** EFFICIENCY
**Efficiency
is an expression of the degree of perfection.

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}
**
**

**Thermal Efficiency **is the ratio of the ** rate
of addition of kinetic energy to the working fluid** to the

**in the form of heat of reaction of the fuel.**

*rate of addition of heat*For
a single-flow jet engine (only one exhaust),
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}

For a shaft-powered
engine,
* _{
}*where

_{ }is the shaft power.

**Propulsive Efficiency** is the ratio of ** thrust
power** to the rate of addition
of kinetic energy.

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f
we ignore the pressure thrust term, and assume that f is very much smaller than
1,
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}

**Overall efficiency **is the product of these two
efficiencies.

*Note:
*

*1. Thermal efficiency depends on*

*a) thermodynamic cycle*

*b) combustion efficiency (how much of the heat is really released?)*

*2. Propulsive efficiency depends on how close the exit velocity is to the flight velocity. We can easily show that this efficiency reaches 1.0 when the two velocities are equal, but then the thrust is zero. To get a given thrust with high propulsive efficiency, it is thus better to accelerate a large mass flow rate through a small velocity increment, than to accelerate a small mass flow rate through a large velocity increment.*