Flow Past Immersed Bodies MCQ with answer and solution

Concept

Lift force on a body in a moving fluid depends on the lift coefficient, the area, the fluid density and the square of the velocity.

Formula

F_L = C_L × A × ρ × V² / 2, ρ = w / g

Step-by-step solution

1. Density of air: ρ = w/g = 11.3/9.81 = 1.152 kg/m³ 2. Velocity: V = 45 km/h = 45 × 1000/3600 = 12.5 m/s 3. Area: A = 1.5 × 1.5 = 2.25 m² 4. F_L = C_L × A × ρ × V² / 2 = 0.75 × 2.25 × 1.152 × 12.5² / 2 5. F_L = 0.75 × 2.25 × 1.152 × 156.25 / 2 = 151.9 N

Explanation

Lift force is found from the lift equation F_L = C_L A ρ V²/2. First change the specific weight into density by dividing by g, and change the speed from km/h to m/s. Putting in the values gives about 151.9 N.

Why the other options are wrong

A (120.4 N): wrong value, maybe from a calculation slip. C (180.4 N): this is close to ρV² (about 180), so the area, C_L and 1/2 were not applied correctly. D (225.9 N): wrong value, likely from using specific weight or the speed wrongly.

Shortcut

Divide km/h by 3.6 to get m/s. Then F_L = 0.5 × 0.75 × 2.25 × (11.3/9.81) × 12.5².

Common mistake

Using specific weight (11.3 N/m³) directly as density, or not changing km/h to m/s.