or
2
2
ft
55.6
500 ft s
(0.022) 440 ft
ft
1.2 ft 232.2
s
L
h
==
Transition range
Laminar flow
Wholly turbulent flow
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.05
0.04
0.03
0.02
0.015
0.01
Problem 8.65
Assume a car’s exhaust system can be approximated as 14ft of 0.125-ft- diameter cast-iron
pipe with the equivalent of six 90 flanged elbows and a muffler. The muffler acts as a
resistor with a loss coefficient of =8.5
L
K. Determine the pressure at the beginning of the
exhaust system if the flowrate is 0.10 cfs , the temperature is 250 F , and the exhaust has
the same properties as air.
Solution 8.65
4
Thus,
Equivalent Roughness,
ε
Pipe Feet Millimeters
Riveted steel 0.003–0.03 0.9–9.0
Concrete 0.001–0.01 0.3–3.0
Wood stave 0.0006–0.003 0.18–0.9
K
L
m
= 8.5
K
L
el
= 0.3
MIDAS
(1)
(2)
V
2
so that with
()
ρ
µ
−
−
×
== =
⋅
×
3
3
7
2
slug ft
1.74 10 8.15 0.125ft
s
ft
Re 3770
lb s
4.7 10 ft
VD
We obtain from the figure below, =0.047f
Hence,
Transition range
Laminar flow
Wholly turbulent flow
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.05
0.04
0.03
0.02
0.015
0.01
Problem 8.66
The pressure at section (2) shown in the figure below is not to fall below 60 psi when the
flowrate from the tank varies from 0 to 1.0 cfs and the branch line is shut off. Determine
the minimum height, h, of the water tank under the assumption that (a) minor losses are
negligible, (b) minor losses are not negligible
Solution 8.66
With section (1) at the water tank surface,
γγ
++=+ ++ +
22 2
11 2 2 2
12
22 2
L
p
VpV V
zzfK
ggDg
, where ===+
111
0, 0, 16ft
p
Vz h
and =
20z Thus, with =2
VV
Hence,
Branch line (2) Main
line
6 ft
10 ft
All pipe is 6-in.-diameter plastic
( /D = 0), flanged fittings
h
600 ft
with 15
90° elbows
900 ft
ε
=0.0155f (see the figure below)
(a) Neglect minor losses
()
=
0
L
K:
From Eq. (1),
(b) Include minor losses:
Transition range
Laminar flow
Wholly turbulent flow
0.1
0.09
0.08
0.07
0.06
0.05
0.05
0.04
0.03
0.02
0.015
Thus, from Eq. (1),
Problem 8.67
The pressure at section (2) shown in the figure below is not to fall below 60 psi when the
flowrate from the tank varies from 0 to 1.0 cfs and the branch line is open so that half of
the flow from the tank goes into the branch, and half continues in the main line. Determine
the minimum height, h, of the water tank under the assumption that (a) minor losses are
negligible, (b) minor losses are not negligible
Solution 8.67
For the flow from (1) to (2):
where
()
a and
()
b denote pipes “a” and “b” as indicated in the figure.
Branch line (2)
(a) (b) Main
line
6 ft
10 ft
All pipe is 6-in.-diameter plastic
( /D = 0), flanged fittings
h
600 ft
with 15
90° elbows
900 ft
ε
(1)
•
(a) Neglect minor losses
()
==
0
ab
LL
KK
:
From Eq. (2),
Transition range
Laminar flow
Wholly turbulent flow
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.05
0.04
0.03
0.02
0.015
0.01
0.008
and
==
0.2
btee
LL
KK
From Eq. (2),
Problem 8.68
The 1-in.-
2diameter hose shown in the figure below can withstand a maximum pressure of
200 psi without rupturing. Determine the maximum length, , allowed if the friction
factor is 0.022 and the flowrate is 0.010 cfs. Neglect minor losses.
Solution 8.68
Thus, with =0.022f, Eq. (1) becomes (using =1
VV
)
3 ft
L
D
= 0.50 in.
Nozzle tip diameter = 0.30 in.
Water
Q
=
0.010 cfs
10 ft
𝓵
Pump
3 ft
L
D = 0.50 in.
Nozzle tip diameter = 0.30 in.
Water
(1)
•
(2)
Q =
0.010 cfs
10 ft
𝓵
Pump
•
Problem 8.69
The hose shown in the figure below will collapse if the pressure within it is lower than
10 psi below atmospheric pressure. Determine the maximum length, , allowed if the
friction factor is 0.015 and the flowrate is 0.010 cfs . Neglect minor losses.
Solution 8.69
γγ
++=+ ++
22
2
11 2 2
12
222
pV p V LV
zzf
ggDg
, (1)
Thus, with =0.015f, Eq. (1) becomes
3 ft
L
D
= 0.50 in.
Nozzle tip diameter = 0.30 in.
Water
Q
=
0.010 cfs
10 ft
𝓵
Pump
(1)
•
(2)
•
Problem 8.70
According to fire regulations in a town, the pressure drop in a commercial steel horizontal
pipe must not exceed 1.0 psi per 150 ft of pipe for flowrates up to gal
500 min . If the water
temperature is above 50 F , can a 6-in.– diameter pipe be used?
Solution 8.70
Determine the pressure drop in a 6-in.- diameter pipe.
From the table below,
ε
=0.00015 ft so that
ε
−−
×
==×
44
1.5 10 310
6ft
12
D
Equivalent Roughness,
ε
Pipe Feet Millimeters
Riveted steel 0.003–0.03 0.9–9.0
The largest −
12
p
p will occur with the largest f, which occurs with
the smallest Re , or largest
ν
. Since the viscosity of water increases as
the temperature decreases, we consider the coldest case 50 F=
T.
From Table B.1 Physical Properties of Water (BG/EE Units), at
f
Thus,
Hence, with =×
5
Re 2.01 10 and
ε
−
=× 4
310
D, we obtain from the figure below, =0.018f
Therefore, from Eq. (1),
()
γ
−
==
2
12
2
ft
5.67
150ft s
0.018 2.70 ft
6ft
ft 232.2
12 s
pp
Transition range
Laminar flow
Wholly turbulent flow
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.05
0.04
0.03
0.02
0.015
0.01
Re = VD
_____
μ
ρ