Chapters 1 Solutions - Fluid Mechanics , Chemical Engineering

# Chapters 1 Solutions - Fluid Mechanics , Chemical Engineering Notes - Chemical Engineering

## Document Description: Chapters 1 Solutions - Fluid Mechanics , Chemical Engineering for Chemical Engineering 2022 is part of Chemical Engineering preparation. The notes and questions for Chapters 1 Solutions - Fluid Mechanics , Chemical Engineering have been prepared according to the Chemical Engineering exam syllabus. Information about Chapters 1 Solutions - Fluid Mechanics , Chemical Engineering covers topics like and Chapters 1 Solutions - Fluid Mechanics , Chemical Engineering Example, for Chemical Engineering 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Chapters 1 Solutions - Fluid Mechanics , Chemical Engineering.

Introduction of Chapters 1 Solutions - Fluid Mechanics , Chemical Engineering in English is available as part of our Chemical Engineering preparation & Chapters 1 Solutions - Fluid Mechanics , Chemical Engineering in Hindi for Chemical Engineering courses. Download more important topics, notes, lectures and mock test series for Chemical Engineering Exam by signing up for free. Chemical Engineering: Chapters 1 Solutions - Fluid Mechanics , Chemical Engineering Notes - Chemical Engineering
``` Page 1

Introduction to Fluid Mechanics 7
th
Edition
Fox, Pritchard, & McDonald
Answers to Selected Problems, Chapter 1

1.5 M = 5913 kg
1.7 L = 27.25 in.  D = 13.75 in.
1.9
2
2
05 . 2
t g
W
y =
1.11 d = 0.109 mm
1.15 y = 0.922 mm
1.17 a) N·m/s, lbf·ft/s b) N/m
2
, lbf/ft
2
c) N/m
2
, lbf/ft
2
, d) 1/s, 1/s e) N·m, lbf·ft
f) N·s, lbf·s  g) N/m
2
, lbf/ft
2
h) m
2
/s
2
·K, ft
2
/s
2
·R i) 1/K, 1/R j) N·m·s, lbf·ft·s
1.19 a) 6.89 kPa  b) 0.264 gal  47.9 N·s/m
2

1.21 a) 0.0472 m
3
/s  b) 0.0189 m
3
c) 29.1 m/s  d) 2.19 x 10
4
m
2

1.23 101 gpm
1.25 SG = 13.6  v = 7.37 x 10
-5
m
3
/kg  ?
E
= 847 lbf/ft
3
,  ?
M
= 144 lbf/ft
3

1.27 2.25 kgf/cm
2

1.29 c = 0.04 K
1/2
·s/m
0
0
max
36 . 2
T
p A
m
t
·
= & (ft
2
, psi, R)
1.31 C
D
is dimensionless
1.33 c: N·s/m, lbf·s/ft k: N/m, lbf/ft  f: N, lbf
1.35 H(m) = 0.457 - 3450·(Q(m
3
/s))
2

1.37 ? = 0.0765 ± 2.66 x 10
-4
lbm/ft
3
(± 0.348%)
1.39 ? = 1130 ± 21.4 kg/m
3
SG = 1.13 ± 0.0214
1.41 ? = 930 ± 27.2 kg/m
3

1.43 t = 1, 5, 5 s   Flow rate uncertainty = ± 5.0, 1.0, 1.0%
1.45 µ = 1.01 x 10
-3
N·s/m
2
± 0.609%
1.47 dx = ± 0.158 mm
1.49 H = 57.7 ± 0.548 ft  ?
min
= 31.4
o

Page 2

Introduction to Fluid Mechanics 7
th
Edition
Fox, Pritchard, & McDonald
Answers to Selected Problems, Chapter 1

1.5 M = 5913 kg
1.7 L = 27.25 in.  D = 13.75 in.
1.9
2
2
05 . 2
t g
W
y =
1.11 d = 0.109 mm
1.15 y = 0.922 mm
1.17 a) N·m/s, lbf·ft/s b) N/m
2
, lbf/ft
2
c) N/m
2
, lbf/ft
2
, d) 1/s, 1/s e) N·m, lbf·ft
f) N·s, lbf·s  g) N/m
2
, lbf/ft
2
h) m
2
/s
2
·K, ft
2
/s
2
·R i) 1/K, 1/R j) N·m·s, lbf·ft·s
1.19 a) 6.89 kPa  b) 0.264 gal  47.9 N·s/m
2

1.21 a) 0.0472 m
3
/s  b) 0.0189 m
3
c) 29.1 m/s  d) 2.19 x 10
4
m
2

1.23 101 gpm
1.25 SG = 13.6  v = 7.37 x 10
-5
m
3
/kg  ?
E
= 847 lbf/ft
3
,  ?
M
= 144 lbf/ft
3

1.27 2.25 kgf/cm
2

1.29 c = 0.04 K
1/2
·s/m
0
0
max
36 . 2
T
p A
m
t
·
= & (ft
2
, psi, R)
1.31 C
D
is dimensionless
1.33 c: N·s/m, lbf·s/ft k: N/m, lbf/ft  f: N, lbf
1.35 H(m) = 0.457 - 3450·(Q(m
3
/s))
2

1.37 ? = 0.0765 ± 2.66 x 10
-4
lbm/ft
3
(± 0.348%)
1.39 ? = 1130 ± 21.4 kg/m
3
SG = 1.13 ± 0.0214
1.41 ? = 930 ± 27.2 kg/m
3

1.43 t = 1, 5, 5 s   Flow rate uncertainty = ± 5.0, 1.0, 1.0%
1.45 µ = 1.01 x 10
-3
N·s/m
2
± 0.609%
1.47 dx = ± 0.158 mm
1.49 H = 57.7 ± 0.548 ft  ?
min
= 31.4
o

Introduction to Fluid Mechanics 7
th
Edition
Fox, Pritchard, & McDonald
Answers to Selected Problems, Chapter 2

2.3 Streamlines:
x
c
y =
2.5 Streamlines:
t
a
b
x c y
-
=
2.7 Streamlines:
?
?
?
?
?
?
?
?
+
=
c
x a
b
y
2
1

2.9 Streamlines: y = 3x  ?t = 0.75 s
2.11 Streamlines: x
2
+ y
2
= c
2.13 Pathlines: y = 2/x  Streamlines: y = 2/x
2.15
a
K
p
?
2
=
2.17 Pathlines:
t C
e y y
0
= ,
()
2
2
1
0
At t B
e x x
+
=  Streamlines:
t
x y
5 . 0 1
1
+
=
2.19 Pathlines:
t b
e y y
-
=
0
,
2
2
1
0
at
e x x =  Streamlines:
t a
b
Cx y
-
=
2.21 Pathlines: 1 4 + = t y ,
2
05 . 0
3
t
e x =  Streamlines:
?
?
?
?
?
?
+ =
3
ln
40
1
x
t
y
2.23 Streamlines: () ( )( )
0 0 0
sin t t t v t y - = ? , ( ) ( )
0 0 0
t t u t x - =
2.25 Streaklines:
() t -
=
t
e y ,
() ()
2 2
1 . 0 t t - + -
=
t t
e x Streamlines:
() t
x y
2 . 0 1
1
+
=
2.29 Streamlines: 4
4
2
+ =
x
y (4 m, 8 m) (5 m, 10.25 m)
2.31 (2.8 m, 5 m)   (3 m, 3 m)
2.33
T
S
T b
'
+
'
=
1
2
3
?   b´ = 4.13 x 10
-9
m
2
/s·K
3/2
S´ = 110.4 K
2.35 t
yx
= - 4.56 N/m
2

2.39 a = - 0.491 ft/s
2
2.41 L = 2.5 ft
2.43 t = 1.93 s
2.45
?
?
?
?
?
?
?
?
- =
- t
Md
A
e
A
Mgd
V
µ
µ
?
1
sin
V = 0.404 m/s  µ = 1.08 N·s/m
2

2.47 F = 2.83 N
2.49 F = 0.0254 N
2.51 µ = 8.07 x 10
-4
N·s/m
2

2.53
H R V
a Mgr
m
3
2
2 p
µ =  µ = 0.0651 N·s/m
2

Page 3

Introduction to Fluid Mechanics 7
th
Edition
Fox, Pritchard, & McDonald
Answers to Selected Problems, Chapter 1

1.5 M = 5913 kg
1.7 L = 27.25 in.  D = 13.75 in.
1.9
2
2
05 . 2
t g
W
y =
1.11 d = 0.109 mm
1.15 y = 0.922 mm
1.17 a) N·m/s, lbf·ft/s b) N/m
2
, lbf/ft
2
c) N/m
2
, lbf/ft
2
, d) 1/s, 1/s e) N·m, lbf·ft
f) N·s, lbf·s  g) N/m
2
, lbf/ft
2
h) m
2
/s
2
·K, ft
2
/s
2
·R i) 1/K, 1/R j) N·m·s, lbf·ft·s
1.19 a) 6.89 kPa  b) 0.264 gal  47.9 N·s/m
2

1.21 a) 0.0472 m
3
/s  b) 0.0189 m
3
c) 29.1 m/s  d) 2.19 x 10
4
m
2

1.23 101 gpm
1.25 SG = 13.6  v = 7.37 x 10
-5
m
3
/kg  ?
E
= 847 lbf/ft
3
,  ?
M
= 144 lbf/ft
3

1.27 2.25 kgf/cm
2

1.29 c = 0.04 K
1/2
·s/m
0
0
max
36 . 2
T
p A
m
t
·
= & (ft
2
, psi, R)
1.31 C
D
is dimensionless
1.33 c: N·s/m, lbf·s/ft k: N/m, lbf/ft  f: N, lbf
1.35 H(m) = 0.457 - 3450·(Q(m
3
/s))
2

1.37 ? = 0.0765 ± 2.66 x 10
-4
lbm/ft
3
(± 0.348%)
1.39 ? = 1130 ± 21.4 kg/m
3
SG = 1.13 ± 0.0214
1.41 ? = 930 ± 27.2 kg/m
3

1.43 t = 1, 5, 5 s   Flow rate uncertainty = ± 5.0, 1.0, 1.0%
1.45 µ = 1.01 x 10
-3
N·s/m
2
± 0.609%
1.47 dx = ± 0.158 mm
1.49 H = 57.7 ± 0.548 ft  ?
min
= 31.4
o

Introduction to Fluid Mechanics 7
th
Edition
Fox, Pritchard, & McDonald
Answers to Selected Problems, Chapter 2

2.3 Streamlines:
x
c
y =
2.5 Streamlines:
t
a
b
x c y
-
=
2.7 Streamlines:
?
?
?
?
?
?
?
?
+
=
c
x a
b
y
2
1

2.9 Streamlines: y = 3x  ?t = 0.75 s
2.11 Streamlines: x
2
+ y
2
= c
2.13 Pathlines: y = 2/x  Streamlines: y = 2/x
2.15
a
K
p
?
2
=
2.17 Pathlines:
t C
e y y
0
= ,
()
2
2
1
0
At t B
e x x
+
=  Streamlines:
t
x y
5 . 0 1
1
+
=
2.19 Pathlines:
t b
e y y
-
=
0
,
2
2
1
0
at
e x x =  Streamlines:
t a
b
Cx y
-
=
2.21 Pathlines: 1 4 + = t y ,
2
05 . 0
3
t
e x =  Streamlines:
?
?
?
?
?
?
+ =
3
ln
40
1
x
t
y
2.23 Streamlines: () ( )( )
0 0 0
sin t t t v t y - = ? , ( ) ( )
0 0 0
t t u t x - =
2.25 Streaklines:
() t -
=
t
e y ,
() ()
2 2
1 . 0 t t - + -
=
t t
e x Streamlines:
() t
x y
2 . 0 1
1
+
=
2.29 Streamlines: 4
4
2
+ =
x
y (4 m, 8 m) (5 m, 10.25 m)
2.31 (2.8 m, 5 m)   (3 m, 3 m)
2.33
T
S
T b
'
+
'
=
1
2
3
?   b´ = 4.13 x 10
-9
m
2
/s·K
3/2
S´ = 110.4 K
2.35 t
yx
= - 4.56 N/m
2

2.39 a = - 0.491 ft/s
2
2.41 L = 2.5 ft
2.43 t = 1.93 s
2.45
?
?
?
?
?
?
?
?
- =
- t
Md
A
e
A
Mgd
V
µ
µ
?
1
sin
V = 0.404 m/s  µ = 1.08 N·s/m
2

2.47 F = 2.83 N
2.49 F = 0.0254 N
2.51 µ = 8.07 x 10
-4
N·s/m
2

2.53
H R V
a Mgr
m
3
2
2 p
µ =  µ = 0.0651 N·s/m
2

2.55 t = 4.00 s
2.57
?
?
?
?
?
?
?
?
- =
- t
C
B
e
B
A
1 ?  ?
max
= 25.1 rpm t = 0.671 s
2.59
h
r
z
µ?
t
?
=
h
R
T
2
4
pµ?
=
2.61 Dilatant   k = 0.0499  n = 1.21 µ = 0.191 N·s/m
2
, 0.195 N·s/m
2

2.63 Bingham plastic  µ
p
= 0.652 N·s/m
2
2.65
a
H R
T
3
2 pµ?
=
b
R
T
2
4
pµ?
=
2.69
() ?
? µ?
t
cos 1
sin
- +
=
R a
R
t
max
= 79.2 N/m
2

2.75 a = 0  b = 2U  c = -U
2.77 V = 229 mph
2.79 M = 2.5 x
trans
= 0.327 m
2.81 SG = 0.9 ? = 8830 N/m3   Laminar flow
2.83 V = 667 km/hr
Page 4

Introduction to Fluid Mechanics 7
th
Edition
Fox, Pritchard, & McDonald
Answers to Selected Problems, Chapter 1

1.5 M = 5913 kg
1.7 L = 27.25 in.  D = 13.75 in.
1.9
2
2
05 . 2
t g
W
y =
1.11 d = 0.109 mm
1.15 y = 0.922 mm
1.17 a) N·m/s, lbf·ft/s b) N/m
2
, lbf/ft
2
c) N/m
2
, lbf/ft
2
, d) 1/s, 1/s e) N·m, lbf·ft
f) N·s, lbf·s  g) N/m
2
, lbf/ft
2
h) m
2
/s
2
·K, ft
2
/s
2
·R i) 1/K, 1/R j) N·m·s, lbf·ft·s
1.19 a) 6.89 kPa  b) 0.264 gal  47.9 N·s/m
2

1.21 a) 0.0472 m
3
/s  b) 0.0189 m
3
c) 29.1 m/s  d) 2.19 x 10
4
m
2

1.23 101 gpm
1.25 SG = 13.6  v = 7.37 x 10
-5
m
3
/kg  ?
E
= 847 lbf/ft
3
,  ?
M
= 144 lbf/ft
3

1.27 2.25 kgf/cm
2

1.29 c = 0.04 K
1/2
·s/m
0
0
max
36 . 2
T
p A
m
t
·
= & (ft
2
, psi, R)
1.31 C
D
is dimensionless
1.33 c: N·s/m, lbf·s/ft k: N/m, lbf/ft  f: N, lbf
1.35 H(m) = 0.457 - 3450·(Q(m
3
/s))
2

1.37 ? = 0.0765 ± 2.66 x 10
-4
lbm/ft
3
(± 0.348%)
1.39 ? = 1130 ± 21.4 kg/m
3
SG = 1.13 ± 0.0214
1.41 ? = 930 ± 27.2 kg/m
3

1.43 t = 1, 5, 5 s   Flow rate uncertainty = ± 5.0, 1.0, 1.0%
1.45 µ = 1.01 x 10
-3
N·s/m
2
± 0.609%
1.47 dx = ± 0.158 mm
1.49 H = 57.7 ± 0.548 ft  ?
min
= 31.4
o

Introduction to Fluid Mechanics 7
th
Edition
Fox, Pritchard, & McDonald
Answers to Selected Problems, Chapter 2

2.3 Streamlines:
x
c
y =
2.5 Streamlines:
t
a
b
x c y
-
=
2.7 Streamlines:
?
?
?
?
?
?
?
?
+
=
c
x a
b
y
2
1

2.9 Streamlines: y = 3x  ?t = 0.75 s
2.11 Streamlines: x
2
+ y
2
= c
2.13 Pathlines: y = 2/x  Streamlines: y = 2/x
2.15
a
K
p
?
2
=
2.17 Pathlines:
t C
e y y
0
= ,
()
2
2
1
0
At t B
e x x
+
=  Streamlines:
t
x y
5 . 0 1
1
+
=
2.19 Pathlines:
t b
e y y
-
=
0
,
2
2
1
0
at
e x x =  Streamlines:
t a
b
Cx y
-
=
2.21 Pathlines: 1 4 + = t y ,
2
05 . 0
3
t
e x =  Streamlines:
?
?
?
?
?
?
+ =
3
ln
40
1
x
t
y
2.23 Streamlines: () ( )( )
0 0 0
sin t t t v t y - = ? , ( ) ( )
0 0 0
t t u t x - =
2.25 Streaklines:
() t -
=
t
e y ,
() ()
2 2
1 . 0 t t - + -
=
t t
e x Streamlines:
() t
x y
2 . 0 1
1
+
=
2.29 Streamlines: 4
4
2
+ =
x
y (4 m, 8 m) (5 m, 10.25 m)
2.31 (2.8 m, 5 m)   (3 m, 3 m)
2.33
T
S
T b
'
+
'
=
1
2
3
?   b´ = 4.13 x 10
-9
m
2
/s·K
3/2
S´ = 110.4 K
2.35 t
yx
= - 4.56 N/m
2

2.39 a = - 0.491 ft/s
2
2.41 L = 2.5 ft
2.43 t = 1.93 s
2.45
?
?
?
?
?
?
?
?
- =
- t
Md
A
e
A
Mgd
V
µ
µ
?
1
sin
V = 0.404 m/s  µ = 1.08 N·s/m
2

2.47 F = 2.83 N
2.49 F = 0.0254 N
2.51 µ = 8.07 x 10
-4
N·s/m
2

2.53
H R V
a Mgr
m
3
2
2 p
µ =  µ = 0.0651 N·s/m
2

2.55 t = 4.00 s
2.57
?
?
?
?
?
?
?
?
- =
- t
C
B
e
B
A
1 ?  ?
max
= 25.1 rpm t = 0.671 s
2.59
h
r
z
µ?
t
?
=
h
R
T
2
4
pµ?
=
2.61 Dilatant   k = 0.0499  n = 1.21 µ = 0.191 N·s/m
2
, 0.195 N·s/m
2

2.63 Bingham plastic  µ
p
= 0.652 N·s/m
2
2.65
a
H R
T
3
2 pµ?
=
b
R
T
2
4
pµ?
=
2.69
() ?
? µ?
t
cos 1
sin
- +
=
R a
R
t
max
= 79.2 N/m
2

2.75 a = 0  b = 2U  c = -U
2.77 V = 229 mph
2.79 M = 2.5 x
trans
= 0.327 m
2.81 SG = 0.9 ? = 8830 N/m3   Laminar flow
2.83 V = 667 km/hr
Introduction to Fluid Mechanics 7
th
Edition
Fox, Pritchard, & McDonald
Answers to Selected Problems, Chapter 3

3.1 M = 62.4 kg   t = 22.3 mm
3.3 z = 9303 ft   ?z = 5337 ft
3.5 F = 45.6 N
3.9 ?p = 972 Pa   ? = 991 kg/m
3

3.11 D = 0.477 in
3.13 ? ?/ ?
0
= 4.34%   ?p/p
0
= 2.15%
3.15 p = - 0.217 psig
3.17 p = 6.39 kPa (gage)  h = 39.3 mm
3.19 p = 128 kPa (gage)
3.21 ?p = 59.5 Pa
3.23 H = 30 mm
3.25 SG = 0.900
3.27 ?p = 1.64 psi
3.29
() []
2
oil
1
D
d
p
L
+
?
=
?
L = 27.2 mm
3.31 h = 1.11 in
3.33 ? = 11.1
o
S = 5/SG
3.35 p
atm
= 14.4 psi   Shorter column at higher temperature
3.37 ?h = 38.1 mm   ?h = 67.8 mm
3.39 ?h = 0.389 cm
3.43 ?z = 587 ft   ?z = 3062 ft
3.45 p = 57.5 kPa   p = 60.2 kPa
3.49 p
A
= 1.96 kPa  p
B
= 8.64 kPa  p
C
= 21.9 kPa  p
air
= - 11.3 kPa p
air
= 1.99 kPa
3.51 F
A
= 79,600 lbf
3.53 W = 68 kN
3.55 F
R
= 0.407 lbf
3.57 F
R
= 8.63 MN   R = (8.34 MN, 14.4 MN)
3.59 F = 600 lbf
3.63 D = 8.66 ft
3.65 d = 2.66 m
3.67 SG = 0.542
3.69 F = - 137 kN
3.71 F
V
= 7.62 kN   x´F
V
= 3.76 kN·m   F
A
= - 5.71 kN
3.73 F
V
= - ?gwR
2
p/4  x´ = 4R/3 p
3.75 F
V
= 1.05 x 10
6
N  x´ = 1.61 m
3.77 F
V
= 1.83 x 10
7
N  a = 19.9
o

3.79 F
V
= 416 kN   F
H
= 370 kN  a = 48.3
o
F = 557 kN
3.81 F
V
= 2.47 kN   x´ = 0.645 m  F
H
= 7.35 kN  y´ = 0.217 m
3.83
()
a
d H L
M
3
4
2
3
-
=
?
M = 583 kg
3.85 () ( )
( )
?
?
?
?
?
?
?
?
?
?
?
?
+ + - =
4
2 sin
2
sin 2
max max
max
? ?
? ? R R d LR M  M = 631 kg
Page 5

Introduction to Fluid Mechanics 7
th
Edition
Fox, Pritchard, & McDonald
Answers to Selected Problems, Chapter 1

1.5 M = 5913 kg
1.7 L = 27.25 in.  D = 13.75 in.
1.9
2
2
05 . 2
t g
W
y =
1.11 d = 0.109 mm
1.15 y = 0.922 mm
1.17 a) N·m/s, lbf·ft/s b) N/m
2
, lbf/ft
2
c) N/m
2
, lbf/ft
2
, d) 1/s, 1/s e) N·m, lbf·ft
f) N·s, lbf·s  g) N/m
2
, lbf/ft
2
h) m
2
/s
2
·K, ft
2
/s
2
·R i) 1/K, 1/R j) N·m·s, lbf·ft·s
1.19 a) 6.89 kPa  b) 0.264 gal  47.9 N·s/m
2

1.21 a) 0.0472 m
3
/s  b) 0.0189 m
3
c) 29.1 m/s  d) 2.19 x 10
4
m
2

1.23 101 gpm
1.25 SG = 13.6  v = 7.37 x 10
-5
m
3
/kg  ?
E
= 847 lbf/ft
3
,  ?
M
= 144 lbf/ft
3

1.27 2.25 kgf/cm
2

1.29 c = 0.04 K
1/2
·s/m
0
0
max
36 . 2
T
p A
m
t
·
= & (ft
2
, psi, R)
1.31 C
D
is dimensionless
1.33 c: N·s/m, lbf·s/ft k: N/m, lbf/ft  f: N, lbf
1.35 H(m) = 0.457 - 3450·(Q(m
3
/s))
2

1.37 ? = 0.0765 ± 2.66 x 10
-4
lbm/ft
3
(± 0.348%)
1.39 ? = 1130 ± 21.4 kg/m
3
SG = 1.13 ± 0.0214
1.41 ? = 930 ± 27.2 kg/m
3

1.43 t = 1, 5, 5 s   Flow rate uncertainty = ± 5.0, 1.0, 1.0%
1.45 µ = 1.01 x 10
-3
N·s/m
2
± 0.609%
1.47 dx = ± 0.158 mm
1.49 H = 57.7 ± 0.548 ft  ?
min
= 31.4
o

Introduction to Fluid Mechanics 7
th
Edition
Fox, Pritchard, & McDonald
Answers to Selected Problems, Chapter 2

2.3 Streamlines:
x
c
y =
2.5 Streamlines:
t
a
b
x c y
-
=
2.7 Streamlines:
?
?
?
?
?
?
?
?
+
=
c
x a
b
y
2
1

2.9 Streamlines: y = 3x  ?t = 0.75 s
2.11 Streamlines: x
2
+ y
2
= c
2.13 Pathlines: y = 2/x  Streamlines: y = 2/x
2.15
a
K
p
?
2
=
2.17 Pathlines:
t C
e y y
0
= ,
()
2
2
1
0
At t B
e x x
+
=  Streamlines:
t
x y
5 . 0 1
1
+
=
2.19 Pathlines:
t b
e y y
-
=
0
,
2
2
1
0
at
e x x =  Streamlines:
t a
b
Cx y
-
=
2.21 Pathlines: 1 4 + = t y ,
2
05 . 0
3
t
e x =  Streamlines:
?
?
?
?
?
?
+ =
3
ln
40
1
x
t
y
2.23 Streamlines: () ( )( )
0 0 0
sin t t t v t y - = ? , ( ) ( )
0 0 0
t t u t x - =
2.25 Streaklines:
() t -
=
t
e y ,
() ()
2 2
1 . 0 t t - + -
=
t t
e x Streamlines:
() t
x y
2 . 0 1
1
+
=
2.29 Streamlines: 4
4
2
+ =
x
y (4 m, 8 m) (5 m, 10.25 m)
2.31 (2.8 m, 5 m)   (3 m, 3 m)
2.33
T
S
T b
'
+
'
=
1
2
3
?   b´ = 4.13 x 10
-9
m
2
/s·K
3/2
S´ = 110.4 K
2.35 t
yx
= - 4.56 N/m
2

2.39 a = - 0.491 ft/s
2
2.41 L = 2.5 ft
2.43 t = 1.93 s
2.45
?
?
?
?
?
?
?
?
- =
- t
Md
A
e
A
Mgd
V
µ
µ
?
1
sin
V = 0.404 m/s  µ = 1.08 N·s/m
2

2.47 F = 2.83 N
2.49 F = 0.0254 N
2.51 µ = 8.07 x 10
-4
N·s/m
2

2.53
H R V
a Mgr
m
3
2
2 p
µ =  µ = 0.0651 N·s/m
2

2.55 t = 4.00 s
2.57
?
?
?
?
?
?
?
?
- =
- t
C
B
e
B
A
1 ?  ?
max
= 25.1 rpm t = 0.671 s
2.59
h
r
z
µ?
t
?
=
h
R
T
2
4
pµ?
=
2.61 Dilatant   k = 0.0499  n = 1.21 µ = 0.191 N·s/m
2
, 0.195 N·s/m
2

2.63 Bingham plastic  µ
p
= 0.652 N·s/m
2
2.65
a
H R
T
3
2 pµ?
=
b
R
T
2
4
pµ?
=
2.69
() ?
? µ?
t
cos 1
sin
- +
=
R a
R
t
max
= 79.2 N/m
2

2.75 a = 0  b = 2U  c = -U
2.77 V = 229 mph
2.79 M = 2.5 x
trans
= 0.327 m
2.81 SG = 0.9 ? = 8830 N/m3   Laminar flow
2.83 V = 667 km/hr
Introduction to Fluid Mechanics 7
th
Edition
Fox, Pritchard, & McDonald
Answers to Selected Problems, Chapter 3

3.1 M = 62.4 kg   t = 22.3 mm
3.3 z = 9303 ft   ?z = 5337 ft
3.5 F = 45.6 N
3.9 ?p = 972 Pa   ? = 991 kg/m
3

3.11 D = 0.477 in
3.13 ? ?/ ?
0
= 4.34%   ?p/p
0
= 2.15%
3.15 p = - 0.217 psig
3.17 p = 6.39 kPa (gage)  h = 39.3 mm
3.19 p = 128 kPa (gage)
3.21 ?p = 59.5 Pa
3.23 H = 30 mm
3.25 SG = 0.900
3.27 ?p = 1.64 psi
3.29
() []
2
oil
1
D
d
p
L
+
?
=
?
L = 27.2 mm
3.31 h = 1.11 in
3.33 ? = 11.1
o
S = 5/SG
3.35 p
atm
= 14.4 psi   Shorter column at higher temperature
3.37 ?h = 38.1 mm   ?h = 67.8 mm
3.39 ?h = 0.389 cm
3.43 ?z = 587 ft   ?z = 3062 ft
3.45 p = 57.5 kPa   p = 60.2 kPa
3.49 p
A
= 1.96 kPa  p
B
= 8.64 kPa  p
C
= 21.9 kPa  p
air
= - 11.3 kPa p
air
= 1.99 kPa
3.51 F
A
= 79,600 lbf
3.53 W = 68 kN
3.55 F
R
= 0.407 lbf
3.57 F
R
= 8.63 MN   R = (8.34 MN, 14.4 MN)
3.59 F = 600 lbf
3.63 D = 8.66 ft
3.65 d = 2.66 m
3.67 SG = 0.542
3.69 F = - 137 kN
3.71 F
V
= 7.62 kN   x´F
V
= 3.76 kN·m   F
A
= - 5.71 kN
3.73 F
V
= - ?gwR
2
p/4  x´ = 4R/3 p
3.75 F
V
= 1.05 x 10
6
N  x´ = 1.61 m
3.77 F
V
= 1.83 x 10
7
N  a = 19.9
o

3.79 F
V
= 416 kN   F
H
= 370 kN  a = 48.3
o
F = 557 kN
3.81 F
V
= 2.47 kN   x´ = 0.645 m  F
H
= 7.35 kN  y´ = 0.217 m
3.83
()
a
d H L
M
3
4
2
3
-
=
?
M = 583 kg
3.85 () ( )
( )
?
?
?
?
?
?
?
?
?
?
?
?
+ + - =
4
2 sin
2
sin 2
max max
max
? ?
? ? R R d LR M  M = 631 kg
3.87 ? = 8829 N/m
3
h = 0.292 m
3.89 V
Not submerged
/ V
Submerged
= 10.5%
3.91 SG = W
a
/(W
a
- W
w
)
3.93 F
B
= 1.89 x 10
-11
lbf  V =  1.15 x 10
-3
ft/s (0.825 in/min)
3.95 L/V
He
= 0.0659 lbf/ft
3
L/V
H2
= 0.0712 lbf/ft
3
L/V
air
= 0.0172 lbf/ft
3
/0.0249 lbf/ft
3

3.97 D = 116 m   M = 703 kg
3.99 ? = 9.1
o
(with A = 25 cm
2
not A = 20 cm
2
)
3.101 x = 0.257 m   f = 6.1 N
3.103 D = 2.57 ft
3.105 f = 0.288 cycle/s ( ? = 1.81 rad/s)
3.107 F = 34.2 lbf
3.113 a = g(h/L)
3.115 ? = 185 rad/s (1764 rpm)
3.117 ?p = ??
2
R
2
3.119 dy/dx = - 0.25   p = 105 - 1.96x (p: kPa, x: m)
3.121 a = 30
o
dy/dx = 0.346
3.123 T = 47.6 lbf   p = 55.3 lbf/ft
2
(gage)
```
 Use Code STAYHOME200 and get INR 200 additional OFF

Track your progress, build streaks, highlight & save important lessons and more!

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;