The wing of a jet plane is assumed to have the profile...

The wing of a jet plane is assumed to have the profile shown. It is traveling horizontally at $900 \mathrm{~m} / \mathrm{s}$, in air having a temperature of $8^{\circ} \mathrm{C}$ and absolute pressure of $85 \mathrm{kPa}$. Determine the pressure that acts on the top surface in front or to the right of the oblique shock at $A$ and in front or to the right of the expansion waves at $B$.

Key Concepts

Aerodynamic Pressure Distribution

Aerodynamic pressure distribution involves the variation of pressure over a body exposed to a flow field, which is crucial for understanding the forces exerted on the body. In high-speed flow regimes, pressure distribution is affected by phenomena like oblique shocks and expansion waves, which alter the local pressure and thereby impact the overall aerodynamic performance.

Oblique Shock Waves

Oblique shock waves occur when a supersonic flow encounters a surface that deflects the flow, resulting in a sudden and discontinuous change in flow properties, including pressure, temperature, and density. These shocks are inclined relative to the flow direction and are analyzed using conservation equations and shock relations which help in determining the downstream flow conditions after the shock.

Expansion Waves

Expansion waves, often described by Prandtl-Meyer expansion theory, arise when a supersonic flow undergoes a smooth, continuous divergence around a convex corner. This process results in an isentropic expansion where the pressure, temperature, and density decrease while the flow accelerates. The analysis of expansion waves relies on understanding the relation between the turning angle and the change in flow properties.

Compressible Flow

Compressible flow refers to the fluid dynamics regime where variations in fluid density are significant, typically occurring at high speeds, such as in supersonic flows. In this regime, the equations governing fluid motion must account for changes in density along with pressure and temperature, influencing phenomena like shock waves and expansion waves.

Mach Number

The Mach number is a dimensionless quantity that represents the ratio of the flow velocity to the local speed of sound. It is a critical parameter in compressible flow, determining whether the flow is subsonic, transonic, or supersonic, and directly influences the formation and characteristics of shock waves and expansion fans.

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