__Question 10.14__:^{–1}and 63 m s

^{–1}respectively. What is the lift on the wing if its area is 2.5 m

^{2}? Take the density of air to be 1.3 kg m

^{–3}.

__Solution__:*V*

_{1}= 70 m/s

Speed of wind on the lower surface of the wing,

*V*

_{2}= 63 m/s

Area of the wing,

*A*= 2.5 m

^{2}

Density of air,

*ρ*= 1.3 kg m

^{–3}

According to Bernoulli’s theorem, we have the relation:

P

_{1 }+ (1/2)

*ρ*V

_{1}

^{2}= P

_{2 }+ (1/2)

*ρ*V

_{2}

^{2}

P

_{2}- P

_{1}= (1/2)

*ρ*(V

_{1}

^{2}- V

_{2}

^{2})

Where,

*P*

_{1}= Pressure on the upper surface of the wing

*P*

_{2}= Pressure on the lower surface of the wing

The pressure difference between the upper and lower surfaces of the wing provides lift to the aeroplane.

Lift on the wing = (P

_{2}- P

_{1}) A

= (1/2)

*ρ*(V

_{1}

^{2}- V

_{2}

^{2}) A

= (1/2) X 1.3 X [ 70

^{2}- 63

^{2}] X 2.5

= 1512.87 N = 1.51 X 10

^{3}N

Therefore, the lift on the wing of the aeroplane is 1.51 × 10

^{3}N.

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