<Problem 1>
(a)
Re
D
=
4 ˙
m
π
D
μ
=
4
⋅
0.5
kg
/
s
(
)
π
⋅
0.005
m
(
)
⋅
8.6
×
10
−
4
N
−
s
/
m
2
(
)
=
148,051
>
2,300
=
Re
D
,
critcal
∴
Turbulent Flow
Re
D
>
Re
D
,
critcal
=
2,300
(
)
(b)
˙
E
in
−
˙
E
out
+
˙
E
gen
=
˙
E
store
˙
E
gen
=
˙
E
store
=
0
˙
E
in
=
˙
m c
p
T
m
+
q
"
⋅
P
⋅
dx
;
P
=
π
⋅
D
˙
E
out
=
˙
m c
p
T
m
+
dT
m
(
)
∴
˙
E
in
−
˙
E
out
=
˙
m c
p
T
m
+
q
"
⋅
P
⋅
dx
−
˙
m c
p
T
m
+
dT
m
(
)
=
0
!"
$
%
$
%
& !$
%
!' ( ')
!
*
!
!"
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˙
m c
p
dT
m
=
q
"
⋅
P
⋅
dx
=
q
"
max
⋅
sin
π
x
2
L
⎛
⎝
⎜
⎞
⎠
⎟
⋅
π
⋅
D
⋅
dx
dT
m
0
x
∫
=
q
"
max
⋅
π
⋅
D
˙
m c
p
⋅
sin
π
x
2
L
⎛
⎝
⎜
⎞
⎠
⎟
dx
0
x
∫
T
m
x
(
)
−
T
in
=
q
"
max
⋅
π
⋅
D
˙
m c
p
⋅ −
2
L
π
cos
π
x
2
L
⎛
⎝
⎞
⎠
⎡
⎣
⎢
⎤
⎦
⎥
0
x
=
2
⋅
q
"
max
⋅
L
⋅
D
˙
m c
p
⋅
1
−
cos
π
x
2
L
⎛
⎝
⎞
⎠
⎡
⎣
⎢
⎤
⎦
⎥
∴
T
m
x
(
)
=
T
in
+
2
⋅
q
"
max
⋅
L
⋅
D
˙
m c
p
⋅
1
−
cos
π
x
2
L
⎛
⎝
⎞
⎠
⎡
⎣
⎢
⎤
⎦
⎥
(c)
q
"(
x
)
=
h
⋅
T
s
x
(
)
−
T
m
x
(
)
[
]
⇒
T
s
x
(
)
=
T
m
x
(
)
+
q
"(
x
)
h
∴
T
s
x
(
)
=
T
in
+
2
⋅
q
"
max
⋅
L
⋅
D
˙
m c
p
⋅
1
−
cos
π
x
2
L
⎛
⎝
⎞
⎠
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 Fall '08
 Staff

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