Example 112
Derive the following expression for the efficiency of the
Diesel cycle in terms of the compression ratio,
r
v
, and the
cutoff ratio,
r
c
()
1
1
1
1
1
k
c
cycle
k
vc
r
rk
r
η
−
⎡⎤
−
=−
⎢⎥
−
⎣⎦
Solution:
Start with this expression for the cycle efficiency:
4
1
1
3
2
2
1
1
1
cycle
T
T
T
T
kT
T
⎛⎞
−
⎜⎟
⎝⎠
−
eq (1)
For the two adiabatic processes in the Diesel cycle
1
12
21
k
TV
−
=
1
3
4
34
k
V
T
−
=
But
14
VV
=
23
P
P
=
2
22
mRT
PV
M
=
3
33
mRT
M
=
2
2
3
3
P
Vm
R
TT
P
R
==
VT
=
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33
22
C
TV
r
==
eq. (2)
1
3
4
4
3
1
1
2
2
1
k
k
V
T
V
T
T
V
T
V
−
−
⎛⎞
⎜⎟
⎝⎠
=
but
14
VV
=
1
1
3
42
13
4
k
k
C
V
TT
r
V
−
−
11
3
4
12
kk
k
CC
T
T
rr
−−
=
eq. (3)
Finally
1
21
k
−
=
1
2
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 Spring '08
 Kaminski

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