1V, = 1961 J Since the compressor is single acting, Nw = N = 200 and B
= 6540 W
178
12.4
Minimum work for multistage compression Minimum work required for a two stage compressor with
complete intercoo
Now,
041
1
2
1
1 2 12 . vr v v T T = =
= 2.7
i.e., T2 = 2.7
x
288 = 778 K At constant pressure from 2 to 3, since pv = RT for a perfect gas, then
2
3
2
3
vv
TT
=
i.e., 1 765 778 1373 2 3 . v v = Ther
1
2 = = p r p p T T T T where rp is the pressure ratio, p2/p 1. i.e. ( ) 1/ 34 = pTrT
and ( ) 1/ 21 = pTrT
B
T2
A
T4
1
2
3
s
4
T
p1
1
23
v
4
p
p2 T 3
T1
p2
p1
Heat rejected
Cooler
Heat supplied
Compre
= = 6.8
Also,
04
1
3
4
4 3 68 . . v v
TT
=
=
= 2.153
i.e.,
2 153 1373
4
. T = = 638 K Heat input, per kg of air, is Q1 = cp(T3 T2) = 1.005(1373 778) = 598 kJ/kg
Heat rejected, per kg of air, is Q2 =
1
23
v
4
p
v2 v1
p3 = p 2
110
Heat supplied, Q1 = c p(T 3 T2) Heat rejected, Q 2 = c v(T 4 T1) There is no heat flow in processes
1-2 and 3-4 since they are isentropic.
By substituting in the equation
Various cylinder arrangements (in-line, Vee, radial, flat, etc.) are used but we shall analyse the simple
in-line arrangement.
Force in con-rod =
MECHANICAL ACTION (static, frictionless) Force on pist
Characteristics of power cycles
The working fluid is a condensable vapour which is in liquid phase during part of the cycle
The cycle consists of a succession of steady-flow processes, with each proce
Gross work output is Work output 4 to 1 + work output 1 to 2
Now, for an isothermal process, Q + W = 0 i.e. W4-1 = Q 4-1 = area under the line 4-1 on Fig (a) =
( s1 s4)
x T1 = 0.214
x
1073 = 229.6 kJ/
987 515 1. 30 54 049 5151. 30 88 += = 3247 kJ/kg of C 2H6
Example 10.10 When all the products of the gaseous hydrocarbon fuel C 2H6 are in the gaseous
phase, the enthalpy of combustion at 25 oC is 475
INTERNAL COMBUSTION (IC) ENGINES
An IC engine is one in which the heat transfer to the working fluid occurs within the engine itself,
usually by the combustion of fuel with the oxygen of air. In exter
Carnot cycle
It consists of two reversible isothermal processes at T a and T b respectively, connected by two
reversible adiabatic (isentropic) processes.
When the working fluid is a condensable vapou
i.e., p2 = 57.2
x
1.01 = 57.8 bar
Then substituting,
578 69 931
3
.
T
= = 1112 K
Now the heat added at constant volume is equal to the heat added at constant pressure in this
example, therefore cv(T3
The DUAL cycle approximates to the processes within a modern high speed diesel engine.
In petrol engines, and large slow speed (< 500 RPM) diesels, the pressure rise because of combustion
is comparati
Supplementary Problems
10.1 A sample of bituminous coal gave the following ultimate analysis by mass: C 81.9%; H 4.9%; O
6%; N 2.3%; and ash 4.9%. Calculate: (a) The stoichiometric A/F ratio (b) The a
For the throttling process, 11-12, h11 = h 12 = 429 kJ/kg The enthalpy of the compressed liquid in the
feed line is approximately equal to that of saturated liquid at the same temperature. Thus h6 = h
o
In the diesel or oil engine, the oil is sprayed under pressure into the compressed air at the end of the
compression stroke, and the combustion is spontaneous due to the high temperature of the air
( ) ( ) [ ] 1 11 1
1
+
=
pvp
p
rrr
r
(8.9)
Thus the thermal efficiency of a dual-combustion cycle depends not only on the compression ratio
but also on the relative amounts of heat supplied at const
Both of these reactions can take place simultaneously in the same combustion process. The
proportions of the constituents adjust themselves to satisfy the equilibrium conditions and their
actual value
Solution The ideal cycle is shown below on a T-s diagram.
From Eq. (8.3)
) /( pr 1 1
1 =
14411
6 12 1 02
1
.) /(.
.
= = 0.401
The net work output of the cycle is given by the work output of the turbi
T1 1
23
s
4
T
D
P1
C
p4
1
2
3
v
4
p
p2
P3
102
1.
The pressure of the gas changes continuously from p 4 to p 1 during the isothermal heat supply and
from p2 to p3 during the isothermal heat rejection.
Pi
i
Mm
M m RTU vapH vap += 0000 ()()
=
+
32 3.41
44 3.15
18 1.26 .153145 2988.43987 = 43900 kJ/kg
Example 10.13 A combustible mixture of carbon monoxide and air which is 10% rich is compressed to
a p
Ratio of cylinder diameters For a single acting two stage reciprocating air compressor with complete
intercooling, the ratio of cylinder diameters is <- <+(F -*) where D1 = diameter of LP cylinder and
8.67 = 0.07 kg. (e) The water vapour in the gaseous products can be found from a hydrogen balance.
Basis: 1 kg of fuel H2O entering with air = 0.07 kg H2O in the fuel = 0.10 kg H2O from the combustion
04
1
2
1
1 2 18 . v v T T = =
= 3.18
i.e., T2 = 3.18
x
T1 = 3.18 x (20 + 273) = 931 K From 2 to 3 the process is at constant volume, hence
2
3
2
3
TT
pp
= since
2
22
3
33
T pv
T pv
= and v3 = v2
i.e.
The feed pump delivers water to the boiler. The pressure inside a boiler is high and so the pressure of
the feed water has to be increased accordingly before it is made to enter the boiler. Generally,