Chapter 2 Properties of Fluids Chapter 2 PROPERTIES OF FLUIDS Notes | EduRev

: Chapter 2 Properties of Fluids Chapter 2 PROPERTIES OF FLUIDS Notes | EduRev

 Page 1


Chapter 2  Properties of Fluids  
Chapter 2 
PROPERTIES OF FLUIDS 
 
 
Density and Specific Gravity 
 
2-1C  Intensive properties do not depend on the size (extent) of the system but extensive properties do. 
 
2-2C The specific gravity, or relative density, and is defined as the ratio of the density of a substance to 
the density of some standard substance at a specified temperature (usually water at 4°C, for which ?
H2O
 = 
1000 kg/m
3
). That is, 
H2O
/ ? ? = SG . When specific gravity is known, density is determined from 
H2O
? ? × = SG . 
 
2-3C  A gas can be treated as an ideal gas when it is at a high temperature or low pressure relative to its 
critical temperature and pressure. 
 
2-4C  R
u
 is the universal gas constant that is the same for all gases whereas R is the specific gas constant 
that is different for different gases.  These two are related to each other by R = R
u
 /M, where M is the molar 
mass of the gas. 
 
2-5  A balloon is filled with helium gas. The mole number and the mass of helium in the balloon are to be 
determined. 
Assumptions   At specified conditions, helium behaves as an ideal gas.   
Properties  The universal gas constant is R
u
 = 8.314 kPa.m
3
/kmol.K. The molar mass of helium is 4.0 
kg/kmol.  
Analysis The volume of the sphere is 
 
3 3 3
m 113.1 m) (3
3
4
3
4
= = = p p r V 
He 
D = 6 m 
20 °C 
200 kPa 
Assuming ideal gas behavior, the mole numbers of He is determined from 
 kmol 9.286 =
· ·
= =
K) K)(293 /kmol m kPa (8.314
) m kPa)(113.1 (200
3
3
T R
P
N
u
V
 
Then the mass of He can be determined from 
 kg  37.1 = = = kg/kmol) kmol)(4.0 (9.286 NM m 
 
 
 
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc.  Limited distribution 
permitted only to teachers and educators for course preparation.  If you are a student using this Manual, you 
are using it without permission.   
2-1
Page 2


Chapter 2  Properties of Fluids  
Chapter 2 
PROPERTIES OF FLUIDS 
 
 
Density and Specific Gravity 
 
2-1C  Intensive properties do not depend on the size (extent) of the system but extensive properties do. 
 
2-2C The specific gravity, or relative density, and is defined as the ratio of the density of a substance to 
the density of some standard substance at a specified temperature (usually water at 4°C, for which ?
H2O
 = 
1000 kg/m
3
). That is, 
H2O
/ ? ? = SG . When specific gravity is known, density is determined from 
H2O
? ? × = SG . 
 
2-3C  A gas can be treated as an ideal gas when it is at a high temperature or low pressure relative to its 
critical temperature and pressure. 
 
2-4C  R
u
 is the universal gas constant that is the same for all gases whereas R is the specific gas constant 
that is different for different gases.  These two are related to each other by R = R
u
 /M, where M is the molar 
mass of the gas. 
 
2-5  A balloon is filled with helium gas. The mole number and the mass of helium in the balloon are to be 
determined. 
Assumptions   At specified conditions, helium behaves as an ideal gas.   
Properties  The universal gas constant is R
u
 = 8.314 kPa.m
3
/kmol.K. The molar mass of helium is 4.0 
kg/kmol.  
Analysis The volume of the sphere is 
 
3 3 3
m 113.1 m) (3
3
4
3
4
= = = p p r V 
He 
D = 6 m 
20 °C 
200 kPa 
Assuming ideal gas behavior, the mole numbers of He is determined from 
 kmol 9.286 =
· ·
= =
K) K)(293 /kmol m kPa (8.314
) m kPa)(113.1 (200
3
3
T R
P
N
u
V
 
Then the mass of He can be determined from 
 kg  37.1 = = = kg/kmol) kmol)(4.0 (9.286 NM m 
 
 
 
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc.  Limited distribution 
permitted only to teachers and educators for course preparation.  If you are a student using this Manual, you 
are using it without permission.   
2-1
Chapter 2  Properties of Fluids  
 
2-6  A balloon is filled with helium gas. The mole number and the mass of helium in the balloon are to 
be determined. The effect of the balloon diameter on the mass of helium is to be investigated, and the 
results are to be tabulated and plotted. 
 
"Given Data" 
{D=6"[m]"} 
{P=200"[kPa]"} 
T=20"[C]" 
P=100"[kPa]" 
R_u=8.314"[kJ/kmol*K]" 
 
"Solution" 
P*V=N*R_u*(T+273) 
V=4*pi*(D/2)^3/3"[m^3]" 
m=N*MOLARMASS(Helium)"[kg]" 
 
D [m] m [kg] 
0.5 0.01075 
2.111 0.8095 
3.722 4.437 
5.333 13.05 
6.944 28.81 
8.556 53.88 
10.17 90.41 
11.78 140.6 
13.39 206.5 
15 290.4 
 
 
0 2 4 6 8 10 12 14
0
100
200
300
400
500
D  [m]
m  [kg]
Mass of Helium in Balloon as function of Diameter
P = 200 kPa
m  [kg]
P = 100 kPa
 
 
 
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc.  Limited distribution 
permitted only to teachers and educators for course preparation.  If you are a student using this Manual, you 
are using it without permission.   
2-2
Page 3


Chapter 2  Properties of Fluids  
Chapter 2 
PROPERTIES OF FLUIDS 
 
 
Density and Specific Gravity 
 
2-1C  Intensive properties do not depend on the size (extent) of the system but extensive properties do. 
 
2-2C The specific gravity, or relative density, and is defined as the ratio of the density of a substance to 
the density of some standard substance at a specified temperature (usually water at 4°C, for which ?
H2O
 = 
1000 kg/m
3
). That is, 
H2O
/ ? ? = SG . When specific gravity is known, density is determined from 
H2O
? ? × = SG . 
 
2-3C  A gas can be treated as an ideal gas when it is at a high temperature or low pressure relative to its 
critical temperature and pressure. 
 
2-4C  R
u
 is the universal gas constant that is the same for all gases whereas R is the specific gas constant 
that is different for different gases.  These two are related to each other by R = R
u
 /M, where M is the molar 
mass of the gas. 
 
2-5  A balloon is filled with helium gas. The mole number and the mass of helium in the balloon are to be 
determined. 
Assumptions   At specified conditions, helium behaves as an ideal gas.   
Properties  The universal gas constant is R
u
 = 8.314 kPa.m
3
/kmol.K. The molar mass of helium is 4.0 
kg/kmol.  
Analysis The volume of the sphere is 
 
3 3 3
m 113.1 m) (3
3
4
3
4
= = = p p r V 
He 
D = 6 m 
20 °C 
200 kPa 
Assuming ideal gas behavior, the mole numbers of He is determined from 
 kmol 9.286 =
· ·
= =
K) K)(293 /kmol m kPa (8.314
) m kPa)(113.1 (200
3
3
T R
P
N
u
V
 
Then the mass of He can be determined from 
 kg  37.1 = = = kg/kmol) kmol)(4.0 (9.286 NM m 
 
 
 
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc.  Limited distribution 
permitted only to teachers and educators for course preparation.  If you are a student using this Manual, you 
are using it without permission.   
2-1
Chapter 2  Properties of Fluids  
 
2-6  A balloon is filled with helium gas. The mole number and the mass of helium in the balloon are to 
be determined. The effect of the balloon diameter on the mass of helium is to be investigated, and the 
results are to be tabulated and plotted. 
 
"Given Data" 
{D=6"[m]"} 
{P=200"[kPa]"} 
T=20"[C]" 
P=100"[kPa]" 
R_u=8.314"[kJ/kmol*K]" 
 
"Solution" 
P*V=N*R_u*(T+273) 
V=4*pi*(D/2)^3/3"[m^3]" 
m=N*MOLARMASS(Helium)"[kg]" 
 
D [m] m [kg] 
0.5 0.01075 
2.111 0.8095 
3.722 4.437 
5.333 13.05 
6.944 28.81 
8.556 53.88 
10.17 90.41 
11.78 140.6 
13.39 206.5 
15 290.4 
 
 
0 2 4 6 8 10 12 14
0
100
200
300
400
500
D  [m]
m  [kg]
Mass of Helium in Balloon as function of Diameter
P = 200 kPa
m  [kg]
P = 100 kPa
 
 
 
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc.  Limited distribution 
permitted only to teachers and educators for course preparation.  If you are a student using this Manual, you 
are using it without permission.   
2-2
Chapter 2  Properties of Fluids  
2-7  An automobile tire is inflated with air. The pressure rise of air in the tire when the tire is heated and the 
amount of air that must be bled off to reduce the temperature to the original value are to be determined. 
Assumptions  1  At specified conditions, air behaves as an ideal gas.  2 The volume of the tire remains 
constant.  
Properties  The gas constant of air is R = 0.287 kPa ·m
3
/kg ·K.  
Analysis Initially, the absolute pressure in the tire is 
  PP P
gatm 1
=+ = + = 210 100 310 kPa
Treating air as an ideal gas and assuming the volume of the tire to 
remain constant, the final pressure in the tire can be determined from 
 kPa 336 kPa) (310
K 298
K 323
1
1
2
2
2
2 2
1
1 1
= = = ?? ? = P
T
T
P
T
P
T
P V V
 
Tire 
25 °C 
210 kPa 
Thus the pressure rise is 
  kPa 26 = - = - = ? 310 336
1 2
P P P
The amount of air that needs to be bled off to restore pressure to its original value is 
 
kg 0.0070 = - = - = ?
=
· ·
= =
=
· ·
= =
0.0836 0.0906
kg 0.0836
K) K)(323 /kg m kPa (0.287
) m kPa)(0.025 (310
kg 0.0906
K) K)(298 /kg m kPa (0.287
) m kPa)(0.025 (310
2 1
3
3
2
2
2
3
3
1
1
1
m m m
RT
P
m
RT
P
m
V
V
 
 
 
2-8E  An automobile tire is under inflated with air. The amount of air that needs to be added to the tire to 
raise its pressure to the recommended value is to be determined. 
Assumptions  1  At specified conditions, air behaves as an ideal gas.  2 The volume of the tire remains 
constant.  
Properties  The gas constant of air is R = 0.3704 psia ·ft
3
/lbm ·R.  
Tire 
0.53 ft
3
 
90 °F 
20 psia 
Analysis The initial and final absolute pressures in the tire are 
 P
1
 = P
g1
 + P
atm
 = 20 + 14.6 = 34.6 psia 
 P
2
 = P
g2
 + P
atm
 = 30 + 14.6 = 44.6 psia 
Treating air as an ideal gas, the initial mass in the tire is 
 lbm 0.0900
R) R)(550 /lbm ft psia (0.3704
) ft psia)(0.53 (34.6
3
3
1
1
1
=
· ·
= =
RT
P
m
V
 
Noting that the temperature and the volume of the tire remain constant, the final mass in the tire becomes 
 lbm 0.1160
R) R)(550 /lbm ft psia (0.3704
) ft psia)(0.53 (44.6
3
3
2
2
2
=
· ·
= =
RT
P
m
V
 
Thus the amount of air that needs to be added is 
 lbm 0.0260 = - = - = ? 0.0900 0.1160
1 2
m m m 
 
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc.  Limited distribution 
permitted only to teachers and educators for course preparation.  If you are a student using this Manual, you 
are using it without permission.   
2-3
Page 4


Chapter 2  Properties of Fluids  
Chapter 2 
PROPERTIES OF FLUIDS 
 
 
Density and Specific Gravity 
 
2-1C  Intensive properties do not depend on the size (extent) of the system but extensive properties do. 
 
2-2C The specific gravity, or relative density, and is defined as the ratio of the density of a substance to 
the density of some standard substance at a specified temperature (usually water at 4°C, for which ?
H2O
 = 
1000 kg/m
3
). That is, 
H2O
/ ? ? = SG . When specific gravity is known, density is determined from 
H2O
? ? × = SG . 
 
2-3C  A gas can be treated as an ideal gas when it is at a high temperature or low pressure relative to its 
critical temperature and pressure. 
 
2-4C  R
u
 is the universal gas constant that is the same for all gases whereas R is the specific gas constant 
that is different for different gases.  These two are related to each other by R = R
u
 /M, where M is the molar 
mass of the gas. 
 
2-5  A balloon is filled with helium gas. The mole number and the mass of helium in the balloon are to be 
determined. 
Assumptions   At specified conditions, helium behaves as an ideal gas.   
Properties  The universal gas constant is R
u
 = 8.314 kPa.m
3
/kmol.K. The molar mass of helium is 4.0 
kg/kmol.  
Analysis The volume of the sphere is 
 
3 3 3
m 113.1 m) (3
3
4
3
4
= = = p p r V 
He 
D = 6 m 
20 °C 
200 kPa 
Assuming ideal gas behavior, the mole numbers of He is determined from 
 kmol 9.286 =
· ·
= =
K) K)(293 /kmol m kPa (8.314
) m kPa)(113.1 (200
3
3
T R
P
N
u
V
 
Then the mass of He can be determined from 
 kg  37.1 = = = kg/kmol) kmol)(4.0 (9.286 NM m 
 
 
 
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc.  Limited distribution 
permitted only to teachers and educators for course preparation.  If you are a student using this Manual, you 
are using it without permission.   
2-1
Chapter 2  Properties of Fluids  
 
2-6  A balloon is filled with helium gas. The mole number and the mass of helium in the balloon are to 
be determined. The effect of the balloon diameter on the mass of helium is to be investigated, and the 
results are to be tabulated and plotted. 
 
"Given Data" 
{D=6"[m]"} 
{P=200"[kPa]"} 
T=20"[C]" 
P=100"[kPa]" 
R_u=8.314"[kJ/kmol*K]" 
 
"Solution" 
P*V=N*R_u*(T+273) 
V=4*pi*(D/2)^3/3"[m^3]" 
m=N*MOLARMASS(Helium)"[kg]" 
 
D [m] m [kg] 
0.5 0.01075 
2.111 0.8095 
3.722 4.437 
5.333 13.05 
6.944 28.81 
8.556 53.88 
10.17 90.41 
11.78 140.6 
13.39 206.5 
15 290.4 
 
 
0 2 4 6 8 10 12 14
0
100
200
300
400
500
D  [m]
m  [kg]
Mass of Helium in Balloon as function of Diameter
P = 200 kPa
m  [kg]
P = 100 kPa
 
 
 
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc.  Limited distribution 
permitted only to teachers and educators for course preparation.  If you are a student using this Manual, you 
are using it without permission.   
2-2
Chapter 2  Properties of Fluids  
2-7  An automobile tire is inflated with air. The pressure rise of air in the tire when the tire is heated and the 
amount of air that must be bled off to reduce the temperature to the original value are to be determined. 
Assumptions  1  At specified conditions, air behaves as an ideal gas.  2 The volume of the tire remains 
constant.  
Properties  The gas constant of air is R = 0.287 kPa ·m
3
/kg ·K.  
Analysis Initially, the absolute pressure in the tire is 
  PP P
gatm 1
=+ = + = 210 100 310 kPa
Treating air as an ideal gas and assuming the volume of the tire to 
remain constant, the final pressure in the tire can be determined from 
 kPa 336 kPa) (310
K 298
K 323
1
1
2
2
2
2 2
1
1 1
= = = ?? ? = P
T
T
P
T
P
T
P V V
 
Tire 
25 °C 
210 kPa 
Thus the pressure rise is 
  kPa 26 = - = - = ? 310 336
1 2
P P P
The amount of air that needs to be bled off to restore pressure to its original value is 
 
kg 0.0070 = - = - = ?
=
· ·
= =
=
· ·
= =
0.0836 0.0906
kg 0.0836
K) K)(323 /kg m kPa (0.287
) m kPa)(0.025 (310
kg 0.0906
K) K)(298 /kg m kPa (0.287
) m kPa)(0.025 (310
2 1
3
3
2
2
2
3
3
1
1
1
m m m
RT
P
m
RT
P
m
V
V
 
 
 
2-8E  An automobile tire is under inflated with air. The amount of air that needs to be added to the tire to 
raise its pressure to the recommended value is to be determined. 
Assumptions  1  At specified conditions, air behaves as an ideal gas.  2 The volume of the tire remains 
constant.  
Properties  The gas constant of air is R = 0.3704 psia ·ft
3
/lbm ·R.  
Tire 
0.53 ft
3
 
90 °F 
20 psia 
Analysis The initial and final absolute pressures in the tire are 
 P
1
 = P
g1
 + P
atm
 = 20 + 14.6 = 34.6 psia 
 P
2
 = P
g2
 + P
atm
 = 30 + 14.6 = 44.6 psia 
Treating air as an ideal gas, the initial mass in the tire is 
 lbm 0.0900
R) R)(550 /lbm ft psia (0.3704
) ft psia)(0.53 (34.6
3
3
1
1
1
=
· ·
= =
RT
P
m
V
 
Noting that the temperature and the volume of the tire remain constant, the final mass in the tire becomes 
 lbm 0.1160
R) R)(550 /lbm ft psia (0.3704
) ft psia)(0.53 (44.6
3
3
2
2
2
=
· ·
= =
RT
P
m
V
 
Thus the amount of air that needs to be added is 
 lbm 0.0260 = - = - = ? 0.0900 0.1160
1 2
m m m 
 
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc.  Limited distribution 
permitted only to teachers and educators for course preparation.  If you are a student using this Manual, you 
are using it without permission.   
2-3
Chapter 2  Properties of Fluids  
2-9E  A rigid tank contains slightly pressurized air. The amount of air that needs to be added to the tank to 
raise its pressure and temperature to the recommended values is to be determined. v 
Assumptions  1  At specified conditions, air behaves as an ideal gas.  2 The volume of the tank remains 
constant.  
Properties  The gas constant of air is R = 0.3704 psia ·ft
3
/lbm ·R.  
Analysis Treating air as an ideal gas, the initial volume and the final mass in the tank are determined to be 
 
lbm 33.73
R) R)(550 /lbm ft psia (0.3704
) ft 3 psia)(196. (35
ft 196.3
 psia 20
R) R)(530 /lbm ft psia 4 lbm)(0.370 (20
3
3
2
2
2
3
3
1
1 1
=
· ·
= =
=
· ·
= =
RT
P
m
P
RT m
V
V
 
Air, 20 lbm
20 psia 
70 °F 
Thus the amount of air added is 
 lbm 13.7 = - = - = ? 20.0 33.73
1 2
m m m 
 
 
 
 
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc.  Limited distribution 
permitted only to teachers and educators for course preparation.  If you are a student using this Manual, you 
are using it without permission.   
2-4
Page 5


Chapter 2  Properties of Fluids  
Chapter 2 
PROPERTIES OF FLUIDS 
 
 
Density and Specific Gravity 
 
2-1C  Intensive properties do not depend on the size (extent) of the system but extensive properties do. 
 
2-2C The specific gravity, or relative density, and is defined as the ratio of the density of a substance to 
the density of some standard substance at a specified temperature (usually water at 4°C, for which ?
H2O
 = 
1000 kg/m
3
). That is, 
H2O
/ ? ? = SG . When specific gravity is known, density is determined from 
H2O
? ? × = SG . 
 
2-3C  A gas can be treated as an ideal gas when it is at a high temperature or low pressure relative to its 
critical temperature and pressure. 
 
2-4C  R
u
 is the universal gas constant that is the same for all gases whereas R is the specific gas constant 
that is different for different gases.  These two are related to each other by R = R
u
 /M, where M is the molar 
mass of the gas. 
 
2-5  A balloon is filled with helium gas. The mole number and the mass of helium in the balloon are to be 
determined. 
Assumptions   At specified conditions, helium behaves as an ideal gas.   
Properties  The universal gas constant is R
u
 = 8.314 kPa.m
3
/kmol.K. The molar mass of helium is 4.0 
kg/kmol.  
Analysis The volume of the sphere is 
 
3 3 3
m 113.1 m) (3
3
4
3
4
= = = p p r V 
He 
D = 6 m 
20 °C 
200 kPa 
Assuming ideal gas behavior, the mole numbers of He is determined from 
 kmol 9.286 =
· ·
= =
K) K)(293 /kmol m kPa (8.314
) m kPa)(113.1 (200
3
3
T R
P
N
u
V
 
Then the mass of He can be determined from 
 kg  37.1 = = = kg/kmol) kmol)(4.0 (9.286 NM m 
 
 
 
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc.  Limited distribution 
permitted only to teachers and educators for course preparation.  If you are a student using this Manual, you 
are using it without permission.   
2-1
Chapter 2  Properties of Fluids  
 
2-6  A balloon is filled with helium gas. The mole number and the mass of helium in the balloon are to 
be determined. The effect of the balloon diameter on the mass of helium is to be investigated, and the 
results are to be tabulated and plotted. 
 
"Given Data" 
{D=6"[m]"} 
{P=200"[kPa]"} 
T=20"[C]" 
P=100"[kPa]" 
R_u=8.314"[kJ/kmol*K]" 
 
"Solution" 
P*V=N*R_u*(T+273) 
V=4*pi*(D/2)^3/3"[m^3]" 
m=N*MOLARMASS(Helium)"[kg]" 
 
D [m] m [kg] 
0.5 0.01075 
2.111 0.8095 
3.722 4.437 
5.333 13.05 
6.944 28.81 
8.556 53.88 
10.17 90.41 
11.78 140.6 
13.39 206.5 
15 290.4 
 
 
0 2 4 6 8 10 12 14
0
100
200
300
400
500
D  [m]
m  [kg]
Mass of Helium in Balloon as function of Diameter
P = 200 kPa
m  [kg]
P = 100 kPa
 
 
 
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc.  Limited distribution 
permitted only to teachers and educators for course preparation.  If you are a student using this Manual, you 
are using it without permission.   
2-2
Chapter 2  Properties of Fluids  
2-7  An automobile tire is inflated with air. The pressure rise of air in the tire when the tire is heated and the 
amount of air that must be bled off to reduce the temperature to the original value are to be determined. 
Assumptions  1  At specified conditions, air behaves as an ideal gas.  2 The volume of the tire remains 
constant.  
Properties  The gas constant of air is R = 0.287 kPa ·m
3
/kg ·K.  
Analysis Initially, the absolute pressure in the tire is 
  PP P
gatm 1
=+ = + = 210 100 310 kPa
Treating air as an ideal gas and assuming the volume of the tire to 
remain constant, the final pressure in the tire can be determined from 
 kPa 336 kPa) (310
K 298
K 323
1
1
2
2
2
2 2
1
1 1
= = = ?? ? = P
T
T
P
T
P
T
P V V
 
Tire 
25 °C 
210 kPa 
Thus the pressure rise is 
  kPa 26 = - = - = ? 310 336
1 2
P P P
The amount of air that needs to be bled off to restore pressure to its original value is 
 
kg 0.0070 = - = - = ?
=
· ·
= =
=
· ·
= =
0.0836 0.0906
kg 0.0836
K) K)(323 /kg m kPa (0.287
) m kPa)(0.025 (310
kg 0.0906
K) K)(298 /kg m kPa (0.287
) m kPa)(0.025 (310
2 1
3
3
2
2
2
3
3
1
1
1
m m m
RT
P
m
RT
P
m
V
V
 
 
 
2-8E  An automobile tire is under inflated with air. The amount of air that needs to be added to the tire to 
raise its pressure to the recommended value is to be determined. 
Assumptions  1  At specified conditions, air behaves as an ideal gas.  2 The volume of the tire remains 
constant.  
Properties  The gas constant of air is R = 0.3704 psia ·ft
3
/lbm ·R.  
Tire 
0.53 ft
3
 
90 °F 
20 psia 
Analysis The initial and final absolute pressures in the tire are 
 P
1
 = P
g1
 + P
atm
 = 20 + 14.6 = 34.6 psia 
 P
2
 = P
g2
 + P
atm
 = 30 + 14.6 = 44.6 psia 
Treating air as an ideal gas, the initial mass in the tire is 
 lbm 0.0900
R) R)(550 /lbm ft psia (0.3704
) ft psia)(0.53 (34.6
3
3
1
1
1
=
· ·
= =
RT
P
m
V
 
Noting that the temperature and the volume of the tire remain constant, the final mass in the tire becomes 
 lbm 0.1160
R) R)(550 /lbm ft psia (0.3704
) ft psia)(0.53 (44.6
3
3
2
2
2
=
· ·
= =
RT
P
m
V
 
Thus the amount of air that needs to be added is 
 lbm 0.0260 = - = - = ? 0.0900 0.1160
1 2
m m m 
 
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc.  Limited distribution 
permitted only to teachers and educators for course preparation.  If you are a student using this Manual, you 
are using it without permission.   
2-3
Chapter 2  Properties of Fluids  
2-9E  A rigid tank contains slightly pressurized air. The amount of air that needs to be added to the tank to 
raise its pressure and temperature to the recommended values is to be determined. v 
Assumptions  1  At specified conditions, air behaves as an ideal gas.  2 The volume of the tank remains 
constant.  
Properties  The gas constant of air is R = 0.3704 psia ·ft
3
/lbm ·R.  
Analysis Treating air as an ideal gas, the initial volume and the final mass in the tank are determined to be 
 
lbm 33.73
R) R)(550 /lbm ft psia (0.3704
) ft 3 psia)(196. (35
ft 196.3
 psia 20
R) R)(530 /lbm ft psia 4 lbm)(0.370 (20
3
3
2
2
2
3
3
1
1 1
=
· ·
= =
=
· ·
= =
RT
P
m
P
RT m
V
V
 
Air, 20 lbm
20 psia 
70 °F 
Thus the amount of air added is 
 lbm 13.7 = - = - = ? 20.0 33.73
1 2
m m m 
 
 
 
 
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc.  Limited distribution 
permitted only to teachers and educators for course preparation.  If you are a student using this Manual, you 
are using it without permission.   
2-4
Chapter 2  Properties of Fluids  
2-10 The variation of density of atmospheric air with elevation is given in tabular form. A relation for the 
variation of density with elevation is to be obtained, the density at 7 km elevation is to be calculated, and 
the mass of the atmosphere using the correlation is to be estimated. v  
Assumptions  1  Atmospheric air behaves as an ideal gas. 2 The earth is perfectly sphere with a radius of 
6377 km, and the thickness of the atmosphere is 25 km.  
Properties The density data are given in tabular form as 
 
r, km 
z, km 
?, kg/m
3
 
6377 
0 
1.225 
6378 
1 
1.112 
6379 
2 
1.007 
6380 
3 
0.9093 
6381 
4 
0.8194 
6382 
5 
0.7364 
6383 
6 
0.6601 
6385 
8 
0.5258 
6387 
10 
0.4135 
6392 
15 
0.1948 
6397 
20 
0.08891 
6402 
25 
0.04008 
 
Analysis Using EES, (1) Define a trivial function rho= a+z in equation window, (2) select new parametric 
table from Tables, and type the data in a two-column table, (3) select Plot and plot the data, and (4) select 
plot and click on “curve fit” to get curve fit window. Then specify 2
nd
 order polynomial and enter/edit 
equation. The results are:  
 
0 5 10 15 20 25
0
0.2
0.4
0.6
0.8
1
1.2
1.4
z, km  
?, kg/m
3
 
 
 
?(z) = a + bz + cz
2
 = 1.20252 – 0.101674z + 0.0022375z
2
    for the unit of kg/m
3
, 
(or, ?(z) = (1.20252 – 0.101674z + 0.0022375z
2
) ×10
9
   for the unit of kg/km
3
) 
 
where z is the vertical distance from the earth surface at sea level. At z = 7 km, the equation would give ? = 
0.60 kg/m
3
.  
 
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc.  Limited distribution 
permitted only to teachers and educators for course preparation.  If you are a student using this Manual, you 
are using it without permission.   
2-5
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