First slide

Fluid dynamics

Question

When an aircraft is flying, let V₁ be the speed of air just below the wings and V₂ be the speed of air just above the wing. Then

Moderate

A

V₁ > V₂
B

V₁ = V₂
C

V₁ < V₂
D

if the density of air is very low, then V₂ > V₁

Solution

Applying Bernoulli's equation between points 1 and 2, we can write, $p_{1} + \frac{1}{2} {ρv}_{1}^{2} = p_{2} + \frac{1}{2} {ρv}_{2}^{2}$
$\Rightarrow p_{1} - p_{2} = \frac{1}{2} ρ (v_{2}^{2} - v_{1}^{2})$
If A be the area of each wing, then total lift on the wings, $L = 2 A \times (p_{1} - p_{2}) = Aρ (v_{2}^{2} - v_{1}^{2})$
Air craft can fly only when $L > 0 i . e . V_{2} > V_{1}$

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