Download 9 The Behavior of Fluids

9 The Behavior of Fluids
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Pressure and Pascal’s Principle
Atmospheric Pressure and the Behavior of Gases
Archimedes’ Principle
Fluids in Motion
Bernoulli’s Principle
Answers to Questions
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q11
Q12
Q13
Q14
Q15
Q16
Q17
Q18
Q19
Q20
Q21
Q22
Q23
Q24
Q25
Q26
Yes. A 100 lb woman can exert pressure high enough to dent an ordinary floor tile if she puts her weight
on narrow spike heels. Pressure is force/area, so a moderate force on a small area results in a large
pressure.
As pressure is defined as force per unit area, the unit of pressure in the foot-pound system would be given
as pounds per square foot (lb/ft2).
The pressure will be greater for the piston with small area since pressure is force/area.
The quarter. The pressure on each coin is the same, but since the quarter has a larger area, it will
experience the greater force.
The area of contact of the bicycle tire is much smaller than that of an auto tire so that even though the car
is much heavier, the bicycle tire requires a higher air pressure to provide the necessary force.
a. The larger piston experiences the greater force since F = p x A.
b. The large-area piston moves a smaller distance than does the small-area piston. The work must be the
same for each, so because of the greater force on the large-area piston, it will move a smaller distance.
No. The output piston exerts a greater force because its surface area is greater.
No. The pressure of any air in the top end would reduce the barometer reading from the true value of
atmospheric pressure.
Yes, except it would have to be a tube 13.6 times as long as that for a mercury barometer—over 10 m long!
That would be awkward to read and would not fit indoors.
a. mm hg
b. gauge pressure
The level would decrease. The barometer is measuring the weight/area of air above it, so as we climb the
mountain the pressure decreases.
The balloon will contract. As the atmospheric pressure outside the balloon increases, the air in the balloon
will contract so that the inside pressure equals the outside pressure.
Atmospheric pressure changes with altitude. When traveling in mountains, the atmospheric pressure will
change faster than the body’s ability to change the pressure in the inner ear; hence, the popping.
The pressure decreases. If the volume is slowly increased, heat can flow in to keep the temperature
constant giving a Boyle's Law situation. The pressure decreases as the volume increases.
A drop in atmospheric pressure generally accompanies storms. The balloon will expand, assuming the
temperature is constant.
Yes, as long as its density is less than that of mercury, 13.6 g/cm 3.
The pressure pushing on the bottom is greater than the pressure pushing on the top. The pressure in a
liquid increases with increasing depth.
Yes, if it is shaped so that it displaces a sufficient volume of water equal to its weight. After all, steel ships
do float.
a. Equal. This is an equilibrium situation.
b. For the body to float, the volume of fluid displaced must be less than the volume of the block.
The water level will increase by the amount of water the bird would displace if it was in the water.
Yes. The density of salt water is slightly higher than that of fresh water, so it can exert a larger buoyant
force for a given displaced volume of water.
Water level in pool drops but the boat will ride higher. The original level of the boat took into account a
displacement of water equal to the weight of the anchor.
It will by partly submerged. The object will sink until the weight of the displaced water is equal to the weight
of the object. If the density of the water is greater than the object, it will float partially submerged.
The velocity of the water decreases. For steady flow, the product of velocity times the area is constant.
Along a streamline, pressure is lower where the velocity is higher. As the water falls, its velocity increases.
The lower pressure in the center of the stream allows the pressure of the atmosphere to constrict it
somewhat.
The liquid with low viscosity will flow more rapidly. Viscosity is a frictional effect retarding the flow.
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Q28
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Q31
Q32
No. The transition from laminar to turbulent flow occurs as one goes from low to higher velocities.
The upward flow of cigarette smoke is accelerated by a buoyant force. Its increased speed and its low
viscosity cause the streamlines to become chaotic.
They come together. The higher air velocity between them means that the pressure will be reduced in that
region, according to Bernoulli's Principle, and atmospheric pressure above and below pushes them
together.
The door will swing shut. It swings toward the plane of the gust of wind that is flowing over its open
surface. Pressure is lowered by the moving air on that side of the open door.
The air will be moving fastest in the center so the air pressure is least at that point.
Ball is spinning so that the bottom of the ball is moving in the same direction as the linear velocity of the
ball. We would call this “back-spin” and it causes the ball to rise.
Answers to Exercises
E1
E2
E3
E4
E5
E6
E7
E8
E9
E10
E11
E12
E13
E14
E15
E16
80 Pa
275 psi
1.25 psi
90 N
a. 400 kPa
b. 8.0 x 104 N
120 N
2250 Pa
0.04 m3
26.67 kPa
4.9 N
500 kg/m3
a. 4500 kg
b. 4.41 x 104 N
1.96 x 103 N
2.0 m/s
1/2
6000 Pa
Answers to Synthesis Problems
SP1
a.
b.
c.
d.
3.14 cm2, 490.87 cm2
156.32:1
1.372 x 104 N
87.8 N
SP2
a.
b.
c.
d.
e.
a.
b.
c.
d.
e.
a.
b.
c.
d.
a.
b.
c.
1.5 m3
1.5 x 103 kg
1.47 x 104 N
29.1 kPa
0.294 atmosphere
2.7 x 10-5 m3
0.21 kg
2.06 N
0.264 N
1.795 N
11760 N
11760 N
1.20 m3
0.267 m
50.26 cm2 , 19.6 cm2
3.85 m/s
The pressure in the narrow portion where the velocity is greater will be less than the pressure in the
wider portion, according to Bernoulli's Principle applied to a horizontal streamline.
SP3
SP4
SP5
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