2.1: PROBLEM DEFINITION
Find:
How density differs from specific weight
PLAN
Consider their definitions (conceptual and mathematical)
SOLUTION
Densit
Density
y is a [ma
[mass]/
ss]/[un
[unit
it volum
volume],
e], and specific weight is a [weight]/[unit
Therefore, they are related by the equation γ = ρg,ρg , and density differs from
weight
weight by the
the factor
factor g , the acceleration of gravity.
,2.2: PROBLEM DEFINITION
Find:
Fluids for which we can (usually) assume density to be nearly constant
Fluids for which density should be calculated as a function of tempera
pressure?
SOLUTION
Density can usually be assumed to be nearly constant for liquids , such as w
cury
cury and oil.
oil. Ho
Howe
weve
ver,
r, even the densit
densityy of a liquid
liquid varie
variess sligh
slightly
tly as a fu
either
either pressur
pressuree or temperatu
temperature.
re. Sligh
Slightt chang
changes
es in the volum
volumee occupie
occupieddb
mass of a liquid as a function of pressure can be calculated using the equ
elasticity.
One must know the temperature and the pressure to determine the density
,2.3: PROBLEM DEFINITION
Find:
Where in this text you can find density data for such fluids as oil and me
SOLUTION
Table A.4 in the Appendix contains density data for such fluids as oil and
, 2.4: PROBLEM DEFINITION
Situation:
An engineer needs to know the local density for an experiment with a glid
z = 2500
2500 ft.
ft.
Find:
Calculate density using local conditions.
Compare calculated density with the value from Table A.2, and make a rec
dation.
Properties:
From Table A.2, R air = 287 kgJ· K , ρ = 1.22kg/
22kg/ m3 .
Local temperature = 74.3 F = 296.
◦
296.7 K.
Local pressure = 27.3 in.-Hg = 92.
92.45 kPa
kPa.
PLAN
Apply the ideal gas law for local conditions.
SOLUTION
Ideal gas law
p
ρ =
RT
92, 450N/ m2
92, 450N/
=
(287kg/ m3 )(296.
(287kg/ )(296.7 K)
= 1.086 kg/m3
ρ = 1.09 kg/m3 (local conditions)
Table value.
value. From Table
Table A.2
ρ = 1.22 kg/m3 (table value)
The density difference (local
(local conditions
conditions versus
versus table value)
value) is about 12%
12%
of this difference is due to the effect of elevation on atmospheric press
Recommendation—use the local value of density because the effects of
REVIEW
Find:
How density differs from specific weight
PLAN
Consider their definitions (conceptual and mathematical)
SOLUTION
Densit
Density
y is a [ma
[mass]/
ss]/[un
[unit
it volum
volume],
e], and specific weight is a [weight]/[unit
Therefore, they are related by the equation γ = ρg,ρg , and density differs from
weight
weight by the
the factor
factor g , the acceleration of gravity.
,2.2: PROBLEM DEFINITION
Find:
Fluids for which we can (usually) assume density to be nearly constant
Fluids for which density should be calculated as a function of tempera
pressure?
SOLUTION
Density can usually be assumed to be nearly constant for liquids , such as w
cury
cury and oil.
oil. Ho
Howe
weve
ver,
r, even the densit
densityy of a liquid
liquid varie
variess sligh
slightly
tly as a fu
either
either pressur
pressuree or temperatu
temperature.
re. Sligh
Slightt chang
changes
es in the volum
volumee occupie
occupieddb
mass of a liquid as a function of pressure can be calculated using the equ
elasticity.
One must know the temperature and the pressure to determine the density
,2.3: PROBLEM DEFINITION
Find:
Where in this text you can find density data for such fluids as oil and me
SOLUTION
Table A.4 in the Appendix contains density data for such fluids as oil and
, 2.4: PROBLEM DEFINITION
Situation:
An engineer needs to know the local density for an experiment with a glid
z = 2500
2500 ft.
ft.
Find:
Calculate density using local conditions.
Compare calculated density with the value from Table A.2, and make a rec
dation.
Properties:
From Table A.2, R air = 287 kgJ· K , ρ = 1.22kg/
22kg/ m3 .
Local temperature = 74.3 F = 296.
◦
296.7 K.
Local pressure = 27.3 in.-Hg = 92.
92.45 kPa
kPa.
PLAN
Apply the ideal gas law for local conditions.
SOLUTION
Ideal gas law
p
ρ =
RT
92, 450N/ m2
92, 450N/
=
(287kg/ m3 )(296.
(287kg/ )(296.7 K)
= 1.086 kg/m3
ρ = 1.09 kg/m3 (local conditions)
Table value.
value. From Table
Table A.2
ρ = 1.22 kg/m3 (table value)
The density difference (local
(local conditions
conditions versus
versus table value)
value) is about 12%
12%
of this difference is due to the effect of elevation on atmospheric press
Recommendation—use the local value of density because the effects of
REVIEW
