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 = P₁- P₂ = 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 = v₂ = ?
Solution:
By using the formula Bernoulli's equation
P₁ + ⍴v₁² + ⍴gh₁ = P₂ + ⍴v₂² + ⍴gh₂
P₁ - P₂ + ⍴v₁² + ⍴gh₁ - ⍴gh₂ = ⍴v₂²
or
⍴v₂² = P₁ - P₂ + ⍴ v₁² - ⍴g (h₂ - h₁)
By putting values
x1.29 kg m⁻³ xv₂² = 1000 N m⁻² + x1.29 kg m⁻³ x (160 m s⁻¹)² - 1.29 kg m⁻³ x9.8 m s⁻² (1 m)
x1.29 kg m⁻³ xv₂² = 1000 N m⁻² + 16512 kg m⁻¹ s⁻² - 12.642 kg m⁻¹ s⁻²
or {kg m⁻¹ s⁻² = N m⁻²}
x1.29 kg m⁻³ xv₂² = 17499.358 N m⁻²
v₂² =
v₂² = 27130.787 m² s⁻²
or
v₂ =
v₂ = 164.72 m s⁻¹
v₂ = 165 m s⁻¹ -----------------Ans.
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