Civil Engineering Reference
In-Depth Information
ξ
is the average of
ξ
, given by Equation (4.29), on the
where the mean density
cross-section:
ρ
0
P
0
p
−
ρ
0
T
0
ξ
=
τ
(4.40)
The expression for
K
can be rewritten with the use of Equation (4.35) as
P
0
K
=
(4.41)
ν
P
0
T
0
κ
ψ(x
1
,x
2
,B
2
ω)
1
−
Let
c
v
be the specific heat at constant volume. Making use of
ρ
0
(c
p
−
c
v
)
=
P
0
/T
0
which is valid for ideal gases, Equation (4.41) can be rewritten as
γP
0
K
=
(4.42)
1
) ψ(x
1
,x
2
,B
2
ω)
γ
−
(γ
−
ψ(x
1
,x
2
,ω)
by
F(ω)
where
γ
=
c
p
/c
v
. Denoting
ψ(x
1
,x
2
,ω)
=
F(ω)
(4.43)
ψ(x
1
,x
2
,B
2
ω)
can be written as
ψ(x
1
,x
2
,B
2
ω)
F(B
2
ω)
=
(4.44)
Equations (4.38) and (4.42) then become
ρ
=
ρ
o
/F(ω)
(4.45)
−
1
)F(B
2
ω)
]
K
=
γP
o
/
[
γ
−
(γ
(4.46)
For air at 18
◦
C with
P
o
10
5
4and
B
2
71 (Gray 1956).
For cylindrical tubes having circular cross-section,
F
is obtained from Equations
(4.18) and (4.45):
=
1
·
0132
×
Pa,
γ
=
1
·
=
0
·
1
−
J
1
(s
√
−
2
s
√
−
j)
F(ω)
=
J
o
(s
√
−
(4.47)
j
j)
The dependence of
F
on
ω
is given via Equation (4.16).
The bulk modulus
K
is obtained from Equation (4.46). It is equal to
γP
o
1
J
1
(Bs
√
−
2
Bs
√
−
j
j)
J
o
(Bs
√
−
j)
K
=
+
(γ
−
1
)
(4.48)
The bulk modulus for slits is obtained in the same way
K
=
γP
o
1
+
(γ
−
1
)
tanh
(Bs
√
j)
Bs
√
j
(4.49)
