Jawaharlal Nehru Technological University Hyderabad B.Tech II AERODYNAMICS I Previous Question Paper (November/December - 2020 - R13)

To determine the lift coefficient, we first identify the given parameters and convert them into SI units:

Weight (W) = 20,000 N

Pressure (P) = 45,000 Pa

Temperature (T) = 0°C = 273.15 K

Velocity (V) = 400 km/h = 400 * (1000 / 3600) = 111.11 m/s

Span (b) = 10 m

Mean chord (c) = 1.5 m

Wing Area (S) = b * c = 10 * 1.5 = 15 m²

First, calculate the air density (ρ) using the ideal gas law, where R = 287 J/(kg·K):

In level flight, the lift (L) is equal to the weight (W):

The lift coefficient (C_L) is defined by the lift equation:

Rearranging to solve for C_L:

Substituting the values:

The lift coefficient for the aircraft is approximately 0.3765.

The aerodynamic force F acting on a body in a fluid flow depends on the characteristic length l, fluid density ρ, flow velocity V, fluid viscosity μ, and the speed of sound a. Mathematically, F = f(l, ρ, V, μ, a).

Using the Buckingham Pi theorem, we identify the number of variables n = 6 and the number of fundamental dimensions m = 3 (Mass M, Length L, Time T). This results in n - m = 3 dimensionless pi groups.

Choosing ρ, V, and l as repeating variables, we derive the following groups:

The functional relationship is expressed as π₁ = φ(π₂, π₃), which leads to the general aerodynamic force equation:

Assumptions:

• The fluid is a continuum.
• The flow is steady and the body is rigid.
• The gravitational and surface tension forces are negligible compared to inertial, viscous, and compressibility forces.
• The geometric shape of the body is constant, meaning the force coefficient is a function only of the dimensionless parameters Re and M.