A long rod of 60-mm diameter and thermophysical properties ρ = 8000 k g / m 3 , c = 500 J / k g ⋅ K , and k = 50 W / m ⋅ K is initially at a uniform temperature and is heated in a forced convection furnace maintained at 750 K. The convection coefficient is estimated to be 1000 W / m 2 ⋅ K . (a) What is the centerline temperature of the rod when the surface temperature is 550 K? (b) In a heat-treating process, the centerline temperature of the rod must be increased from T i = 300 K to T = 500 K . Compute and plot the centerline temperature histories for h = 100 , 500 , and 1000 W / m 2 ⋅ K . In each case the calculation may be terminated when T = 500 K .
A long rod of 60-mm diameter and thermophysical properties ρ = 8000 k g / m 3 , c = 500 J / k g ⋅ K , and k = 50 W / m ⋅ K is initially at a uniform temperature and is heated in a forced convection furnace maintained at 750 K. The convection coefficient is estimated to be 1000 W / m 2 ⋅ K . (a) What is the centerline temperature of the rod when the surface temperature is 550 K? (b) In a heat-treating process, the centerline temperature of the rod must be increased from T i = 300 K to T = 500 K . Compute and plot the centerline temperature histories for h = 100 , 500 , and 1000 W / m 2 ⋅ K . In each case the calculation may be terminated when T = 500 K .
Solution Summary: The author explains how to find the maximum steady state temperature for dry, moist and wet hay.
A long rod of 60-mm diameter and thermophysical properties
ρ
=
8000
k
g
/
m
3
,
c
=
500
J
/
k
g
⋅
K
,
and
k
=
50
W
/
m
⋅
K
is initially at a uniform temperature and is heated in a forced convection furnace maintained at 750 K. The convection coefficient is estimated to be
1000
W
/
m
2
⋅
K
.
(a) What is the centerline temperature of the rod when the surface temperature is 550 K?
(b) In a heat-treating process, the centerline temperature of the rod must be increased from
T
i
=
300
K
to
T
=
500
K
. Compute and plot the centerline temperature histories for
h
=
100
,
500
,
and
1000
W
/
m
2
⋅
K
. In each case the calculation may be terminated when
T
=
500
K
.
Problem (17): water flowing in an open channel of a rectangular cross-section with width (b) transitions from a
mild slope to a steep slope (i.e., from subcritical to supercritical flow) with normal water depths of (y₁) and
(y2), respectively.
Given the values of y₁ [m], y₂ [m], and b [m], calculate the discharge in the channel (Q) in [Lit/s].
Givens:
y1 = 4.112 m
y2 =
0.387 m
b = 0.942 m
Answers:
( 1 ) 1880.186 lit/s
( 2 ) 4042.945 lit/s
( 3 ) 2553.11 lit/s
( 4 ) 3130.448 lit/s
Problem (14): A pump is being used to lift water from an underground
tank through a pipe of diameter (d) at discharge (Q). The total head
loss until the pump entrance can be calculated as (h₁ = K[V²/2g]), h
where (V) is the flow velocity in the pipe. The elevation difference
between the pump and tank surface is (h).
Given the values of h [cm], d [cm], and K [-], calculate the maximum
discharge Q [Lit/s] beyond which cavitation would take place at the
pump entrance. Assume Turbulent flow conditions.
Givens:
h = 120.31 cm
d = 14.455 cm
K = 8.976
Q
Answers:
(1) 94.917 lit/s
(2) 49.048 lit/s
( 3 ) 80.722 lit/s
68.588 lit/s
4
Problem (13): A pump is being used to lift water from the bottom
tank to the top tank in a galvanized iron pipe at a discharge (Q).
The length and diameter of the pipe section from the bottom tank
to the pump are (L₁) and (d₁), respectively. The length and
diameter of the pipe section from the pump to the top tank are
(L2) and (d2), respectively.
Given the values of Q [L/s], L₁ [m], d₁ [m], L₂ [m], d₂ [m],
calculate total head loss due to friction (i.e., major loss) in the
pipe (hmajor-loss) in [cm].
Givens:
L₁,d₁
Pump
L₂,d2
오
0.533 lit/s
L1 =
6920.729 m
d1 =
1.065 m
L2 =
70.946 m
d2
0.072 m
Answers:
(1)
3.069 cm
(2) 3.914 cm
( 3 ) 2.519 cm
( 4 ) 1.855 cm
TABLE 8.1
Equivalent Roughness for New Pipes
Pipe
Riveted steel
Concrete
Wood stave
Cast iron
Galvanized iron
Equivalent Roughness, &
Feet
Millimeters
0.003-0.03 0.9-9.0
0.001-0.01 0.3-3.0
0.0006-0.003 0.18-0.9
0.00085
0.26
0.0005
0.15
0.045
0.000005
0.0015
0.0 (smooth) 0.0 (smooth)
Commercial steel or wrought iron 0.00015
Drawn…
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