Question

An airplane flies on a level path. There is a pressure difference of 587 Pa between the lower and upper surfaces of the wings. The area of each wing surface is about 100 m2. The air moves below the wings at a speed of 80.5 m/s.Estimate the air speed above the wings. Density of air is 1.29 kg/m3.

Answer 1

85.97 m/s

Explanation:

Bernoulli’s theorem is written as:

`P_1+(1)/(2)\cdot\rho\cdot v^2_1+\rho\cdot g\cdot h_1=P_2+(1)/(2)\cdot\rho\cdot v^2_2+\rho\cdot g\cdot h_2`

The potential energy is zero as the height is same, therefore:

`\begin{gathered} \rho\cdot g\cdot h=0 \\ P_1+(1)/(2)\cdot\rho\cdot v^2_1+0=P_2+(1)/(2)\cdot\rho\cdot v^2_2+0 \\ P_1+(1)/(2)\cdot\rho\cdot v^2_1=P_2+(1)/(2)\cdot\rho\cdot v^2_2 \\ \text{ we solve for }v_1\colon \\ (1)/(2)\cdot\rho\cdot v^2_1=P_2-P_1+(1)/(2)\cdot\rho\cdot v^2_2 \\ v^2_1=(2)/(\rho)\cdot(P_2-P_1)+(2)/(\rho)\cdot(1)/(2)\cdot\rho\cdot v^2_2 \\ v^2_1=(\Delta P)/(\rho)+v^2_2 \\ v_1=\sqrt[]{(2\Delta P)/(\rho)+v^2_2} \\ \text{ replacing the values:} \\ v_1=\sqrt[]{(2\cdot587)/(1.29)+80.5^2} \\ v_1=85.97\text{ m/s} \end{gathered}`

The air speed above the wings is 85.97 m/s