Question

The total area of wings of an aeroplane is 10mm. The speed of air above and below the wings is 140m/s and 110m/s. Then the force on the aeroplane by air is?
A) 48750 N
B) 48000 N
C) 95000 N
D) 50000

Answer 1

The density of air is given. The plane is in the air, so we can use Bernoulli’s equation. The atmospheric pressure is neglected. Bernoulli’s equation is applicable for an object moving through fluid.

Complete step by step solution: We are given with area and force is to be calculated. Force and area are related by the following equation:
$P = \dfrac{F}{A}$
Where $P$ is the pressure
$F$ is the force on the aeroplane
$A$ is the area of the wings
Now, in order to find the force, we will have to calculate the pressure.
Since the plane is in air, hence we can use Bernoulli’s theorem as follows:
${P_1} + \dfrac{1}{2}\rho \times {v_1}^2 + \rho g{h_1} = {P_2} + \dfrac{1}{2}\rho \times {v_2}^2 + \rho g{h_2}$
Where $P,{P_2}$ is the pressure on upper and lower sides of the wings respectively
${v_1},{v_2}$ is speed of air on upper and lower sides of the wings respectively
$\rho$ is the density of air
$g$ is the acceleration due to gravity
${h_1},{h_2}$ is the height of upper and lower side of wings from the surface of Earth
$\Rightarrow {P_1} - {P_2} = \dfrac{1}{2}\rho \times ({v_2}^2 - {v_1}^2) + \rho g({h_2} - {h_1})$
The difference in height of wings can be neglected, hence we have
$\Rightarrow {P_1} - {P_2} = \dfrac{1}{2}(1.28) \times (19600 - 12100) + 0$
$\Rightarrow {P_1} - {P_2} = 4800Pa$
Now we have the value of pressure and area of cross section, hence we can calculate the force on the wings due to air:
$P = \dfrac{F}{A}$
$\Rightarrow F = P \times A$
$\Rightarrow F = 4800 \times 10$
$\Rightarrow F = 48000N$
Therefore, the force on the aeroplane by the air is $48000N$

Option B is the correct option.

Note: In such types of questions, try to find a relation between the known quantities and the value which is asked. Firstly, understand the question and write down the given information. Be careful while multiplying with powers. Remember that the height difference will be zero.