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 
 
2.1 1) 1D, Unsteady 2) 1D, Steady  3) 2D, Unsteady 4) 2D, Unsteady 
 5) 1D, Unsteady 6) 3D, Steady  7) 2D, Unsteady 8) 3D, Steady 
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 
 
2.1 1) 1D, Unsteady 2) 1D, Steady  3) 2D, Unsteady 4) 2D, Unsteady 
 5) 1D, Unsteady 6) 3D, Steady  7) 2D, Unsteady 8) 3D, Steady 
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 
 
2.1 1) 1D, Unsteady 2) 1D, Steady  3) 2D, Unsteady 4) 2D, Unsteady 
 5) 1D, Unsteady 6) 3D, Steady  7) 2D, Unsteady 8) 3D, Steady 
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 
 
2.1 1) 1D, Unsteady 2) 1D, Steady  3) 2D, Unsteady 4) 2D, Unsteady 
 5) 1D, Unsteady 6) 3D, Steady  7) 2D, Unsteady 8) 3D, Steady 
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
/2   ? = 7.16 rad/s 
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)