Problem 1.22
Express the following quantities in SI units: (a)
1
60 acres, (b)
1
5 gallons (U.S.), (c)
2
40 miles,
(d)
7
9.1 h
p
, and (e)
6
0.3 °F.
Solution 1.22
a)
22
4252
2
ft m
1
60 acre 160 acre 4.356 10 9.290 10 6.47 10 m
acre ft
1
Problem 1.23
Water flows from a large drainage pipe at a rate of
1
200 gal min. What is this volume rate
of flow in (a) 3
m
s, (b) liters mi
n
, and (c) 3
f
ts
?
Solution 1.23
a)
3
3
52
m
gal m
s
f
lowrate 1200 6.309 10 7.57 10
gal
min s
f
Problem 1.24
The universal gas constant 0
R
is equal to 22
49,700 ft s/°R
, or 22
8
310 m / s K . Show
that these two magnitudes are equal.
Solution 1.24
Problem 1.25
Dimensionless combinations of quantities (commonly called dimensionless parameters)
play an important role in fluid mechanics. Make up five possible dimensionless parameters
by using combinations of some of the quantities listed in Table B.1 Physical Properties of
Water (BG/EE Units).
Solution 1.25
Some possible examples:
Problem 1.26
An important dimensionless parameter in certain types of fluid flow problems is the Froude
number defined as
V
g, where
V
is velocity,
g
is the acceleration of gravity, and is
length. Determine the value of the Froude number for 10 ft s
V
, 2
32.2 ft s
g, and
2 ft. Recalculate the Froude number using SI units for
V
,
g
, and . Explain the signifi-
cance of the results of these calculations.
Solution 1.26
In BG units,
ft
10 s1.25
Problem 1.28
A tank contains 500 kg of a liquid whose specific gravity is 2. Determine the volume of the
liquid in the tank.
Solution 1.28
2
HO
mVSG V
Problem 1.29
A stick of butter at
3
5°
F
measures
1
.25 in. 1.25 in. 4.65 in. and weighs
4
ounces. Find its
specific weight.
Solution 1.29
1lb
Problem 1.30
Clouds can weigh thousands of pounds due to their liquid water content. Often this content
is measured in grams per cubic meter 3
g/m . Assume that a cumulus cloud occupies a
volume of 1 cubic kilometer, and its liquid water content is 3
0.2 g/m . (a) What is the volume
of this cloud in cubic miles? (b) How much does the water in the cloud weigh in pounds?
Solution 1.30
a)
33
393 3
1,000 m 3.281 ft 1 m
V
olume 1 km 10 m 0.240 mi
1 km 1 m 5,280 ft
Problem 1.31
A tank of oil has a mass of
2
5 slugs. (a) Determine its weight in pounds and in Newtons at
the Earth’s surface. (b) What would be its mass (in slugs) and its weight (in pounds) if
located on the moon’s surface where the gravitational attraction is approximately one-sixth
that at the Earth’s surface?
Solution 1.31
a)
w
eight mass
g
Problem 1.32
A certain object weighs
3
00 N at the Earth’s surface. Determine the mass of the object (in
kilograms) and its weight (in newtons) when located on a planet with an acceleration of
gravity equal to 2
4.0 ft s .
Solution 1.32
2
weight 300 N
m
ass 30.6 kg
m
9.81 s
g
Problem 1.33
The density of a certain type of jet fuel is 3
7
75 kg/m . Determine its specific gravity and
specific weight.
Solution 1.33
kg
775 m0.775
Problem 1.34
At 4°C a mixture of automobile antifreeze (
5
0% water and
5
0% ethylene glycol by volume)
has a density of 3
1
064 kg/m . If the water density is
3
1
000 kg/m , find the density of the
ethylene glycol.
Solution 1.34
mixture
44°C °C
eg w
eg w
mm
Smm
The problem statement gives
DISCUSSION If the mixture were at some temperature
T
, then for equal volumes of
mixture and 4°C water,
4°C 4°C
0.5
eg w eg w
TT
ww
mm
Sm
Problem 1.35
A hydrometer is used to measure the specific gravity of liquids. For a certain liquid, a
hydrometer reading indicates a specific gravity of 1.15.What is the liquid’s density and
specific weight? Express your answer in SI units.
Solution 1.35
HO
SG
o
2@4 C
Problem 1.36
An open, rigid-walled, cylindrical tank contains 3
4 ft of water at
4
0 °F. Over a 24-hour
period of time the water temperature varies from
4
0 to 90 °F. Make use of the data in
Appendix B to determine how much the volume of water will change. For a tank diameter
of
2
ft, would the corresponding change in water depth be very noticeable? Explain.
Solution 1.36
m
ass of water
Amount ot mass is not a function of temperature.
Thus, the increase in volume is: 3
4.0186 4.000 0.0186 ft
Problem 1.38
A mountain climber’s oxygen tank contains
1
lb of oxygen when he begins his trip at sea level
where the acceleration of gravity is 2
3
2.174 ft/s . What is the weight of the oxygen in the tank
when he reaches the top of Mt. Everest where the acceleration of gravity is 2
3
2.082 ft/s ?
Assume that no oxygen has been removed from the tank; it will be used on the descent
portion of the climb.
Solution 1.38
W
mg
Problem 1.39
The information on a can of pop indicates that the can contains
3
55 mL. The mass of a full
can of pop is 0.369 kg, while an empty can weighs
0
.153 N. Determine the specific weight,
density, and specific gravity of the pop and compare your results with the corresponding
values for water at
2
0 °C. Express your results in SI units.
Solution 1.39
weight of fluid
volume of fluid
2
Problem 1.40
The variation in the density of water, , with temperature,
T
, in the range
20 °C 50 °CT, is given in the following table.
Density (kg/m3) 998.2 997.1 995.7 994.1 992.2 990.2 988.1
Temperature ( C) 20 25 30 35 40 45 50
Use these data to determine an empirical equation of the form 2
12 3
ccTcT
which
can be used to predict the density over the range indicated. Compare the predicted values
with the data given. What is the density of water at
4
2.1 C?
Solution 1.40
Fit the data to a second order polynomial using a standard curve-fitting program such as
found in Excel. Thus,
As shown in the table below, (predicted) from Eq.(1) is in good agreement with (given).
T -predict -data
(oC) (kg/m^3) (kg/m^3)
20 998.3 998.2
Problem 1.41
If
1
cu
p
of cream having a density of 3
1
005 kg/m is turned into
3
cups of whipped cream,
determine the specific gravity and specific weight of the whipped cream.
Solution 1.41
Mass of cream, cup
3
kg
1005 m
m, were volume.
Problem 1.42
With the exception of the 410 bore, the gauge of a shotgun barrel indicates the number of
round lead balls, each having the bore diameter of the barrel, that together weigh
1
lb. For
example, a shotgun is called a 12 – gauge shotgun if a 1-l
b
12 lead ball fits the bore of the
barrel. Find the diameter of a 12 – gauge shotgun in inches and millimeters. Lead has a
specific weight of 3
0.411 lb/in .
Solution 1.42
3
ball
3
weight 0.20276 in.
l
.
1
1
lb
1
b
04
2
1in.
Problem 1.44
A regulation basketball is initially flat and is then inflated to a pressure of approximately
2
2
4 lb/in absolute. Consider the air temperature to be constant at
7
0 °F. Find the mass of
air required to inflate the basketball. The basketball’s inside radius is
4
.67 in.
Solution 1.44
3
4
3
pp
mR
RT RT