[**515**] Among the
advantages of the turbofan are that, for a given energy addition per
unit time (fuel-flow rate), the turbofan will produce more thrust and
have a higher propulsive efficiency than will a turbojet with a gas
generator of the same size and level of technical sophistication as
the turbofan. These advantages can be explained by the following
highly simplified analysis of an idealized turbofan engine. Assume
the air that enters the inlet of the engine to have a free-stream
velocity of V_{i} and a uniform exhaust velocity from the fan and gas
generator of V_{e}. The mass flow entering the inlet per unit time is m.
The thrust produced by the engine can then be expressed by the
following simple relationship if the static pressure in the exhaust
is assumed to have the free-stream static value where the exhaust
velocity is measured and the momentum of the fuel itself is
neglected:

where T is the thrust.

The amount of energy added to the flow by the fuel may be expressed as the difference between the kinetic energy per unit time entering and exhausting from the engine and is given as follows:

or with the use of equation (E1),

[**516**] The propulsive
efficiency is defined as that fraction of the kinetic energy added to
the mass flow m that is usefully employed in propelling the aircraft.
The propulsive efficiency , can be expressed in the following form:

Substitution of equations (El) and (E3) for the thrust and kinetic energy gives

Equation (E3) clearly shows that for a given
thrust level, the required rate of energy input is reduced as the
value of [Delta] V/V_{i} is decreased. For a
given thrust level, equation (E1) shows that as the value of [Delta]
V is decreased, the mass-flow rate m must increase correspondingly.
The most thrust is therefore obtained for a given energy input rate
from the addition of a small velocity increment to a large mass-flow
rate; and the propulsive efficiency, given by equation (E5), is
increased as the value of [Delta] V is reduced. The turbofan engine
therefore provides higher efficiency and more thrust than a turbojet
engine with the same rate of energy input and having the same
component (compressor, burner, and turbine) efficiencies.