Question
Fri January 28, 2011 By:

a plane is in level flight at constant speed and each wings of area 25M2. if the speed of the air is 50m/s over lower wings and 65m/s over upper wings,determine the mass of the plane(density of the air=1kg/M3)

Expert Reply
Sat January 29, 2011
Dear student,
 
The area of the wings of the plane, A = 2 × 25 = 50 m2

Speed of air over the lower wing, V1 = 180 km/h = 50 m/s

Speed of air over the upper wing, V2 = 234 km/h = 65 m/s

Density of air, ρ = 1 kg m–3

Pressure of air over the lower wing = P1

Pressure of air over the upper wing= P2
 
The upward force on the plane can be obtained using Bernoulli’s equation as:
 
P1+ 0.5 row V1^2 = P2 + 0.5 row V2 ^2
 
P1- P2 = 0.5 row( V2^2- V1^2)


The upward force (F) on the plane can be calculated as:
 
(P1-P2)*A = 43125N
 
Using Newton’s force equation, we can obtain the mass (m) of the plane as:

F =m g = 4400.51 kg
 
∼ 4400 kg

Hence, the mass of the plane is about 4400 kg.
Hope this helps.
Thanking you
Team
Topperlearning.com
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