Problem 1.8:
The engine of a small jet aircraft develops a thrust of
kN
when the aircraft is flying at a speed of
km/h
at an altitude where the ambient pressure is
kPa.
The air flow rate through the engine is
kg/s
and the engine uses fuel at a rate of
kg/s.
The pressure on the engine discharge plane is
kPa
and the area of the engine exit is
m2.
Find the jet efflux velocity.
Solution:
Given:
Thrust =
,
fuel rate =
Inlet
,
,
.
Outlet
,
,
\( V_{2}=?\,\text{m/s} \).
The schematic diagram of the problem description is shown in Fig. 1.
Using the mass conservation equation,
$$ \dot{m}_{2}=\dot{m}_{1}+\dot{m}_{\text{fuel}} $$Using the conservation of momentum along horizontal direction,
$$ \begin{aligned} \text{Thrust} =&\ \text{rate of momentum exiting }-\text{ rate of momentum entering}\\ & +\text{ pressure force at exit }-\text{ pressure force at inlet}\\ \\ \text{Thrust} =&\ \dot{m}_{2}V_{2}-\dot{m}_{1}V_{1}+\left(p_{2}-p_{1}\right)A_{\text{exit}} \end{aligned} $$