First slide

Fluid dynamics

Question

The speeds of air-flow on the upper and lower surfaces of a wing of an aeroplane are v₁ and v₂ respectively. If A is the cross-sectional area of the wing and 'p' is the density of air,
then the upward lift is :

Easy

A

$\frac{1}{2} ρA (v_{1} - v_{2})$
B

$\frac{1}{2} ρA (v_{1} + v_{2})$
C

$\frac{1}{2} ρA (v_{1}^{2} - v_{2}^{2})$
D

$\frac{1}{2} ρA (v_{1}^{2} + v_{2}^{2})$

Solution

$P_{1} + \frac{1}{2} {ρv}_{1}^{2} = P_{2} + \frac{1}{2} {ρv}_{2}^{2} \Rightarrow ∆ P = P_{2} - P_{1} = \frac{1}{2} ρ (v_{1}^{2} - v_{2}^{2})$
Upward lift $= ∆ P \times A = \frac{1}{2} ρA (v_{1}^{2} - v_{2}^{2})$

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