An airplane design calls for a "lift" due to the net force of the moving air on the wing of about 1000 N m⁻² of wing area. Assume that air flows past the wing of an air craft with streamline flow. If the speed of flow past the lower wing surface is 160 m s⁻¹, what is the required speed over the upper surface to give a "lift" of 1000 N m⁻²? The density of air is 1.29 Kg m⁻³ and assume maximum thickness of wing to be one meter.(Ans: 165 m s⁻¹)



Data Given:


Pressure at Wing area = P₁P₂   = 1000 N m⁻² 

Velocity at lower of the wing  = v₁ = 160 m s⁻¹

value of g = 9.8 m s⁻² 

Density of air = ⍴ = 1.29 kg m⁻³

Difference in height = h₂ - h₁ = 1 m 


To Find:


Velocity at top of the wing  = v = ?


Solution:


By using the formula Bernoulli's equation


P₁ + 12v₁² + ⍴gh₁ =  P₂ + 12v₂²⍴gh₂  

P₁ - P₂ + 12v₁²  + ⍴gh₁ ⍴gh₂   =   12v₂²

or

12v₂² = P₁ - P₂   + 12v₁² - ⍴g (h₂ - h₁)


By putting values

12 1.29 kg m⁻³ v₂² = 1000 N m⁻²  + 12x1.29 kg m⁻³  (160 m s⁻¹)² - 1.29 kg m⁻³ x9.8 m s⁻²  (1 m)

12 1.29 kg m⁻³ v₂² = 1000 N m⁻²  + 16512 kg m⁻¹ s² - 12.642  kg m⁻¹ s⁻²

or {kg m⁻¹ s⁻² = N m⁻²}

12 1.29 kg m⁻³ v₂² = 17499.358 N m⁻² 

v₂² = 217499.358Nm²1.29kgm³

v₂² = 27130.787 m² s⁻²

or

v₂ = 27130.787m²s²

v₂ = 164.72 m s⁻¹ 

v₂ = 165 m s⁻¹ -----------------Ans.





************************************

Shortcut Links For 


1. Website for School and College Level Physics   
2. Website for School and College Level Mathematics  
3. Website for Single National Curriculum Pakistan - All Subjects Notes 

© 2022-Onwards by Academic Skills and Knowledge (ASK    

Note:  Write me in the comment box below for any query and also Share this information with your class-fellows and friends.