Problem 2.19
[Difficulty: 3]
Given:
Velocity field
Find:
Plot of pathline traced out by particle that passes through point (1,1) at t = 0; compare to streamlines through same
point at the instants t = 0, 1 and 2s
Solution:
Governing equations:
up =
For pa

Problem 2.40
[Difficulty: 2]
Given:
Velocity distribution between flat plates
Find:
Shear stress on upper plate; Sketch stress distribution
Solution:
Basic equation
du
yx =
dy
yx =
At the upper surface
Hence
y=
du
=
dy
d
dy
u max 1
2
2 y = u 4 2 y = 8

Problem 2.41
[Difficulty: 2]
Given:
Velocity distribution between parallel plates
Find:
Force on lower plate
Solution:
Basic equations
du
dy
so
du
yx =
dy
F = yx A
=
d
dy
yx =
u max 1
8 u max y
h
At the lower surface
y=
h
F=
and
2
2
m
2
A = 1 m
3 N s

Problem 2.42
[Difficulty: 2]
Open-Ended Problem Statement: Explain how an ice skate interacts with the ice surface.
What mechanism acts to reduce sliding friction between skate and ice?
Discussion: The normal freezing and melting temperature of ice is 0C

Problem 2.43
[Difficulty: 2]
Given: Velocity profile
Find:
Plot of velocity profile; shear stress on surface
Solution:
2
h y y sin( )
u=
2
2
g
The velocity profile is
u
Hence we can plot
u max
y
= 2
h
1
2
y
u max =
so the maximum velocity is at y = h

Problem 1.1
Given:
[Difficulty: 3]
Common Substances
Tar
Sand
Silly Putty
Jello
Modeling clay
Toothpaste
Wax
Shaving cream
Some of these substances exhibit characteristics of solids and fluids under different conditions.
Find:
Explain and give examples.
S

Problem 1.2
Given:
Five basic conservation laws stated in Section 1-4.
Write:
A word statement of each, as they apply to a system.
Solution:
[Difficulty: 2]
Assume that laws are to be written for a system.
a.
Conservation of mass The mass of a system is c

Problem 2.44
Given:
Ice skater and skate geometry
Find:
[Difficulty: 2]
Deceleration of skater
yx =
y
Solution:
Governing equation:
du
yx =
dy
Fx = M ax
du
dy
V = 20 ft/s
h
x
L
Assumptions: Laminar flow
The given data is
W = 100 lbf
V = 20
5 lbf s
=

Problem 1.3
[Difficulty: 3]
Open-Ended Problem Statement: The barrel of a bicycle tire pump becomes quite warm during use.
Explain the mechanisms responsible for the temperature increase.
Discussion: Two phenomena are responsible for the temperature incre

Problem 2.45
Given:
Block pulled up incline on oil layer
Find:
[Difficulty: 2]
Force required to pull the block
Solution:
Governing equations:
U
du
yx =
dy
y
x
x
f
N
W
d
Fx = M ax
Assumptions: Laminar flow
The given data is
W = 10 lbf
U = 2
= 3.7 10
2

Problem 1.4
[Difficulty: 3]
Open-Ended Problem Statement: Consider the physics of skipping a stone across the water surface
of a lake. Compare these mechanisms with a stone as it bounces after being thrown along a roadway.
Discussion: Observation and expe

Problem 1.5
Given:
Dimensions of a room
Find:
[Difficulty: 1]
Mass of air
Solution:
p
Basic equation:
=
Given or available data
p = 14.7psi
Rair T
T = ( 59 + 460)R
V = 10 ft 10 ft 8 ft
Then
=
p
Rair T
M = V
= 0.076
Rair = 53.33
V = 800 ft
lbm
ft
3
M = 6

Problem 2.46
Given:
Block moving on incline on oil layer
Find:
[Difficulty: 2]
Speed of block when free, pulled, and pushed
Solution:
y
U
Governing equations:
x
x
du
yx =
dy
f
N
W
Fx = M ax
d
Assumptions: Laminar flow
M = 10 kg
W = M g
W = 98.066 N
d = 0

Problem 1.6
[Difficulty: 1]
Given:
Data on oxygen tank.
Find:
Mass of oxygen.
Solution:
Compute tank volume, and then use oxygen density (Table A.6) to find the mass.
The given or available
data is:
D = 16 ft
p = 1000 psi
RO2 = 48.29
ft lbf
lbm R
T = ( 7

Problem 2.47
[Difficulty: 2]
Given:
Data on tape mechanism
Find:
Maximum gap region that can be pulled without breaking tape
Solution:
Basic equation
du
yx =
dy
F = yx A
and
FT = 2 F = 2 yx A
Here F is the force on each side of the tape; the total force

Problem 1.7
Given:
[Difficulty: 3]
Small particle accelerating from rest in a fluid. Net weight is W, resisting force FD = kV, where V
is speed.
Find:
Time required to reach 95 percent of terminal speed, Vt.
Solution:
Consider the particle to be a system.

Problem 1.8
Given:
[Difficulty: 2]
Small particle accelerating from rest in a fluid. Net weight is W,
resisting force is FD = kV, where V is speed.
Find:
FD = kV
Distance required to reach 95 percent of terminal speed, Vt.
Solution:
Particle
Consider the

Problem 2.38
Given:
Sutherland equation with SI units
Find:
[Difficulty: 2]
Corresponding equation in BG units
1
Solution:
=
b T
2
1+
Governing equation:
S
Sutherland equation
T
Assumption: Sutherland equation is valid
The given data is
6
b = 1.458 10
kg

Problem 2.37
[Difficulty: 2]
Given:
Sutherland equation
Find:
Corresponding equation for kinematic viscosity
1
Solution:
=
b T
2
1+
Governing equation:
S
p = R T
Sutherland equation
Ideal gas equation
T
Assumptions: Sutherland equation is valid; air is an

Problem 2.20
[Difficulty: 3]
Given:
Velocity field
Find:
Plot of pathline traced out by particle that passes through point (1,1) at t = 0; compare to streamlines through
same point at the instants t = 0, 1 and 2s
Solution:
up =
dx
dt
= B x ( 1 + A t)
A =

Problem 2.21
[Difficulty: 3]
Given:
Eulerian Velocity field
Find:
Lagrangian position function that was at point (1,1) at t = 0; expression for pathline; plot pathline and compare to
streamlines through same point at the instants t = 0, 1 and 2s
Solution:

Problem 2.22
[Difficulty: 3]
Given:
Velocity field
Find:
Plot of pathline of particle for t = 0 to 1.5 s that was at point (1,1) at t = 0; compare to streamlines through same
point at the instants t = 0, 1 and 1.5 s
Solution:
Governing equations:
up =
For

Problem 2.23
[Difficulty: 3]
Given:
Velocity field
Find:
Plot of pathline of particle for t = 0 to 1.5 s that was at point (1,1) at t = 0; compare to streamlines through same
point at the instants t = 0, 1 and 1.5 s
Solution:
Governing equations:
up =
dx

Problem 2.25
[Difficulty: 3]
Given:
Flow field
Find:
Pathline for particle starting at (3,1); Streamlines through same point at t = 1, 2, and 3 s
Solution:
dx
For particle paths
Separating variables and integrating
dy
= u = a x t
dx
x
an
d
= a t dt
dt
or

Problem 2.26
[Difficulty: 4]
Given:
Velocity field
Find:
Plot streamlines that are at origin at various times and pathlines that left origin at these times
Solution:
v
For streamlines
u
=
dy
dx
v 0 sin t
=
u0
v 0 sin t
So, separating variables (t=const)

Problem 2.27
Given:
Velocity field
Find:
[Difficulty: 5]
Plot streakline for first second of flow
Solution:
Following the discussion leading up to Eq. 2.10, we first find equations for the pathlines in form
(
x p( t) = x t , x 0 , y 0 , t0
)
and
(
y p( t)

Problem 2.28
[Difficulty: 4]
Given:
Velocity field
Find:
Plot of streakline for t = 0 to 3 s at point (1,1); compare to streamlines through same point at the instants t = 0, 1
and 2 s
Solution:
Governing equations:
For pathlines
up =
dx
vp =
dt
dy
v
For s

Problem 2.29
[Difficulty: 4]
Given:
Velocity field
Find:
Plot of streakline for t = 0 to 3 s at point (1,1); compare to streamlines through same point at the instants t = 0, 1
and 2 s
Solution:
Governing equations:
For pathlines
up =
dx
vp =
dt
dy
v
For s