CBE 320
September 3, 2010
Introductory Transport Phenomena
Problem Session I
Part B: Review of Mathematical Topics
Review Appendices A and C in
Transport Phenomena
before doing this assignment.
1. Sketch the following functions; be sure to label the axes carefully.
a.
y
(
x
)=
cosh
bx
cosh
b
,
−∞
<x<
∞
,b
= constant
b.
y
(
x
e
bx
,
−∞
∞
= constant
c.
y
(
x
tanh
x
x
,
−∞
∞
d.
v
z
(
r
v
0
±
1
−
²
r
R
³
2
´
,
0
≤
r
≤
R,
v
0
,R
= constant
e.
v
z
(
r
v
0
ln(
r/R
)
ln
κ
,κ
R
≤
r
≤
R,
v
0
,R,κ
= constant
,
0
<κ<
1
2. A particle is located at
x
=4
,
y
=2
,
z
=1
in Cartesian (rectangular) coordinates.
a. What are the cylindrical coordinates of the particle
(
r, θ, z
)
?
b. What are the spherical coordinates of the particle
(
r, θ, φ
)
?
3. A particle, located at
x
,
y
,
z
=0
, is moving in a Northeasterly direction with speed 8 cm/sec (“North” = direction
of the
+
y
-axis; “East” = direction of the
+
x
-axis). By means of a carefully labelled sketch, show the vector
v
(assume
one unit in distance is numerically equal to one cm/sec). Then show the Cartesian components
v
x
and
v
y
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