__Question 10.27__:^{2}. If the speed of the air is 180 km/h over the lower wing and 234 km/h over the upper wing surface, determine the plane’s mass. (Take air density to be 1 kg m

^{–3}).

__Solution__:*A*= 2 × 25 = 50 m

^{2}

Speed of air over the lower wing,

*V*

_{1}= 180 km/h = 50 m/s

Speed of air over the upper wing,

*V*

_{2}= 234 km/h = 65 m/s

Density of air,

*ρ*= 1 kg m

^{–3}

Pressure of air over the lower wing =

*P*

_{1}

Pressure of air over the upper wing=

*P*

_{2}

The upward force on the plane can be obtained using Bernoulli’s equation as:

P

_{1}+ (1/2)

*ρ*V

_{1}

^{2}= P

_{2}+ (1/2)

*ρ*V

_{2}

^{2}

P

_{1}- P

_{2}= (1/2)

*ρ*( V

_{2}

^{2}- V

_{1}

^{2}) .....(i)

The upward force (

*F*) on the plane can be calculated as:

(P

_{1}- P

_{2})A = (1/2)

*ρ*( V

_{2}

^{2}- V

_{1}

^{2}) A

= (1/2) X 1 X (65

^{2}- 50

^{2}) X 50

= 43125 N

Using Newton’s force equation, we can obtain the mass (

*m*) of the plane as:

F = mg

∴ m = 43125 / 9.8 = 4400.51 kg

∼ 4400 kg

Hence, the mass of the plane is about 4400 kg.

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