First slide

Fluid dynamics

Question

The flow speeds of air on the lower and upper surfaces of the wing of an aeroplane are v and $\sqrt{2}$ v respectively. The density of air is p and surface area of wing is A. The dynamic lift on the wing is

Moderate

A

${ρv}^{2} A$
B

$\sqrt{2} {ρv}^{2} A$
C

$(1 / 2) {ρv}^{2} A$
D

$2 {ρv}^{2} A$

Solution

According to Bernoulli's theorem
$P_{1} + \frac{1}{2} {ρv}_{1}^{2} = P_{2} + \frac{1}{2} {ρv}_{2}^{2} Given that v_{1} = \sqrt{2} v and v_{2} = v P_{1} + \frac{1}{2} ρ (2 v^{2}) = P_{2} + \frac{1}{2} {ρv}^{2} ∴ (P_{2} - P_{1}) = {ρv}^{2} / 2 Now, force of dynamic lift = Pressure difference x surface area of wing = (P_{2} - P_{1}) \times A = \frac{1}{2} {ρv}^{2} A$

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