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MAE 101A: Introductory Fluid Mechanics
Homework 6
Due Friday March 12, 5:00 PM
Problem 1
The
y
component of velocity in a steady incompressible ﬂow ﬁeld in the
xy
plane is
v
=
2
xy
(
x
2
+
y
2
)
2
Show that the simplest expression for the
x
component of velocity is
u
=
1
x
2
+
y
2

2
y
2
(
x
2
+
y
2
)
2
Problem 2
The
y
component of velocity in a steady, incompressible ﬂow ﬁeld in the
xy
plane is
v
=
Axy
(
y
2

x
2
), where
A
= 2
m

3
·
s

1
and
x
and
y
are measured in meters. Find
the simplest
x
component of velocity for this ﬂow ﬁeld.
Problem 3
Consider the incompressible ﬂow of a ﬂuid through a nozzle as shown in ﬁgure.
The area of the nozzle is given by
A
=
A
0
(1

bx
) and the inlet velocity varies according to
U
=
U
0
(1

e

λt
) where
A
0
= 0
.
5
m
2
,
L
= 5
m
,
b
= 0
.
1
m

1
,
λ
= 0
.
2
s

1
, and
U
0
= 5
m/s
.
Find and plot the acceleration on the centerline, with time as a parameter.
Figure 1: Problem 3
Problem 4
Consider the incompressible, inviscid ﬂow of air between two parallel disks of
radius
R
= 75
mm
, as shown in the ﬁgure. Air enters through a pipe of radius
R
i
= 25
mm
and exits radially, reaching
R
= 75
mm
at a velocity
V
= 15
m/s
.
(a) Apply continuity equation and simplify the equation.
1
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View Full Document(b) From (a) show that
~
V
=
V
(
R/r
)
~
e
r
, for
R
i
< r < R
.
(c) Calculate the radial acceleration of a particle at
r
=
R
i
and at
r
=
R
.
Figure 2: Problem 4
Problem 5
The inviscid incompressible ﬂow between two parallel disks. The upper disk is
rotating at an angular velocity
ω
as shown in the ﬁgure, while the lower disk is stationary. It
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 Spring '08
 Sakar

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