In the static test of a jet engine and exhaust nozzle...

In the static test of a jet engine and exhaust nozzle assembly, air is sucked into the engine at the rate of $30 \mathrm{kg} / \mathrm{s}$ and fuel is burned at the rate of $1.6 \mathrm{kg} / \mathrm{s}$ The flow area, static pressure, and axial-flow velocity for the three sections shown are as follows: $$\begin{array}{lccc} & \text { Sec. } A & \text { Sec. } B & \text { Sec. } C \\ \text { Flow area, } \mathrm{m}^{2} & 0.15 & 0.16 & 0.06 \\ \text { Static pressure, } \mathrm{kPa} & -14 & 140 & 14 \\ \text { Axial-flow velocity, } \mathrm{m} / \mathrm{s} & 120 & 315 & 600 \end{array}$$ Determine the tension $T$ in the diagonal member of the supporting test stand and calculate the force $F$ exerted on the nozzle flange at $B$ by the bolts and gasket to hold the nozzle to the engine housing.

In the static test of a jet engine and exhaust nozzle assembly, air is sucked into the engine at the rate of $30 \mathrm{kg} / \mathrm{s}$ and fuel is burned at the rate of $1.6 \mathrm{kg} / \mathrm{s}$ The flow area, static pressure, and axial-flow velocity for the three sections shown are as follows:
$$\begin{array}{lccc}
& \text { Sec. } A & \text { Sec. } B & \text { Sec. } C \\
\text { Flow area, } \mathrm{m}^{2} & 0.15 & 0.16 & 0.06 \\
\text { Static pressure, } \mathrm{kPa} & -14 & 140 & 14 \\
\text { Axial-flow velocity, } \mathrm{m} / \mathrm{s} & 120 & 315 & 600
\end{array}$$
Determine the tension $T$ in the diagonal member of the supporting test stand and calculate the force $F$ exerted on the nozzle flange at $B$ by the bolts and gasket to hold the nozzle to the engine housing.

Key Concepts

Control Volume Analysis

This concept involves selecting a region in space (the control volume) through which fluid flows, allowing us to account for the mass, momentum, and energy exchanges between the fluid and its surroundings. In engine testing, a control volume is applied to determine the net forces acting on the assembly by analyzing the inflow and outflow of mass and momentum across the boundaries.

Momentum Conservation

Momentum conservation is the fundamental principle stating that the rate of change of momentum within a control volume is equal to the net external force acting on that volume. In the context of a jet engine test, applying this principle helps in analyzing the changes in the momentum flux due to the different sectional velocities and mass flow rates, which in turn are used to compute reaction forces such as the tension in support members.

Pressure Force Calculation

Pressure forces arise from differences in static pressure acting over an area. By integrating the static pressure over the surfaces of a component, one can determine the net force exerted by the fluid. This is crucial in assessing the force on structural components like the nozzle flange, where the pressure differences across the areas lead to a net reaction force that must be balanced by bolts or gaskets.

Force Equilibrium Analysis

Force equilibrium analysis involves summing all the forces acting on a system and setting this sum equal to zero, as required by Newton’s laws for a system in steady state. In static testing, the support structure must counteract the aerodynamic and pressure-induced forces. Understanding this concept is essential for determining the required tension in the diagonal test stand member as well as the forces transferred to the engine housing components.

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