ENSC-283
Assignment #8
Assignment date: Monday Mar. 23, 2009
Due date: Monday Mar. 30, 2009
Problem1: (Noncircular conduit)
Air at a temperature of 50 and standard pressure flows from a furnace through a
20 cm diameter pipe with an average velocity of 3 /

ENSC 283 Week # 4, Tutorial # 3 Hydrostatic Forces
C
Problem 1: In the figure the surface AB is a
circular arc with a radius of 2 m. The
distance DB is 4 m. If water is the liquid
supported by the surface and if atmospheric
pressure prevails on the other

ENSC-283
Assignment #9
Assignment date: Monday Mar. 30, 2009
Due date: Monday Apr. 6, 2009
Problem1: (Pressure drop in pipe flow)
The pressure drop, , for steady, incompressible viscous flow through a straight
horizontal pipe depends on the pipe length, ,

ENSC 283 Week # 5, Tutorial # 4 Conservation of Mass
Problem 1: The open tank in the
figure contains water at 20C. For
incompressible flow, (a) derive an
analytic expression for dh/dt in terms
of (Q1, Q2, Q3). (b) If h is constant,
determine V2 for the gi

ENSC 283 Week # 11, Tutorial # 7 Capillary Viscometer
Problem: A simple and accurate viscometer can be made from a length of
capillary tubing. If the flow rate and pressure drop are measured, and the
tube geometry is known, the viscosity of a Newtonian li

ENSC 283 Week # 8, Tutorial # 5 First Law Analysis
volume is connected to a high-pressure air
Problem 1: A tank of 0.1
line; both line and tank are initially at a uniform temperature of 20 . The
initial tank gage pressure is 100
. The absolute line pressu

4
(ii)
This curve is a right-handed helix with an elliptic projection on the xy-plane. As t
increases, the z-coordinate of the point on the helix corresponding to t increases also
increases, and the projection of the point onto the xy plane moves around t

3
we have
V
T
= . Thus
P
k
P V T
kT
= 2
V T P
V
8.
k
P
V
k
=
kT
= 1.
VP
ex cos x sin x ex
cos x sin x
=
.
2x
e
ex
(ii) The chain rule gives g (y) = (sec2 (y2 + cos y) (2y sin y).
1
(1 + 3w2 cos(w3 + 4).
(iii) The chain rule gives h (w) =
w + sin(w3 + 4)

2
2
1
2
1
1
2
5.
(i)
Call the function f ; so f (x, y) = ln(x+2y), and the domain is cfw_ (x, y) R2 | x+2y > 0 .
By denition the range of f is cfw_ ln(x + 2y) | (x, y) R2 and x + 2y > 0 . Observe that
if t is any positive real number then there is a point

2
2
(i)
1
2
1
1
1
2
(ii)
If there is a limit, it must be a single number with the property that values of f (x)
can be made as close as we like to by choosing x sufciently close to 1. The graph
shows that f (x) = 1 whenever x is less than 1, and so if the

3
(3, 1, 0)
(3, 0, 1)
(iii) This is an ellipsoid with centre at (0, 0, 0). It has axial lengths of 4 (along the x-axis),
6 (along the y-axis) and 2 (along the z-axis). Equivalently, the semiaxes are 2, 3 and 1.
(0, 3, 0)
(2, 0, 0)
(iv) A paraboloid: it is

ENSC283 INTRODUCTION TO FLUID MECHANICS
27 February 2009
Midterm Examination
M. Bahrami
This is a 2-1/2 hours, closed-book and notes examination.
You are permitted to use one 8.5 in. 11 in. crib sheet (double-sided) and the
property tables.
There are 5 qu

ENSC-283
Assignment #1
Assignment date: Monday Jan. 12, 2009
Due date: Monday Jan. 19, 2009
Problem: (Newtonian fluid shear stress)
The velocity distribution for the flow of a Newtonian fluid between two wide,
parallel plates (see Figure) is given by the

ENSC-283
Assignment #3
Assignment date: Monday Jan. 26 2009
Due date: Monday Feb. 2, 2009
Problem1: (force components on a curved submerged surface)
The gate shown in Fig. 1 is hinged at and has constant width,
5 . The
equation of the surface is
/ , where

ENSC-283
Assignment #2
Assignment date: Monday Jan. 19, 2009
Due date: Monday Jan. 26, 2009
Problem1: (hydrostatic force on a plane circular surface)
The 4-m diameter circular gate of Figure 1 is located in the inclined wall of a large
reservoir containin

ENSC 283 Quiz #1
Jan. 27, 2009
Name: Student ID:.
Time: 45 minutes or less. Develop answers on available place. The quiz has 5% (bonus) of
the total mark. Closed books & closed notes.
Problem 1 (50%):
A square, side dimension a (m), has its top edge H (m)

ENSC-283
Assignment #7
Assignment date: Monday Mar. 9, 2009
Due date: Monday Mar. 16, 2009
Problem1: (Fully developed laminar flow down an inclined plane surface)
A liquid flows down an inclined plane surface in a steady, fully developed laminar
film of t

ENSC-283
Assignment #6
Assignment date: Monday Feb. 23, 2009
Due date: Monday Mar. 2, 2009
Problem: (Flow under a sluice gate: hydrostatic pressure force)
Water in an open channel is held in by a sluice gate. Compare the horizontal force
of the water on t

ENSC-283
Assignment #5
Assignment date: Monday Feb. 9, 2009
Due date: Monday Feb. 16, 2009
Problem1: (choice of control volume for momentum analysis)
Water from a stationary nozzle strikes a flat plate as shown. The water leaves the
nozzle at 15 / ; the n

ENSC-283
Assignment #4
Assignment date: Monday Feb. 2, 2009
Due date: Monday Feb. 9, 2009
Problem1: (Nozzle)
The converging-diverging nozzle shown in Fig. 1 expands and accelerates dry air
to supersonic speeds at the exit, where
8
and
240 . At the
284
,
6

ENSC 283 Week # 10, Tutorial # 6 Plane Couette Flow
h
Problem 1: A wide moving belt passes
through a container of a viscous liquid. The
belt moves vertically upward with a
constant velocity as illustrated in the
figure. Because of viscous forces the belt

ENSC 283 Week # 3, Tutorial # 2 Pressure Distribution in a Fluid
Problem 1: A manometer connects an oil pipeline and a water pipeline as
shown in the figure. Determine the difference in pressure between the two
pipelines using the readings on the manomete

ENSC 283 Week # 2, Tutorial # 1 Dimensionless Quantities
Problem 1: A dimensionless combination of
variables that is important in the study of
viscous flow through pipes is called the
Reynolds number, Re, defined as /
where, as indicated in the figure, is

ENSC 283 Week # 12, Tutorial # 8 Flow in an Irrigation System
Problem: Spray heads in an agricultural spraying system are to be supplied
with water through 50 of drawn aluminum tubing from an engine-driven
pump. In its most efficient operating range, the

ENSC 283 Week # 13, Tutorial # 9 Capillary Effect: Use of
Dimensional Matrix
Problem: When a small tube is dipped
Tube
into a pool of liquid, surface tension
causes a meniscus to form at the free
h
surface, which is elevated or depressed
depending on the

ENSC 283
INTRODUCTION TO FLUID MECHANICS
Assignment 4
Due date: Feb 18
Turn in your homework problems in order, and always write down all the steps that led you to
the answer. If you do not turn in a problem, write the number and letter, e.g. 2(b), and
wr

EN
NSC 283
3
INTR
RODUC
CTION TO FLU
T
UID MEC
CHANIC
CS
Assign
nment 2
Due date: Jan 28
n
Turn in your homewor problems in order, an always wr
y
rk
nd
rite down al the steps that led y
ll
s
you to
the answer. If you do not turn in a prob lem, write the n

ENSC 283
INTRODUCTION TO FLUID MECHANICS
Assignment 6
Due date: March 11
Turn in your homework problems in order, and always write down all the steps that led you to
the answer. If you do not turn in a problem, write the number and letter, e.g. 2(b), and

ENSC 283
INTRODUCTION TO FLUID MECHANICS
Solution for Assignment 1
Problem 1:
A block of weight W is being pulled over a table by another weight W0, as shown in the figure. Find an
algebraic formula for the steady velocity U, of the block if it slides on