be allowed to sit in the exam.
Syllabus: Viscous Fluid Flow
Properties of Fluids, Fundamental equations of fluid flow: Derivation of
Navier-Stokes, continuity and energy equations, Boundary conditions for
viscous flow, Some discussion on potential flows: stream function, potential
function, Flow separation, Dimensionless parameters, Laminar boundary
layers, similarity solutions: Blasius velocity profile for flow over a flat plate,
Transition to turbulence: linear stability analysis, Introduction to Turbulence:
RANS equations, modeling, etc.
Books:
1.Viscous fluid flow by Frank M. White.
2.Boundary-layer theory by H. Schlichting and K. Gersten
3.Hydrodynamics by H. Lamb
Proposed Course Outline
Topics No of classes
Introduction 1 Properties of Fluids 1NS/Conti/Energy Equations 6Potential Flows 2Flow separation 2Boundary layer theory 6Linear Stability analysis 6Introduction to turbulence 2
Grading
Mid Term: 30 MarksEnd Term: 50 MarksAssignments: 10 MarksOther (Seminar/attendance): 10 Marks
1. What is a fluid?
Any material deforms when a shear stress is applied.
Solid: Deforms a fixed amount or breaks completely when a stress is applied on it.
Fluid: Deforms continuously as long as any shear stress is applied. This definition
includes gases and liquids.
2. What is Mechanics?
Mechanics: The study of motion and the forces which cause (or prevent) motion.
(a) Kinematics (Kinetics): The description of motion: displacement, velocity,
acceleration.
(b) Statics: The study of force acting on particles or bodies at rest.
(c) Dynamics: The study of force acting on particles or
bodies at motion.
3. Continuum Mechanics?
Three types of mechanics:
(a) Particle mechanics
(b) Rigid body mechanics
(c) Continuum mechanics
The continuum hypothesis
• Matters are aggressions of molecules; the molecules of fluid are more closely
packed then that of gas. Attractive forces between the molecules in liquid are also
much larger than those of gas.
• The molecules in a lattice are not fixed but move freely relative to each other.
• In most engineering applications, there is a very large number of molecules in the
region under consideration.
• The materials behaves in the same as if the mass was distributed continuously.
• In fluid mechanics, we may treat the fluid as a continuum rather than a collection of
discrete molecules.
•It may be mentioned here that most gases have the molecules density of
•Molecules/m3.
2 52 .7 1 0×
4. Body Forces and Surface forces:
Forces exerted on an element of fluid may come from long-range or short-range
interactions.
Body forces: Long range-no direct contact, e.g. gravity, electrostatic. Proportional
to volume of the fluid element.
Surface forces: Short range-direct contact, e.g. pressure,friction. Proportional to
area of the fluid element. e.g., Stress
5. How many components does stress have?
Stress is force (a vector) per unit surface area (a scalar).
Stress depends on the direction of the surface normal.
e.g. Stress in y-direction on a surface perpendicular to x-axis.
First subscript corresponds to direction normal to surface.
Second subscript corresponds to direction of force component.
:xyσ
The quantity stress is a tensor. The sign convection for stress components
on a Cartesian element is shown below.
y
z
x
xxσ
xyσ
xzσ
zxσ
zyσ
zzσ
yxσ
yyσ
yzσ
The stress tensor can be written as
xx xy xz
ij yx yy yz
zx zy zz
σ σ σ
σ σ σ σ
σ σ σ
=
The stress tensor: symmetric.
This symmetric is required to
satisfy equilibrium of moments
about the three axes of the
element.
ij jiσ σ=
6. Type of stresses:
Normal Stresses:
There are three normal stress components:
The pressure is (minus) the average of these:
Shear Stresses: There are three distinct shear stress components since it can
be shown that the stress tensor is symmetric:
, ,xx yy zzσ σ σ
( ) / 3xx yy zzp σ σ σ= − + +
, ,xy yx yz zy zx xzσ σ σ σ σ σ= = =
7. Definition of viscosityIt is a measure of resistance of a fluid which is being deform by the application of
shear stress.
In everyday terms viscosity is “thickness”. Thus, water is “thin” having a lower
viscosity, while honey is “think” having a higher viscosity.
Although it is a fluid property, the effect of this property is understood when the
fluid is in motion.
Newton's law of viscosity:
where the constant of proportionality is known as the coefficient of viscosity
or simply the dynamic viscosity.
Common fluids, e.g., water, air, mercury obey Newton's law of viscosity and
are known as Newtonian fluid. Other classes of fluids, e.g., paints, polymer
solution, blood do not obey the typical linear relationship of and du/dy . They
are known as non-Newtonian fluids.
The study which describe the properties of Newtonian and non-Newtonian
fluids is known as Rheology.
,du
dyτ µ=
τ
Viscosity of common fluids:
Air:
Density= 1.3 kg/m3
Dynamic Viscosity=1.8 X 10-5 Pas
Kinematic viscosity = 1.4 X 10-5 m2/s
Water:
Density= 103 kg/m3
Dynamic Viscosity= 10-3 Pas
Kinematic viscosity = 10-6 m2/s