-HW6
W:8-1
A cam that is designed for cycloidal motion drives a flat-faced follower.
During the rise, the follower displaces 1 in for 180o of cam rotation. If the cam
angular velocity is constant at 100 rpm, determine the displacement, velocity,
and accel
Homework 5 (due June 7, 2013)
(1) Consider the uniform potential flow over a sphere. Obtain the stream
function in a symmetric plane, plot the stream patterns, and calculate
the force on the sphere.
(2) Consider the two-dimensional potential flow due to a
Chapter
p 8
What
h hhave we learned
l
d?
What are we going to study next ?
Fluid Mechanics (Spring 2013) Chapter 8 - U. Lei ()
Summary
Introduction
Physical and mathematical formulations of fluid
mechanics
Some exact solutions for illustrating variou
Chapter 6 : Potential flow
Inviscid (incompressible) main flow:
u = 0,
0
u
+ u u = P
t
V ti it equation:
Vorticity
ti
d
dt
=
( P : modified pressure )
+ u = u
t
The
h baroclinic,
b
li i the
h compression
i andd the
h viscous
i
diffusion
diff i mechanism
Fundamentals of Fluid Dynamics
()
Lecturer: U. Lei ()
Office: Room 220, IAM Building
Tel.: 33665673, E-mail: leiu@iam.ntu.edu.tw
Time: 9:10
Ti
9 10 10:00,
10 00 M
Monday;
d
10:20
10 20 12:10,
12 10 W
Wednesday
d d
Place: Room 109, IAM Building
Office hour
Fluid Mechanics
Problem 1
Problem 2
Homework 3
Problem 3
Problem 4
Problem 5
v
x
v
x
y
v
y
x
x 2
y 2
y
x 2
y 2
y
y
cos( t
y
y ) sin( t
y)
2
2
2
( t n ),
4
n 0, 1, 2,.
Problem 6
Problem 7
The governing equation:
- (1)
Boundary conditions: (Note that a=R
Homework 4 (due May 29, 2013)
(1) Consider the low Reynolds number flow around a sphere. (i)
Calculate the drag by first finding the dissipation of energy in the
fluid-filled space. (ii) Compute n at the surface of a sphere.
Find its integral over the sur
Chapter 3: Exact solutions of the
governing equations
The
Th governing
i equations
i
for
f continuum
i
fluid
fl id
mechanics derived in chapter 2 are sets of coupled
nonlinear
li
partial
i l diff
differential
i l equations,
i
which
hi h cannot
be solved
90 6 11 ()
92 5 30 ()
93 6 30 ()
Lecture notes on
Introduction to Fluid Mechanics
U. Lei
Institute of Applied Mechanics
National Taiwan University
June 11, 2001 (first draft)
May 30, 2003 (revised)
June 30, 2004 (revised)
ii
Contents
(1) Introduction
Chapter 1: Introduction
Definition of fluids
The subject of fluid mechanics
Applications
pp
of fluid mechanics
Microscopic (molecular) versus macroscopic
(continuum) approach
pp
Continuum approach
Eulerian and Lagrangian
g g description
p
Reynolds
Homework 3 (due May 3, 2013)
(Problems from page 113 - 115 of the lecture notes)
(1) The cross section of a tube in an equilateral triangle with sides of
length l and a horizontal base. Flow in the tube is produced by an
imposed pressure gradient dp/dx. V
Chapter 3: Exact solutions of the
governing equations
The
Th governing
i equations
i
for
f continuum
i
fluid
fl id
mechanics derived in chapter 2 are sets of coupled
nonlinear
li
partial
i l diff
differential
i l equations,
i
which
hi h cannot
be solved
Chapter
p 1: Introduction
Definition of fluids
The subject of fluid mechanics
Applications of fluid mechanics
Microscopic (molecular) versus macroscopic
( ti
(continuum)
) approachh
Continuum approach
Eulerian and Lagrangian description
Reynolds
y
Homework 6 (due June 19, 2013)
(1) For steady boundary layer flow over an axial symmetric body as
shown below. The governing equations are
(ru ) + (rv) = 0 ,
x
y
and
u
u
u
dU s
2u
+ v
= Us
+
.
x
y
dx
y 2
(1a)
(1b)
The Manglers transformation (1948) is de
Fluid Mechanics
Homework 1 (due March 20, 2013)
(1) As we have discussed some interesting problems in the applications of
fluid mechanics in the class, you may probably be interested by some
of the problems. Would you please choose one problem in fluid
me
Chapter 5 : Low Reynolds number flows
We mayy have low Reynolds
y
number flow
- when the characteristic velocity is small,
- when the characteristic length
g is small, and/or
- when the viscosity is large.
For steadyy flow, the ggoverning
g equations
q
Fluid Mechanics
Homework 2
Problem 1:
Conservation of angular momentum equation:
Subsititue
into the angular momentum equation, we get
The first term on the left hand side equals that on the right hand side, thus the above equation reduces
to
The ith-comp
Chapter 2 : Physical and Mathematical
formulations of Fluid Mechanics
Continuum fluid mechanics
Conservation of mass, momentum (Newtons 2nd
law) and energy (1st law of thermodynamics)
Use the Lagrangian description to derive the
equations and the Euler
Fluid Mechanics
Problem 1
Homework 4
Problem 2
From continuity & momentum equation: (h L h/L 1)
U
0
L h
h
U
L
Uh2 Uh2
P
h2
~
1
UL L2
L
L
set P =UL/h2
h2
Uh4 Uh4
h4 h2
~
1
L3
L3
L4 L2
so that
Problem 3