Flow in a constant area duct with friction and without heat transfers is described by a curve is known as Fanno line or Fanno curve.

**Fanno line or Fanno curve
(Governing equation)**

Flow in a constant area duct with friction and without
heat transfers is described by a curve is known as Fanno line or Fanno curve.

Weknow
that,

From continuity equation,

Density ρ is a function of entropy and enthalpy.

Substitute the value for ρinthe equation for ‘h’

The above equation can be used to show a fanno-line in
h-s diagram.

In
the line

Ø Point
F is the sonic point

Ø Point
lying below are super sonic points

Ø Points
lying above are subsonic flow

Since entropy can only increase the processes that happen
will always coverage to the sonic point F.The curve consists of two branches AF
and FB. At point F the flow is sonic i,e, M=1

The flow A to F is subsonic
(M<1) and B to F is Supersonic (M>1 )

In subsonic flow region (A to F), the effect of friction
will increase the velocity and Mach number and to decrease the enthalpy and
pressure of the gas.

In supersonic flow region (B to F), the effect of
friction will decrease the velocity and Mach number and to increase the
enthalpy and pressure of the gas.

We know by the second law o thermodynamics that for an
adiabatic flow, the entropy may increase but cannot decrease. So the processes
in the direction F to A and F to B are not possible because they lead to decrease
in entropy.

Fanno curves are drawn for different vales of mass flow
density (G).When G increases, the velocity increases and pressure decreases in
the sub sonic region. When G increases, the pressure increases and velocity
decreases in the super sonic region

**Important features of Fanno curve**

From the second law of
thermodynamics, the entropy of the adiabatic flow increases but not decreases.
Thus, the path of states along the Fanno curve must be toward the right.

In the
subsonic region, the effects of
friction will be to increase
the velocity and Mach number and to
decrease the enthalpy and pressure
of the stream .

In the supersonic region, the
effects of friction will be to decrease the velocity andMach number and to
increase the enthalpy and pressure of the stream.

A subsonic flow can never
become supersonic, due to the
limitation of second law of thermodynamics, but in can approach to sonic
i.e,M=1.

A supersonic
flow can never become subsonic,
unless a discontinuity (shock)is present.

In the case of isentropic
stagnation, pressure is reduced whether the flow is subsonic or supersonic.

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

Mechanical : Gas Dynamics and Jet Propulsion : Flow Through Ducts : Fanno line or Fanno curve (Governing equation) |

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