Question

Consider the supersonic flow over an infinitely thin flat plate with length L = 1.1 m (pressures are constant on upper and lower surfaces), at a free stream velocity of 402 m/s and a free stream pressure of 101800 Pa. At an angle of attack of 13°, the pressure on the upper surface is 78044 Pa, while the pressure on the lower surface is 119617 Pa. Find the moment coefficient at the quarter chord location. Give the answer to three decimal places. (Assume air density = 1.225 kg/m³)

Cₘ,/₄ = _______

Answer 1

To find the moment coefficient at the quarter chord location of the supersonic flow over a flat plate, use the equation Cₘ,/₄ = (P_upper - P_lower) / (0.5 * ρ * V² * c), where P_upper is the pressure on the upper surface, P_lower is the pressure on the lower surface, ρ is the air density, V is the free stream velocity, and c is the chord length.

Step-by-step explanation:

To find the moment coefficient at the quarter chord location, we can use the equation:

Cₘ,/₄ = (P_upper - P_lower) / (0.5 * ρ * V² * c)

Where:

• Cₘ,/₄ is the moment coefficient at the quarter chord location
• P_upper is the pressure on the upper surface of the flat plate
• P_lower is the pressure on the lower surface of the flat plate
• ρ is the air density
• V is the free stream velocity
• c is the chord length

Plugging in the given values, we get:

Cₘ,/₄ = (78044 - 119617) / (0.5 * 1.225 * 402² * 1.1)

Calculating this expression will give us the moment coefficient at the quarter chord location.