Question

The velocity of air over the upper surface of the wing of an aeroplane is $40m/s$ and that on the lower surface is $30m/s$. If the area of the wing is $5{{m}^{2}}$ and the mass of the wing is 300 kg, the net force acting on the wing is (Density of air = $1.3kg/{{m}^{3}}\,and\,g=10m/{{8}^{2}}$)
(A) 725N upward
(B) 725N downward
(C) 2275N upward
(D) 2275N downward

Answer 1

Hint: To answer this question we should know that the simplified form of Bernoulli's equation can be summarized in the following memorable word equation: static pressure + dynamic pressure = total pressure. Every point in a steadily flowing fluid, regardless of the fluid speed at that point, has its own unique static pressure p and dynamic pressure q. Bernoulli's principle relates the pressure of a fluid to its elevation and its speed. Bernoulli's equation can be used to approximate these parameters in water, air or any fluid that has very low viscosity. Using this concept we have to solve this question.

Complete step-by step answer:
Let us consider the wing to be of negligible height.
So, from Bernoulli’s equation we can write that;
We can simply apply Bernoulli's Equation between inlet and outlet points and calculate the unknown pressure assuming that the change in elevation is zero. In this example there is no change in elevation. The converging nozzle causes fluid to accelerate.
Pressure develop across top and bottom of the wing is given as,
$P=\dfrac{1}{2}P\left( P_{1}^{2}-V_{2}^{2} \right)\,$
$=\dfrac{1}{2}\times 1.3\times \left( {{40}^{2}}-{{30}^{2}} \right)=455\,Pa$
This pressure provides an up thrust F of,
$F=P\times A=455\times 5=2275N\left[ A:Area\,of\,wing \right]$
Thus, Net force on the wing is given as,
$N=mg-F$
$=300\times 10-2275$
$\Rightarrow N=725N$

Hence, the correct answer is Option A.

Note: We should know that Bernoulli's principle is then cited to conclude that since the air moves slower along the bottom of the wing, the air pressure must be higher, pushing the wing up. However, there is no physical principle that requires equal transit time and experimental results show that this assumption is false. An example of Bernoulli's principle is the wing of an airplane; the shape of the wing causes air to travel for a longer period on top of the wing, causing air to travel faster, reducing the air pressure and creating lift, as compared to the distance travelled, the air speed and the air pressure that is experienced.