JNTU B.Tech III AERODYNAMICS II Previous Question Paper (August - 2022 - R13)

The effect of Mach number (M) on compressibility is characterized by the deviation of fluid behavior from the incompressible flow assumption. As M increases, the density changes within the flow field become significant, requiring the use of compressible flow equations.

For low Mach numbers (M < 0.3), the flow is considered incompressible, and the density variation is negligible. As M approaches 1.0, the compressibility effects become dominant, leading to the formation of shock waves and expansion fans. The relationship is governed by the pressure coefficient correction, such as the Prandtl-Glauert rule for subsonic flow:

This shows that as M increases, the pressure coefficient increases, indicating that compressibility magnifies the pressure effects on an aerodynamic body.

To find the highest possible velocity, we consider the isentropic expansion of air into a vacuum, where the internal energy is fully converted into kinetic energy. This corresponds to the maximum velocity (V_max) attained when the static temperature reaches absolute zero (T = 0 K).

Given the standard temperature T_0 = 15°C = 288.15 K, the gas constant for air R = 287 J/(kg·K), and the ratio of specific heats γ = 1.4, the maximum velocity is calculated using the energy equation:

Since Cp = (γ * R) / (γ - 1), we substitute the values:

Thus, the highest possible velocity is approximately 760.9 m/s.