# Fluids, elasticity

```A fluid is
(a) a liquid.
(b) a gas.
(c) anything that flows.
(d) anything that can be made to change shape.
(e) All of the above
In the drawing on the
right, the dotted line
represents the volume of
fluid equal to the volume
of the object on the right.
Fluid
Fbuoyant
Volume
of fluid
equal to
object at
right.
Displaced
volume of
fluid
Suspended
object
1. What is the buoyant force on the fluid inside the dotted line, if
the fluid is stationary?
(a) Equal to the weight of the object
(b) Equal to the weight of the fluid inside
the dotted line
(c) Equal to (a) - (b)
(d) Zero
2. What is the buoyant force on the object?
1
3
4
When blocks 2 and 5 are placed in the
2
liquid, they end up as shown. Which
of the following best represents the
positions of the other blocks if placed
5
in the liquid? All blocks have the
same volume.
m1 &lt; m2 &lt; m3 &lt; m4 &lt; m5
(b)
(a)
1
1
2
2
3
4
3
5
(c)
4
5
(d)
1
1
2
2
3
4
3
4
5
5
An open cylinder of water of radius R
has a circular hole of area A at a depth d
below the surface. To determine the
speed of the water stream as it leaves the
hole we use
p0
d
(a) The continuity equation: v1 A1  v2 A2
1 2
(b) Bernoulli's equation: p0  v  gd  constant
2
(c) Archimedes' principle
v
p0
An open cylinder of water of radius R
has a circular hole of area A at a depth d
below the surface. We solve for v from
1 2
(a) p0  v  gd  0
2
1 2
(b) gd  v
2
1 2
(c) p0  gd  v
2
1 2
(d) p0  2 v  gd
d
v
For which of the following is Bernoulli’s equation a
conservation law? (Answer (a) for yes and (b) for no)
1. momentum
2. energy
3. mass
4. streamlines
Liquid flows through a pipe. You can't see into the pipe, but there is
transparent tubing feeding vertically off it at different positions, with
the top end of the tubing open to the atmosphere. The height of the
liquid in the is shown below. At which point in the tube is the flow
speed the greatest?
Liquid
1
2
(a) Point 1
(b) Point 2
(c) Point 3
(d) Not enough information to tell
3
Area A2
Area A1

p1
Flow

 x2

p2
y
y2
y1

 x1
In the figure above for an incompressible fluid, a volume of fluid
of length )x1 enters on the left as an equal volume of length )x2
leaves on the right.
Which of the following represents the net work
done on the fluid in this flow tube in this time?
(a) p1A1
(b) p2A2
(c) p1A1 - p2A2 ....
Which situation can be described with Bernoulli’s equation?
(Answer (a) for yes and (b) for no)
1. the flow of water out of a tank having a small hole near its bottom
2. the steady flow of water in a fire hose
3. the flow of air around an airfoil
4. fluid flow through a pump equipped with a piston
Which of the following gives the correct definition of the bulk
modulus B?
V
 Bp
a)
V
b)  V   BV
V
c) p   B
V
V
d) p  B
V
e)
F
l
 B
A
l
Aluminum has a bulk modulus of 100 GPa (giga = 109). Hydrostatic
pressure of 100 atmospheres is applied to a cube of aluminum 2 cm to
a side.
What is the change in volume of the cube?
(1 atmosphere ~ 100 kPa)
(a) -8 x 10-4 cm3
(b) 8 x 10-4 cm3
(c) -2 x 10-9 cm3
(d) 2 x 10-9 cm3
(e) -8 x 10-1 cm3
The bodies A, B and C are
held at the positions shown on
the right.
A 50 g
Liquid
B 40 g
C 50 g
1. They have the same volume. Rank, from largest to smallest, the
sizes of the buoyant forces FA, FB, FC on each of them.
(a) FA = FB = FC
(b) FC &gt; FB &gt; FA
(d) FC = FA &gt; FB
(e) FA &gt; FC &gt; FB
(c) FA &gt; FB &gt; FC
2. Now they have the same density but not
necessarily the same volume. Rank, from largest
to smallest, the sizes of the buoyant forces FA, FB,
FC on each of them.
(a) FA = FB = FC
(c) FA &gt; FB &gt; FC
(e) FA &gt; FB &gt; FC
(b) FC &gt; FB &gt; FA
(d) FC = FA &gt; FB
The buoyant force on an immersed body has the same magnitude as
(Answer (a) for yes and (b) for no)
1. the weight of the body.
2. the weight of the fluid displaced by the body.
3. the difference between the weights of the body and the displaced
fluid.
4. the average pressure of the fluid times the
surface area of the body.
For which cube is the buoyant force the greatest?
(a) A
(b) B
(c) the forces are the same
A liquid is
(a) more compressible than a gas
(b) highly compressible, but less than a gas
(c) almost incompressible
The equation of continuity says that the velocity of fluid flow in
a pipe is inversely proportional to the cross-sectional area
(a) only for an incompressible fluid.
(b) only for a horizontal pipe.
(c) both (a) and (b)
(d) always
In the figure on the right, an
incompressible fluid flows
Area
from left to right. The
A1
volume shown at the left
entering this region of flow is
the same as that leaving at the
right over the same time
interval.
Area A2
Flow

v1
Which of the following statements is true?
(a) v1 = v2
(b) A1v1 = A2v2
(c) A1/v1 = A2/v2
(d) None of these

v2
Compared to its solid form, a liquid usually
(a) has a higher density
(b) has a lower density
(c) Has the same density
Rank, in order from largest to
smallest, the densities of A, B,
and C.
(a) A&gt;B&gt;C
(b) A&gt;C&gt;B
(d) B&gt;C&gt;A
(e) C&gt;A&gt;B
A
B
(c) B&gt;A&gt;C
Because:
(a) the heaviest object displaces the most water
(b) the buoyant force on the object is equal to the
weight of the water it displaces
(c) the least dense object displaces the least
amount of water
C
A floating object displaces a volume of fluid
(a) whose weight is equal to the product of the pressure in the fluid
and the surface area submerged
(b) whose weight is equal to the weight of the floating object
(c) whose mass is equal to the density of the object multiplied by
the volume submerged
(d) equal to the volume of the object
A floating wooden block sinks until
(a) the weight of fluid displaced equals the weight of the block
(b) the product of the surface area of the bottom of the block, and
the gauge pressure there, equals the weight of the block
(c) the submerged volume of the block, times the density of water,
is equal to the weight of the block
(d) both (a) and (c)
(e) all of (a), (b), (c)
The diagram on the right is the free body
diagram of an object sitting on a table.
Which of the following is the most appropriate free body diagram for
the object when floating (ignoring forces on the sides)?
(a)
(b)
(c)
A and B are rectangular tanks full of water. Their y and z dimensions
are the same, but their x dimensions are different
z
y
x
A
B
The total force on the bottom of tank A is
(a) greater than the force on the bottom of B
(b) the same as the force on the bottom of B
(c) smaller than the force on the bottom of B
A and B are rectangular tanks full of water. Their y and z dimensions
are the same, but their x dimensions are different
z
y
x
A
B
The total force of the liquid on the front wall of tank A is
(a) greater than the force on the front wall of B
(b) the same as the force on the front wall of B
(c) smaller than the force on the front wall of B
Air enclosed in a cylinder has density 1.4 kg/m3.
What will be the density of the air if the length of the cylinder is
doubled while the radius is unchanged?
(a) 1.4 kg/m3
(b) 2.8 kg/m3
(c) 0.7 kg/m3
What will be the density of the air if the length of the
cylinder is doubled while the radius is halved?
(a) 1.4 kg/m3
(b) 2.8 kg/m3
(c) 0.7 kg/m3
The gauge pressure is the pressure in a fluid in excess of atmospheric
pressure.
The gauge pressure a the bottom of a cylinder of liquid reads pg =
0.4 atm. The liquid is poured into another cylinder with twice the
radius of the first cylinder. What is the gauge pressure at the bottom
of the second cylinder?
(a) 0.1 atm
(b) 0.2 atm
(c) 0.4 atm
(d) 0.8 atm
(e) none of the above
Wind
Wind flows over the house above. A window on the ground floor is
open. Does air flow
(a) in the window and out the chimney
or
(b) down the chimney and out the window?
Rank in order, from largest to smallest, the magnitudes of the forces
required to balance the masses. The masses are in kilograms.
1. F2 &gt; F1 &gt; F3
2. F2 &gt; F1 = F3
3. F3 &gt; F2 &gt; F1
4. F3 &gt; F1 &gt; F2
5. F1 = F2 = F3
from Knight
An inflated balloon does not collapse under the atmosphere's
pressure because
(a) there are more collisions of air molecules against the inside of
the balloon wall than against the outside
(b) so much extra air is put inside that the air molecules start to
push against each other, making the air almost incompressible
(c) the air inside warms under the pressure, so
the molecules inside are moving faster than
outside
A small wooden block is placed in a bowl of water initially full to
the brim. The block has a volume of 15 cm3 and a density 2/3 that
of water. What volume of water overflows from the bowl?
(a) 5 cm3
(b) 10 cm3
(c) 15 cm3
A blood platelet drifts along with the flow of blood through an artery
that is partially blocked by deposits. As the platelet moves from the
narrow region to the wider region, it experiences
(a) an increase in pressure.
(b) no change in pressure
(c) a decrease in pressure
PI
A blood platelet drifts along with the flow of blood through an artery
that is partially blocked by deposits. As the platelet moves from the
narrow region to the wider region, its speed
(a) increases
(b) decreases
(c) remains the same
PI
In the figure on the right,
a tensile stress is applied
to the rod.
Force
l
transverse
Poisson's ratio is defined as:   
longitudinal
Where  represents strain.
1. transverse is
(a) w / l
(b)
l / w (c) w / w (d) l / l
2. Poisson's ratio is
(a) Negative
(b) positive
w
Force
A cylindrical metal wire is 10-m long and has a Poisson's ratio of
0.4. It is extended 10 mm by applying a tensile stress. What is the
(a) -4 x 10-4 m
(b) 4 x 10-4 m
(c) -16 x 10-8 m
(d) 16 x 10-8 m
(e) -4 x 10-6 m
The pressure exerted by each of your feet on the floor is
closest to
(a) 10 Pa
(b) 100 Pa
(c) 1000 Pa
(d) 10,000 Pa
column of liquid of height h, area
A and mass density D as
Liquid
sketched below. What is the
downwards pressure on the
bottom of the container?
(a) patm
(b) patm + DAhg
(c) patm + Dhg
(d) DAhg
(e) Dgh
A
patm = atmospheric
pressure
h
A static fluid in a container is subject to both atmospheric
pressure at its surface and Earth’s gravitation. The pressure at
the bottom of the container
(a) depends on the height of the fluid column.
(b) depends on the shape of the container.
(c) is equal to the atmospheric pressure.
Rank in order, from smallest to largest, the pressure at each point
shown below. The top of the tank is open to the atmosphere.
(a) C, D, E, A, B
(b) C, D=E, A=B
(c) C, E, D, A, B
(d) D, C, E, A=B
(e) C, D, E, A=B
Which statement does not apply? In the steady flow of an
incompressible fluid,
(a) the flow velocity at a point is tangent to the streamline
through that point.
(b) the density of the fluid is proportional to the density of
streamlines.
(c) the wider the streamline spacing, the lower the velocity of the
flow.
(d) streamlines cannot cross each other.
Ceiling
Suction
cup
m
In the figure above, the suction cup is held to the ceiling by
(a) the suction of the vacuum formed between it
and the wall.
(b) the unbalanced force of the air molecules
bouncing off the bottom of it.
(c) the molecular attraction between the suction
cup and the ceiling, where they are in contact.
(d) the centrifugal force of the Earth's rotation.
Compare the gas pressure inside the cylinder
to the pressure of the surrounding air. The gas
pressure inside the cylinder is
(a) equal to the gas pressure outside the
cylinder
(b) equal to the gas pressure outside the
cylinder plus the mg/A where m is the mass of
the block and A is the area of the piston
(c) equal to the gas pressure outside the
cylinder plus the mg/A where m is the mass of
the block and A is the area of the block
Fan
A vacuum cleaner is constructed
as on the right. A fan forces air
out of the canister, creating a
partial vacuum in the hose.
Ejected
air
Hose
Paper
A vacuum-cleaner hose is placed near a piece of a paper lying on the floor.
The paper enters the vacuum-cleaner hose because the partial vacuum in the
hose
(a) removes air molecules from above the paper, leaving an excess of
molecules below the paper to push it into the hose.
(b) makes the pressure above the paper lower than
below it, so the paper is forced up
(c) sucks the paper inside.
(d) does both (a) and (b)
(e) does both (b) and (c)
A wire of length l and cross-section A has a tensile force F applied
to it. The extension )l is proportional to which of the following?
(Answer (a) for yes and (b) for no)
1. l
2. A
3. F
4. 1/l
5. 1/A
6. 1/F
A force stretches a wire by 1 mm.
1. A second wire of the same material has the same cross section and
twice the length. How far will it be stretched by the same force?
(a) 1/4 mm
(b) 1/2 mm
(c) 1 mm
(d) 2 mm
(e) 4 mm
2. Another wire of the same material has the same length and twice
the diameter of the of the first wire. How far will it be stretched by
the same force?
(a) 1/4 mm
(b) 1/2 mm
(d) 2 mm
(e) 4 mm
(c) 1 mm
A wire of square cross-section has a side of 0.1 mm and is 10-m
long. The wire is suspended from a high ceiling and a mass of 10
kg is hung on the bottom end. The wire stretches 10 mm. What is
the Young's modulus of the wire, roughly?
(a) 1 x 106 N/m2
(b) 1 x 108 N/m2
(c) 1 x 1010 N/m2
(d) 1 x 1011 N/m2
(e) 1 x 1013 N/m2
```