Consider supersonic airflow through a 12-cmdiameter adiabatic duct with inlet conditions of T₁ = 500 K, P₁ = 80 kPa, and Ma₁ = 3. Taking the average friction factor to be 0.03, determine the duct length required to decelerate the flow to a Mach number of unity. Also, calculate the duct length at Mach number intervals of 0.25, and plot the duct length against the Mach number for 1 ≤ Ma ≤ 3. Discuss the results.