JNTU B.Tech II LOW SPEED AERODYNAMICS Previous Question Paper (November/December - 2020 - R16)

The aerodynamic centre (AC) is the point about which the pitching moment coefficient is independent of the angle of attack. The pitching moment about the leading edge (LE) is given by M_LE = M_AC + L(X_AC). Differentiating with respect to the lift coefficient C_L:

Since M_AC is constant by definition, d(M_AC)/d(C_L) = 0. Substituting L = qScC_L, where q is dynamic pressure, S is planform area, and c is chord length:

Dividing by qSc² to express in coefficient form:

Thus, the position of the aerodynamic centre is defined as the rate of change of the leading-edge pitching moment coefficient with respect to the lift coefficient.

Dynamic similarity requires that two flow fields have identical flow patterns, which occurs when all dimensionless parameters governing the flow are equal. The primary governing parameters are the Reynolds number (Re = ρvL/μ), Mach number (M = v/a), and Froude number (Fr = v/√(gL)).

The statement is justified in low-speed aerodynamics because:

1. In incompressible flow, the Mach number effect is negligible (M < 0.3), effectively removing compressibility as a variable.
2. In most aerodynamic applications, gravitational effects are insignificant compared to inertial and viscous forces, rendering the Froude number irrelevant.
3. Consequently, the Reynolds number becomes the sole dominant ratio of inertial forces to viscous forces. If the Reynolds number is matched, the ratio of viscous to inertial effects remains identical between the model and the prototype, ensuring similar boundary layer development, separation characteristics, and wake structures.

Therefore, for low-speed, incompressible, and non-buoyant flows, the Reynolds number serves as the sufficient criterion for achieving dynamic similarity.