JNTU B.Tech IV BASICS OF AERONAUTICAL ENGINEERING Previous Question Paper (July/August - 2022 - R18)

The atmosphere is divided into layers based on temperature gradients, which directly influence pressure and density. According to the hydrostatic equation, the change in pressure with altitude is given by dP = -ρg dh, where pressure decreases as altitude increases. In the troposphere, temperature decreases linearly with altitude, leading to a rapid decline in both pressure and density. As altitude increases, the air becomes less dense because the weight of the overlying air column decreases. The relationship is governed by the ideal gas law, P = ρRT, where pressure and density are linked to the local temperature. At higher altitudes, such as in the stratosphere, the temperature gradient changes, causing the rate of pressure and density decay to differ from that in the lower atmosphere.

To find the ambient pressure at an altitude of 10,668 m (which corresponds to 35,000 ft), we use the International Standard Atmosphere (ISA) model. In the troposphere, the temperature decreases linearly with altitude at a lapse rate of 0.0065 K/m. The pressure at any altitude h in the troposphere is calculated using the formula:

Where:

• P₀ = 101,325 Pa (Sea level pressure)
• T₀ = 288.15 K (Sea level temperature)
• a = 0.0065 K/m (Lapse rate)
• g = 9.80665 m/s² (Acceleration due to gravity)
• R = 287.05 J/(kg·K) (Specific gas constant for air)

At h = 10,668 m, the temperature T is 288.15 - (0.0065 × 10,668) = 218.81 K. Substituting these values:

The ambient air pressure far ahead of the airplane is approximately 23,842 Pa or 23.84 kPa.