Fluid Mechanics with teacher's notes

27. What increase of pressure is required to change the
temperature of a sample of nitrogen by 1.00 percent?
Assume the volume of the sample remains
constant.
28. A balloon filled with air is compressed to half its
initial volume. If the temperature inside the balloon
remains constant, what happens to the pressure of
the air inside the balloon?
Practice problems
29. An ideal gas is contained in a vessel of fixed volume
at a temperature of 325 K and a pressure of 1.22 ×
10 5 Pa. If the pressure is increased to 1.78 × 10 5 Pa,
what is the final temperature of the gas?
(See Sample Problem 9E.)
30. The pressure in a constant-volume gas thermometer
is 7.09 × 10 5 Pa at 100.0°C and 5.19 × 10 4 Pa at
0.0°C. What is the temperature when the pressure is
4.05 × 10 3 Pa?
(See Sample Problem 9E.)
MIXED REVIEW
31. An engineer weighs a sample of mercury (r = 13.6 ×
10 3 kg/m 3 ) and finds that the weight of the sample is
4.5 N. What is the sample’s volume.
32. How much force does the atmosphere exert on
1.00 km 2 of land at sea level?
33. A 70.0 kg man sits in a 5.0 kg chair so that his
weight is evenly distributed on the legs of the chair.
Assume that each leg makes contact with the floor
over a circular area with a radius of 1.0 cm. What is
the pressure exerted on the floor by each leg?
34. A swimmer has 8.20 × 10 −4 m 3 of air in his lungs
when he dives into a lake. Assuming the pressure of
the air is 95 percent of the external pressure at all
times, what is the volume of the air at a depth of
10.0 m? Assume that the atmospheric pressure at the
surface is 1.013 × 10 5 Pa, the density of the lake water
is 1.00 × 10 3 kg/m 3 , and the temperature is constant.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
35. An air bubble has a volume of 1.50 cm 3 when it is
released by a submarine 100.0 m below the surface
of the sea. What is the volume of the bubble when it
reaches the surface? Assume that the temperature of
the air in the bubble remains constant during ascent.
36. A frog in a hemispherical
bowl, as
shown in Figure 9-21,
just floats in a fluid
with a density of 1.35
× 10 3 kg/m 3 . If the
bowl has a radius of
6.00 cm and negligible
mass, what is the mass
of the frog?
37. A circular swimming pool at sea level has a flat bottom
and a 6.00 m diameter. It is filled with water to
a depth of 1.50 m.
a. What is the absolute pressure at the bottom?
b. Two people with a combined mass of 150 kg
float in the pool. What is the resulting increase
in the average absolute pressure at the bottom?
38. The wind blows with a speed of 30.0 m/s over the
roof of your house.
a. Assuming the air inside the house is relatively
stagnant, what is the pressure difference at the
roof between the inside air and the outside air?
b. What net force does this pressure difference
produce on a roof having an area of 175 m 2 ?
39. A bag of blood with a density of 1050 kg/m 3 is
raised about 1.00 m higher than the level of a
patient’s arm. How much greater is the blood pressure
at the patient’s arm than it would be if the bag
were at the same height as the arm?
40. The density of helium gas at 0.0°C is 0.179 kg/m 3 .
The temperature is then raised to 100.0°C, but the
pressure is kept constant. Assuming that helium is
an ideal gas, calculate the new density of the gas.
41. When a load of 1.0 × 10 6 N is placed on a battleship,
the ship sinks only 2.5 cm in the water. Estimate the
cross-sectional area of the ship at water level. (Hint:
See Table 9-1 for the density of sea water.)
Fluid Mechanics
Figure 9-21
345
9 REVIEW & ASSESS
26. It expands as it rises and stops
expanding when the density of
the air equals the total average
density of the helium and the
balloon. Because of the mass
of the balloon itself, the density
of the helium will be slightly
less than the density of the
air at that height.
27. 1.00 percent
28. The pressure doubles.
29. 474 K
30. 21.3 K
31. 3.4 × 10 −5 m 3
32. 1.01 × 10 11 N
33. 5.9 × 10 5 Pa
34. 4.2 × 10 −4 m 3
35. 16.5 cm 3
36. 6.11 × 10 −1 kg
37. a. 1.16 × 10 5 Pa
b. 52 Pa
38. a. 5.80 × 10 2 Pa
b. 1.02 × 10 5 N upward
39. 1.03 × 10 4 Pa
40. 0.131 kg/m 3
41. 4.0 × 10 3 m 2
345