Fanno and Rayleigh line, when plotted on h-s plane, for same mass velocity G, intersect at 1 and 2.as shown in fig.

**Intersection
of Fanno and a Rayleigh Line **

Fanno and
Rayleigh line, when plotted on h-s plane, for same mass velocity G, intersect
at 1 and 2.as shown in fig. All states of Fanno line have same stagnation
temperature or stagnation enthalpy, and all states of Rayleigh line have same
stream thrust F / A. Therefore, 1 and 2 have identical values of G, h0 and F /
A. from 1 to 2 possible by a compression shock wave without violating Second
Law Thermodynamics. A shock is a sudden compression which increases the
pressure and entropy of the fluid but the velocity is decrease from supersonic
to subsonic.

A
change from states 2 to 1 from subsonic to supersonic flow is not possible in
view Second Law Thermodynamics. (Entropy can not decrease in a flow process)

3.The
pressure temperature and Mach no. of air in combustion chamber are 4 bar,100°C
and 0.2 respectively. The stagnation temperature of air in combustion chamber
is increased 3 times the initial value. Calculate:

1.
The mach no., pressure and temperature at
exit.

2.
Stagnation pressure

3.
Heat supplied per Kg of air

**Solution**

Refer isentropic flow table
for γ=1.4and m1=.2

**Tutorial Problems of Flow
Through Ducts:**

1.A
circular duct passes 8.25Kg/s of air at an exit Mach number of 0.5. The entry
pressure temperature are 3.45 bar and 38°C respectively and
the coefficient of friction 0.005.If the Mach number at entry is 0.15,
determine : I. The diameter of the duct,

II.
Length of the duct, III. Pressure and temperature at the exit, IV. Stagnation
pressure loss, and V. Verify the exit Mach number through exit velocity and
temperature.

2) A
gas (γ
=1.3,R=0.287 KJ/KgK) at p1 =1bar, T1 =400 k enters a 30cm diameter duct at a
Mach number of 2.0.A normal shock occurs at a Mach number of 1.5 and the exit
Mach number is1.0, If the mean value of the friction factor is 0.003 determine:

1)Lengths
of the duct upstream and downstream of the shock wave, 2)Mass flow rate of the
gas and downstream of the shock.

3) Air enters a long circular duct ( d =12.5cm,f=0.0045)
at a Mach number 0.5, pressure 3.0 bar and temperature 312 K.If the flow is
isothermal throughout the duct determine (a) the length of the duct required to
change the Mach number to 0.7,(b) pressure and temperature of air at M =0.7 (c)
the lengthof the duct required to attain limiting Mach number, and (d) state of
air at the limiting Mach umber.compare these values with those obtained in
adiabatic flow.

4.
Show that the upper and lower branches of a Fanno curve represent subsonic and
supersonic flows respectively . prove that at the maximum entropy point Mach
number is unity and all processes approach this point .How would the state of a
gas in a flow change from the supersonic to subsonic branch ? Flow in constant
area ducts with heat transfer(Rayleigh flow)

5)
The Mach number at the exit of a combustion chamber is 0.9. The ratio of
stagnation temperature at exit and entry is 3.74. If the pressure and
temperature of the gas at exit are 2.5 bar and 1000°C
respectively determine (a) Mach number, pressure and temperature of the gas at
entry, (b) the heat supplied per kg of the gas and (c) the maximum heat that
can be supplied. Take γ= 1.3, Cp= 1.218 KJ/KgK

6)
The conditions of a gas in a combuster at entry are: P1=0.343 bar ,T1 = 310K
,C1=60m/s.Detemine the Mach number ,pressure ,temperature and velocity at the
exit if the increase in stagnation enthalpy of the gas between entry and exit
is 1172.5KJ/Kg. Take Cp=1.005KJ/KgK, γ =1.4

7) A combustion chamber in a
gas turbine plant receives air at 350 K ,0.55bar and 75 m/s

.The
air –fuel
ratio is 29 and the calorific value of the fuel is 41.87 MJ/Kg .Taking γ=1.4
and R =0.287 KJ/kg K for the gas determine.

a)
The initial and final Mach numbers

b)Final pressure, temperature
and velocity of the gas

c)Percent stagnation pressure
loss in the combustion chamber, and

d)The maximum stagnation temperature attainable.

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