A subsonic aerofoil section has

PHYSICS · Subjective · Fermi University Physics · Fluids & Continuum Physics · Waves, acoustics and compressible flow · Waves, acoustics and compressible flow

Signal Speeds in Fluids, Ch Steady compressible flow: energy, stagnation and the Mach number

Problem

A subsonic aerofoil section has, at low speed (Mach number effectively zero), a minimum pressure coefficient Cp,min⁡=−0.35C_{p,\min}=-0.35. Using the Prandtl-Glauert rule Cp=Cp01−M∞2C_p=\frac{C_{p0}}{\sqrt{1-M_\infty^2}} and the sonic pressure coefficient Cp∗(M∞)=2γM∞2[(2+(γ−1)M∞2γ+1)γ/(γ−1)−1]C_p^*(M_\infty)=\frac{2}{\gamma M_\infty^2}\left[\left(\frac{2+(\gamma-1)M_\infty^2}{\gamma+1}\right)^{\gamma/(\gamma-1)}-1\right] with γ=1.4\gamma=1.4, find the critical free-stream Mach number McritM_{\rm crit} at which sonic flow first appears on the aerofoil, i.e. the root of Cp,min⁡1−M∞2=Cp∗(M∞),\frac{C_{p,\min}}{\sqrt{1-M_\infty^2}}=C_p^*(M_\infty), to two significant figures, by evaluating both sides at a few trial Mach numbers.

Browse the problem library