Mechanics of Fluids SI Edition 5th Edition by Potter - Test Bank

Mechanics of Fluids SI Edition 5th Edition by Potter – Test Bank

Instant Download – Complete Test Bank With Answers

Sample Questions Are Posted Below

Mechanics of Fluids Chapter 3: Introduction to Fluids in Motion
17
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Sections 3.1 and 3.2
1. In a steady flow in a long pipe, such as the Alaska oil pipe line, the Eulerian description of the
velocity field would express the velocity V in the pipe as:
(A) V(t)
(B) V(r)
(C) V(r, t)
(D) V(r, z)
2. A single bar of soap has a small light attached. The bar is released in a river and a snapshot is
taken every second from a blimp which is stationary over the river. The snapshots are all
superimposed on one large picture. The line formed by connecting the dots is:
(A) A streamline
(B) A streakline
(C) A pathline
(D) A line that has not been defined
3. The velocity vector at a point in a fluid flow is given by 5i + 12j. The unit vector which is
perpendicular to the streamline passing through the point is:
(A) (−12i + 5j)/13
(B) (−12i − 5j)/13
(C) (5i + 12j)/13
(D) (−5i + 12j)/13
4. The velocity vector in a particular flow field is given by V = 2x2yi
− 4y2xj m/s. The accelera-
tion at (1, −1) is:
(A) 16i m/s 2
(B) 16i – 40j m/s 2
(C) −24j m/s 2
(D) 0
5. If a sensor were placed in the flow of Problem 4, it would rotate about the z-axis at what
angular velocity at (1, −1)?
(A) 5 rad/s
(B) 4 rad/s
(C) 3 rad/s
(D) 2 rad/s

Mechanics of Fluids Chapter 3: Introduction to Fluids in Motion
20
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Sections 3.3 and 3.4
1. Oil flows through the Alaska pipe line on a clear, sunny day. The flow in the pipe can best be
classified as:
(A) Uniform
(B) Developed
(C) Two-dimensional
(D) Cylindrical
2. Select the flow which must be classified a viscous flow, a flow in which effects of viscosity
cannot be neglected:
(A) Flow through a pipe contraction
(B) Flow through a rocket’s nozzle
(C) Flow around an airfoil
(D) Flow in the entrance region of a pipe
3. Water is flowing placidly in a canal at a depth of 2 cm and a width of 2 m with a velocity of
0.4 m/s. It’s a nice sunny day in Arizona near Phoenix in the summertime. Is the flow laminar
or turbulent?
(A) Laminar
(B) Turbulent
(C) It can alternate between being laminar and turbulent
(D) Insufficient information to decide
4. A laminar flow is desired from a tank with a well-rounded entrance to a 6-mm-diameter pipe
that drains the tank. A container catches 20 L of 20°C water in 4 minutes. Determine the
Reynolds number so one can decide if the flow is laminar.
(A) 972
(B) 1220
(C) 1770
(D) 1920
5. The wind speed of the air flowing over a 16-cm-diameter outside mirror is significantly higher
than the speed of a vehicle. If the pressure on the front of the mirror is assumed to be
stagnation pressure and the pressure on the rear is assumed to be atmospheric, the power
needed to move the mirror, if the air velocity around the mirror is 30 m/s, is nearest:
(A) 0.44 hp
(B) 0.39 hp
(C) 0.34 hp
(D) 0.29 hp
Mechanics of Fluids, 4 th Edition Chapter 3: Introduction to Fluids in Motion
21
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
6. Air at 30°C and 200 kPa is flowing in a 30-cm-diameter pipe and
passes through the bend shown. An estimate of the pressure
difference between the inside of the bend and the outside of the
bend is approximately:
(A) 110 Pa
(B) 140 Pa
(C) 180 Pa
(D) 240 Pa
40 cm
8 m/s

Mechanics of Fluids Chapter 3: Introduction to Fluids in Motion
18
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Solutions for Sections 3.1 and 3.2
1. In a steady flow in a long pipe, such as the Alaska oil pipe line, the Eulerian description of the
velocity field would express the velocity V in the pipe as:
(B) V(r)
In a steady flow, every dependent variable does not depend on time. In a long pipe,
the velocity would depend only on the radial variable r.
2. A single bar of soap has a small light attached. The bar is released in a river and a snapshot is
taken every second from a blimp which is stationary over the river. The snapshots are all
superimposed on one large picture. The line formed by connecting the dots is:
(D) A line that has not been defined
The line does not satisfy any of the definitions of a streamline, a streakline, or a
pathline.
3. The velocity vector at a point in a fluid flow is given by 5i + 12j. The unit vector which is
perpendicular to the streamline passing through the point is:
(A) (−12i + 5j)/13
By definition, the velocity vector is tangent to the streamline, so the unit vector is
perpendicular to the velocity vector so that V·n = 0. The velocity vector has only x-
and y-components so the unit vector will have only x- and y-components. We have
(5 12 ) ( ) 0 or 5 12 0x y x yn n n n⋅ = + ⋅ + = + =V n i j i j
The unit vector requires that 2 2 1x yn n+ = giving two equations and two unknowns:
( )2 2 12
12 /5 1 5/13 and 12/13
5
.y y y x yn n n n n− + = ∴ = = − = −
The unit vector is written as n = (−12i + 5j/)13. The unit vector (12i − 5j/)13 in the
opposite direction would also be normal to the streamline.
Mechanics of Fluids, 4th Edition Chapter 3: Introduction to Fluids in Motion
19
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
4. The velocity vector in a particular flow field is given by V = 2x2yi
− 4y2xj m/s. The accelera-
tion at (1, −1) is:
(C) −24j
Use Eq. 3.2.8 to find
u v w
x y z
∂ ∂ ∂
= + +
∂ ∂ ∂
V V V
a
2 2 2 2
2 (4 4 ) 4 )(2 8 )
2( 4 4 ) 4(2 8 ) 24
(x y xy y y x x yx= − + − −
= − − − − + = −
i j i j
i j i j j
5. If a sensor were placed in the flow of Problem 4, it would rotate about the z-axis at what
angular velocity at (1, −1)?
(C) 3 rad/s
The angular velocity is given by Eq. 3.2.15:
( )2 21 1 4 2 3 rad/s 3 rad/s
2 2 .z
v u y x
x y
⎛ ⎞∂ ∂
Ω = − = − − = − ∴Ω =⎜ ⎟
∂ ∂⎝ ⎠

Mechanics of Fluids Chapter 3: Introduction to Fluids in Motion
22
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Solutions for Sections 3.3 and 3.4
1. Oil flows through the Alaska pipe line on a clear, sunny day. The flow in the pipe can best be
classified as:
(B) Developed
The flow is definitely not 2D nor is it cylindrical (this is not a type of flow, only a
certain coordinate system), so that leaves either (A) or (B). The flow would be at
most one-dimensional, u = u(r). It is certainly a developed flow, i.e., the velocity does
not depend on the flow direction, u ≠ u(x).
2. Select the flow which must be classified a viscous flow, a flow in which effects of viscosity
cannot be neglected:
(D) Flow in the entrance region of a pipe
In a contraction, a fluid is accelerated and viscous effects can be ignored. The same is
true in a rocket nozzle. Around an airfoil viscous effects are ignored except for a very
thin layer of the flow next to the airfoil surface. Viscous effects cannot be ignored in
the entrance region of a pipe; viscous effects cause the flow to assume the profile that
exists downstream of the entrance region.
3. Water is flowing placidly in a canal at a depth of 2 cm and a width of 2 m with a velocity of
0.4 m/s. It’s a nice sunny day in Arizona near Phoenix in the summertime. Is the flow laminar
or turbulent?
(B) Turbulent
In the summer near Phoenix, the temperature is between 40°C and 50°C. Table B.1
gives the kinematic viscosity about 6
0 6 10. −
× m2 /s. The Reynolds number is
6 2
0 4 m/s 0 02 m
Re 13 300
0 6 10 m /s
. .
.
Vh
ν −
×
= = =
×
which represents turbulent flow. The width of the channel is unimportant. Even if
the flow were in Michigan where the temperature could be as low as 10°C, the flow
would be turbulent.
Mechanics of Fluids, 4th Edition Chapter 3: Introduction to Fluids in Motion
23
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
4. A laminar flow is desired from a tank with a well-rounded entrance to a 6-mm-diameter pipe
that drains the tank. A container catches 20 L of 20°C water in 4 minutes. Determine the
Reynolds number so one can decide if the flow is laminar.
(C) 1770
The average velocity is needed. It is (use the units to obtain the velocity with units of
m/s)
3
2 2
Volume/time (20 L 0.001 m /L)/(4 60) s 2 95 m/s
Area 0 006 /4 m .
.
V
π
× ×
= = =
×
The Reynolds number is then
5
2 95 0 006
Re 1770
10
. .VD
ν −
×
= = =
The flow would be laminar.
5. The wind speed of the air flowing over a 16-cm-diameter outside mirror is significantly higher
than the speed of a vehicle. If the pressure on the front of the mirror is assumed to be
stagnation pressure and the pressure on the rear is assumed to be atmospheric, the power
needed to move the mirror if the air velocity around the mirror is 30 m/s is nearest:
(A) 0.44 hp
The stagnation pressure is found using Bernoulli’s equation to be
2
2V 2 12 1
2 2
pp V
ρ
+ = +
2
2
2
30 540 Pa
1 2 2
. .
.
p p
ρ = ∴ =
Assuming the pressure on the rear is zero gage, the force is
2
540 0 08 10 86 N.. .F pA
π= = × × =
The power P is then found using P = F×V:
10 86 30 326 W or 0.44 hp.P F V= × = × =
Mechanics of Fluids, 4th Edition Chapter 3: Introduction to Fluids in Motion
24
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
6. Air at 30°C and 200 kPa is flowing in a 30-cm-diameter pipe and passes through the bend
shown. An estimate of the pressure difference between the outside of the bend and the inside
of the bend is approximately:
(A) 110 Pa
The difference in pressure normal to curved streamlines is given by Eq. 3.4.15:
2 2
200 8 0 3 110 Pa
0 287 (273 30) 0 4 .
. .
V
p n
R
ρΔ = Δ = × × =
× +
We have dropped the minus sign since the equation gives the difference between the
inside and the outside.