Some General Points about Drag and Lift
Drag on a Sphere
As noted in Chapter 7 of your textbook, the common dimensional parameters often used to correlate the
drag force acting on an object, FD , are given by the density, ; the relative velocity of the ob

M353 Tutorial 6 (S. Zhang)
On-line computer exercise 6, due 10/10
1. (2.5:c1)
Use Jacobi method to solve Ax = b within 6
correct decimal places (forward error in the innity norm)
for n = 100 and n = 100, 000. The correct solution is
[(1)i1 ]. Initial x0 =

M353 Tutorial 1 (S. Zhang)
1. For nding the root of the function:
f (x) = x3 + x 1,
(a) Find an interval of length 1 that constains a root.
(b) Do 9 steps of becsions to nd an approximate root
within 210 of the true root.
(c) Print your program and output

1
2. Approximate 0 x2 dx by averaging the function,
with the Linear congruential generator:
M353 9.1 (S. Zhang)
1. Find the period of the Linear congruential generator:
a = 2, b = 1, m = 5, x0 = 0.
a = 2, b = 1, m = 8
(1) for innitely many random numbers.

(b) Finite dierence method with h = 1/2.
Central dierence:
M353 7.2 (S. Zhang) FD
0. 7.2 Finite dierence method.
x1 =
Find y = y(t) in the BVP:
y = f (t, y, y ),
y(a) = , y(b) = .
x1 =
(1) Finite dierence: at each unknown yi , replacing yi and yi by the c

CIEG 212
Solution for Homework Assignment #8 probfem 5L1 4.1 and 4.2 Knowing that. the couple shown acts in a vertical plane, determine the
stress at (a) pom: A, (b) pomt B.
For Mclmvxe I = 151' £7173
00+Sl'ap walk-«ape 2 I = 7% (80M [21.3)3
In: 11.5226 m

M353 Tutorial 5 (S. Zhang)
166.3137
1. (2.3:c1)
For the nn matrix with entries Aij = 3/(4i+
5j8), set x = [1, ., 1]T and b = Ax. Use Matlab backslash
command (A\ b) to compute xc , the double-precision computed solution. Find the innity norm of the forwar

M353 Tutorial 7 (S. Zhang)
end
method4=coef % The same!
p5=rot90(method4)
polyval(p5,[0 1 2 3])
1. Find the Lagrange interpolation polynomial P5 (x) which
ts the data
i
0
1
2
3
4
5
xi 0.2 0.8 1.5
2
2.2 2.8
yi
0
1
2
2.5 1.7
0
Output the 6 coecients of P5 (

M353 Hw 2 (S. Zhang) 1.1, 1.2, 1.4
f (0) = 10, f (1) = 10, f (2) = 2, f (3) = 44
0. 1.1: 2ab, 4ab, 5
1. (1.1:4b)
root.
[a, b] = [2, 3]
Find an interval of length one that contains a
Error bound:
sin x = 6x + 5
|r cn |
Apply two steps of bisection method

M353 Hw 3 (S. Zhang) 1.5 2.1
ans:
(a)
0. 1.5: 1bc, 2bc, 7
(A) Linear convergence, rate 1/2.
1. (1.5:1b)
Apply two steps of the secant method for the
root of the function:
(B) Superlinear, nearly quadratic convergence, r = 0.
(C)
ex + x = 7, x0 = 1, x1 = 2

M353 Study Guide 1 (S. Zhang)
Please practice on your own rst. Solutions will be posted online.
.718281828 = .101101111110002
So the rst 15 bits are
1. Write 1/8 in the binary form.
ans:
e = 10.101 10111 111002
(whole)
1
8 (2)
3. Convert binary number 110

M353 Study Guide 2 (S. Zhang)
Please practice on your own rst. Solutions will be posted online.
AT A =
1. Find the least-squares solution for the over-determined system. Find the root-mean-square-error.
1 1 0
2
0 1 1
2
1 2 1 x = 3 .
1 0 1
4
AT b =
3 2

CIEG 212
Solution for Homework Assignment #7 Problem 3.37
3.37 The aluminum rod AB (G = 27 GPa) is bonded to the brass rod BD (G = 39
GPa). Knowing that portion CD of the brass rod is hollow and has an inner diameter
of40 mm determine the angle of twist a

A car goes o the road and lands in the water. When should the driver try to exit the vehicle?
You can see this question addressed empirically on Mythbusters (Season 5, Episode 3, as seen here
http:/www.youtube.com/watch?v=ef2LmRmSQWk&feature=related) Give

ENME 331
FLUID MECHANICS
Hydrostatics Lab Experiment
In this experiment you will be applying the principles of hydrostatics to determine the net force (and moment) acting
on a container by a uid at rest within it. The uid container consists of a quadrant

ENME 331 FLUID MECHANICS
Bernoullis Equation Lab Experiment
Principle of Lab
Under the assumption of steady, incompressible, inviscid ow in a gravitational eld, Bernoullis equation,
p+
u2
+ gz = constant,
2
(1)
can be obtained from a spatial integration o

ENME 331
FLUID MECHANICS
Control Volume Lab: Jet impact.
1
Background
A moving stream of uid possesses kinetic, potential and internal energy. The conversion of the energy of a uid jet
into mechanical work is the object of such devices as turbines, pelton

Project Matlab Assignment #2
For this assignment, you will calculate the trajectory of a spherical particle subject to the forces of gravity and
aerodynamic drag in a quiescent (still) environment. Specically, use the following parameters and initial cond

If a vortex is made in a pool with its axis of rotation
normal to the surface, its leaves a visible signature
by causing a depression or dimple in the free surface due to its low pressure (see photograph at right
showing a pair for vortices made by a padd

ENME 331 Project Assignment #1
Project milestones:
You should have mostly completed a read through chapter 7 by now, and attempted
several problems to make sure you understand how to perform a dimensional analysis.
Sections 7.1 7.6 instruct you o

A jet engine is tested in a stationary test stand to measure its static thrust. Over a spherical
surface with R = 3 m centered on the intake opening, the velocity has a uniform magnitude, Vi ,
and is directed radially inward (see gure and inset at right).

Water ows out of a downward pointing nozzle with an axial exit velocity, wo . Once
it leaves the nozzle, the water falls in a jet, with an Eulerian velocity given by:
u 0
v 0
w =
2
wo + 2gz
where z is the coordinate in the direction of gravity (with z = 0