(a) Suppose you find that you can only suck wa
ter up to a height of 1
.
0 m. What is the minimum
pressure inside the straw?
√
(b) Superman, strong as he is, can suck out all
the air from a (strongwalled) straw. What is the
tallest straw through which Superman can drink
water out of a lake?
√
10d2
The first transatlantic telegraph cable
was built in 1858, lying at a depth of up to 3.2
km.
What is the pressure at this depth, in at
mospheres?
10d3
One way to measure the density of an
unknown liquid is by using it as a barometer.
Suppose you have a column of length
L
of the
unknown liquid (inside a vacuum tube), which
provides the same pressure as atmospheric pres
sure
P
0
.
(a) What is the density of the unknown liquid?
√
(b) Mercury barometers have
L
= 760 mm at
standard atmospheric pressure
P
0
=
1
.
013
×
10
5
Pa.
Given these data, what is the density
of mercury to three significant figures?
√
10d4
A Ushaped tube, with both ends ex
posed to the atmosphere, has two immiscible liq
uids in it: water, and some unknown liquid. The
unknown liquid sits on top of the water on the
right side of the tube in a column of height
H
.
Also, the water extends a height
h
above the
unknownwater interface. If the density of water
is
ρ
w
, what is the density of the unknown liquid?
√
10d5
Typically the atmosphere gets colder
with increasing altitude.
However, sometimes
there is an
inversion layer
, in which this trend is
reversed, e.g., because a less dense mass of warm
air moves into a certain area, and rises above the
122
CHAPTER 10.
FLUIDS
Problem 10d4.
denser colder air that was already present. Sup
pose that this causes the pressure
P
as a func
tion of height
y
to be given by a function of the
form
P
=
P
o
e

ky
(1 +
by
), where constant tem
perature would give
b
= 0 and an inversion layer
would give
b >
0. (a) Infer the units of the con
stants
P
o
,
k
, and
b
. (b) Find the density of the
air as a function of
y
, of the constants, and of
the acceleration of gravity
g
. (c) Check that the
units of your answer to part b make sense.
.
Solution, p. 156
10d6
Estimate the pressure at the center
of the Earth, assuming it is of constant density
throughout. The gravitational field
g
is not con
stant with repsect to depth.
It equals
Gmr/b
3
for
r
, the distance from the center, less than
b
,
the earth’s radius.
Here
m
is the mass of the
earth, and
G
is Newton’s universal gravitational
constant, which has units of N
·
m
2
/
kg
2
.
(a) State your result in terms of
G
,
m
, and
b
.
√
(b) Show that your answer from part a has the
right units for pressure.
(c) Evaluate the result numerically.
√
(d) Given that the earth’s atmosphere is on the
order of one thousandth the earth’s radius, and
that the density of the earth is several thousand
times greater than the density of the lower atmo
sphere, check that your result is of a reasonable
order of magnitude.
You've reached the end of your free preview.
Want to read all 160 pages?
 Spring '08
 Kenney
 pH, The American, The Land, Velocity, B. Crowell