Question

A plane is in level flight at constant speed and each of its two wings has an area of 25 m². 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).

Answer 1

Given:

Area of the two wings =25  m 2

Speed of the air over the lower wing =180  km/h

Speed of the air over the upper wing =234  km/h

Let mass of the plane be m kg

Here,

Lower wing has speed of air as υ 1 =180  km/h =180× 5 18 =50 m/s

Speed over upper wing is υ 2 =234  km/h =234× 5 18 =65 m/s .

The pressure difference between the wings is,

P d = P 1 − P 2 P d = 1 2 ρ( υ 2 2 − υ 1 2 )

Substitute the values.

P d = 1 2 ×1×( 65 2 − 50 2 ) P d =862.5 Pa

Net upward force is,

F= P d A mg= P d A m= P d A g

Here,

A=area of whole wings =2×25=50  m 2

Then,

m= 862.5×50 9.8 m=4400 kg

Hence, the mass of the plane is 4400 kg.