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Question: -In a wind tunnel experiment, the pressures on the upper and lower surfaces of the wings are \[0.90{...

-In a wind tunnel experiment, the pressures on the upper and lower surfaces of the wings are 0.90x105  Pa0.90{\rm{ }}x{10^5}\;{\rm{Pa}} and 0.91x105  Pa0.91{\rm{ }}x{10^5}\;{\rm{Pa}} respectively. If the area of the wing is 40m240{\rm{ }}{{\rm{m}}^{\rm{2}}} the net lifting force on the wing is
A. 2×104  N2 \times {10^4}\;{\rm{N}}
B. 4×104  N4 \times {10^4}\;{\rm{N}}
C. 6×104  N6 \times {10^4}\;{\rm{N}}
D. 8×104  N8 \times {10^4}\;{\rm{N}}

Explanation

Solution

This question is based on the lift. We know that the lift of any object and the airplane is due to Bernoulli’s theorem. Bernoulli’s theorem states that when the pressure of the fluid flowing inside the narrow section increases, the velocity decreases. It is the addition of all the energies present in the fluid under steady-state conditions. When the object is in the air, then the pressure on the upper surface is higher than the pressure on the lower surface of the airplane.

Complete step by step answer:
Given: The pressure on the lower surface is P1=0.90×105  Pa{P_1} = 0.90 \times {10^5}\;{\rm{Pa}} , the pressure on the upper surface is P2=0.91×105  Pa{P_2} = 0.91 \times {10^5}\;{\rm{Pa}} and the area of the wing is A=40  m2A = 40\;{{\rm{m}}^{\rm{2}}}.

To find the net lifting force, we use the given formula,
F=(P2−P1)×AF = \left( {{P_2} - {P_1}} \right) \times A

As, we know that the lift of any object is due to the difference in the pressure. On the upper surface the velocity is less, while on the lower surface the velocity is more.

To find the lift of the object the area is also responsible for it. So, the lifting force becomes equal to the pressure difference and area.
Therefore,
F=(P2−P1)×AF = \left( {{P_2} - {P_1}} \right) \times A
Now, substitute the values in the above equation we get,
F=(0.91×105  Pa−0.90×105  Pa)×40  m2   ⟹  F=4×104  N F = \left( {0.91 \times {{10}^5}\;{\rm{Pa}} - 0.90 \times {{10}^5}\;{\rm{Pa}}} \right) \times 40\;{{\rm{m}}^{\rm{2}}}\\\ \implies F = 4 \times {10^4}\;{\rm{N}}
Therefore, from the above results, the net lifting force is 4×104  N4 \times {10^4}\;{\rm{N}}.

Thus, from the given options, the correct option is (B).

Note:
In this question, students must have the knowledge of Bernoulli's theorem. Bernoulli's principle is also applicable on fluids. When the fluid is incompressible, irrotational and non-viscous. The total energy at any point in the fluid remains constant.