"av-
lernoulli Streamline Theorem
Consider steady Eulers equation for an incompressible 2D ow
The above equation transforms into
(Vx 5) xi =1! '7 lag?)
5
The gravitational force per unit volume p 62, can be expressed in the following way:
_ V X
In View
THE LIQUID MIRROR TELESCOPE
The fact that a liquid under uniform (solid body) rotation forms a parabolic free surface profile is known since the times
of Sir Isaac Newton. Here we will derive the prole using the differential form of the conservation equat
Assignement No. 2
1. Determine which of the following functions is possible velocity potential for inviscid
incompressible flow.
(a) sin ( x / l ) + sin ( y / l )
(b) sin ( xy / l 2 )
(
)
(c) arc tan 2yc / "# x 2 + y 2 c 2 $%
(d) A ( r + a / r ) cos ( B /
PROBLEM: Consider the velocity field given by
q =i A x - j A y
(a)
(b)
(d)
(e)
(f)
where
A =2
Show that the flow satisfies continuity and that it is irrotational.
Determine the shapes of - lines
What is the acceleration at point (1,1)?
If the stagnation p
Oseen - Hamel Vortex (or Lamb-Oseen)
Consider the laminar, incompressible vortex flow in an infinite domain. Assume
that:
v r = vz = 0 and v = f n t, r)
Under the above assumptions, the equations simplify into:
r - momentum
v 2 p
r =
r
- momentum
v
2v
PROBLEM No. 7. PROBLEM
A very thinNo.
liquid
is flowing
down
on adown
very steadily
large on a very large
7. film
A very
thin liquid
filmsteadily
is flowing
= 0) , shown
ertical plate (v /zvertical
in
Figure
1.
Consider
the
flow
to
be
laminar
and
that
u l
Boundary Layer II
The Laminar Boundary Layer
Consider
a
semi-infinite
stationary
wedge,
immersed
in
an
infinite
incompressible fluid that is moving uniformly in the x-direction. The wedge is
aligned with the flow and is thin ( is small) as shown in Fig. 1
PROBLEM 1
In a spacecraft travelling in deep space, a rocket, that produces a constant frame
acceleration of ax, is fired. Based on continuity and the Navier-Stokes equations and
applying Galilean transformation show that the liquid fuel (with density ) w
U
CON CORDIA UNIVERSITY
ENGR 244/1: Mechanics of Materials
Section AA, Summer 2013
Mid-Term 2 (Monday — 1“-June-2012 - From 16:40 to 18:10 (90 minutes)
Instructors: Dr. John Cheung
Type of examination: Closed book exam.
Materials Allowed: ENCS approved st
1
HEATING, VENTILATION
AND AIR CONDITIONING
SYSTEMS
Dr. Suraj JOSHI
"Heating, Ventilating and Air Conditioning - Analysis and Design," 6th Edition,
F.C. McQuiston, J. D. Parker and J.D. Spitler, John Wiley & Sons, 2000.
This material is reproduced with pe
1
LECTURE 10
EXTENDED SURFACE
HEAT EXCHANGERS
Chapter 14
2
Heat exchangers
Almost all heating and cooling design projects require one or
more heat exchangers.
Externally finned tubes are used in water-to-air and refrigerant-
to-air coils.
Only sensible
1
LECTURE 11
REFRIGERATION
Chapter 15
2
Refrigeration in HVAC
Every HVAC system depends on a refrigeration system to provide either
a cold liquid such as water or brine or a direct removal of sensible and
latent heat from an airstream.
Refrigeration sys
1
LECTURE 2
MOIST AIR PROPERTIES
AND CONDITIONING
PROCESSES
Chapter 3
2
Moist air and the standard atmosphere
Ideal gas equation for air:
= Universal gas constant
= 1545.32 (ft-lbf)/(lb mole-R) = 8314 J/ (kg mole-K)
Ma = molecular mass of dry air = 28.
1
LECTURE 9
FANS AND BUILDING AIR
DISTRIBUTION
Chapter 12
2
Fan
The fan is an essential component of almost all heating
and air-conditioning systems.
A fan is used to move air through ducts and to induce air
motion in the space.
An understanding of the
1
LECTURE 4
SPACE HEATING LOAD
Chapter 6
2
Maximum probable heat
Prior to the design of the heating system, an estimate must be
made of the maximum probable heat loss of each room or
space to be heated.
There are two kinds of heat losses:
Heat transmitt
1
LECTURE 7
Chapter 8: Heat Balance Method
Chapter 10: Flow, Pumps and Piping Design
2
Overview of the heat balance method
3
For exterior surface:
Correct this in book
For interior surface:
+
=
4
Limitations
qconduction,ext,j,q
qconduction,in,j,q , un
1
LECTURE 3
HEAT TRANSMISSION IN
BUILDING STRUCTURES
Chapter 5
2
Building envelope
In HVAC work the term building envelope refers to the
walls, roof, floors, and any fenestrations that enclose the
building
It is through these components of a building th
1
LECTURE 5
SOLAR RADIATION
Chapter 7
2
Solar radiation
Important effects on both heat gain and heat loss of building
These effects depend to a great extent on location of the
sun in the sky, clearness of the atmosphere, and nature and
orientation of bu
1
LECTURE 6
Chapter 8: The Cooling Load
Chapter 9: Energy Calculations
DD Method
2
Chapter 8: The Cooling Load
Heat gain is the rate at which energy is transferred to or
generated within a space. It has two components:
(i) sensible heat, and
(ii) latent
1
LECTURE 8
FLOW, PUMPS & PIPING DESIGN
Chapter 10
2
Fluid flow basics
The adiabatic, steady flow of a fluid in a pipe or conduit is governed
by the first law of thermodynamics, which leads to the equation
The sign convention is such that work done on t
Orthogonal Curvilinear Coordinates
Suppose that , , and represent a set of orthogonal curvilinear coordinates and i
, i , and i are the unit vectors along the , , and directions respectively. The
relationship with the Cartesian coordinates is,
x = x (, ,
The Reynolds Experiment
In 1883 Reynolds performed his classical experiment on pipe flow. A schematic
of the apparatus is shown underneath. It consisted from a water tank, a pipe with
a bell-mouth entrance immersed into the water tank, an assembly to inje
1
Dr. Georgios H. Vatistas, November 2000
Chapter I
Fundamental Concepts of
Fluid Mechanics
"For we do not think that we know a thing until
we acquainted with its primary conditions or first
principles and have carried our analysis as far as
its simplest
Types of Fluid Element Motions and Deformations
Fluid elements can undergo two types of motion as a whole (without any structural
change): solid body translation (i) and rotation (ii).
The two other motions involve structural change (deformation) of the f
Conservation Equations
in Differential Form
The fundamental laws governing fluid behavior are:
(i)
The law of conservation of mass: "mass can not be created not destroyed"
(ii)
Newton's second law of motion: "the total force external the system is equal t
September 2006
Ancient Wisdom
and the Laws of Nature
Georgios H. Vatistas
Department of Mechanical and Industrial Engineering
Concordia University
Montreal Canada
Summary. The laws of nature as we see them are the foundations of science and technology. Th