GATE_AE_2027_MOCK_04_Q47
GATE 2027 Aerospace Engineering All-India Master Mock 04 (Aerospace Structures, Thin-Walled Beams & Aeroelasticity)
NAT · 2 Marks
Flight Mechanics & Space Dynamics • Atmospheric Flight Mechanics • Level Flight, Thrust & Power Required
A twin-engine jet aircraft of mass m = 12000 kg flies in steady level flight at speed V = 150 m/s. The drag polar is C_D = 0.025 + 0.040 C_L^2. The wing area is S = 40 m^2 and air density is ho = 0.60 kg/m^3. Taking g = 9.81 m/s^2, what is the total drag force D in kilonewtons (kN)? (Round to two decimal places).
Answer Key:
9.05
Step-by-Step Verified Solution
### Solution: Weight W = 12000 * 9.81 = 117720 N. Dynamic pressure q_inf = 0.5 * ho * V^2 = 0.5 * 0.60 * (150)^2 = 0.30 * 22500 = 6750 Pa. Lift coefficient C_L = W / (q_inf * S) = 117720 / (6750 * 40) = 117720 / 270000 = 0.436. C_D = 0.025 + 0.040 * (0.436)^2 = 0.025 + 0.040 * 0.1901 = 0.025 + 0.0076 = 0.0326. Drag D = q_inf * S * C_D = 270000 * 0.0326 = 8802 N ≈ 8.80 kN. Let's verify with exact numbers: 270000 * (0.025 + 0.04*(117720/270000)^2) = 6750 + 270000 * 0.04 * 0.190099 = 6750 + 2053.07 = 8803 N ≈ 8.80 kN.