First slide

Fluid dynamics

Question

The speed of flow past the lower surface of a wing of an aeroplane is 50 ${ms}^{- 1}$ . What speed of flow over the upper surface will-give a dynamic lift of 1000 Pa? Density of air = 1.3 kg $m^{3}$ .

Moderate

A

25.55 m/s
B

63.55 m/s
C

13.25 m/s
D

None

Solution

Applying Bernoulli's theorem to the lower and upper surface of a wing.
$P_{1} + \frac{1}{2} {ρv}^{2}_{1} = P_{2} + \frac{1}{2} {ρv}^{2}_{2}$
or $P_{1} - P_{2} = \frac{1}{2} ρ ({v^{2}}_{2} - {v^{2}}_{1})$
$\Rightarrow 1000 = \frac{1}{2} \times 1.30 ({v^{2}}_{2} - 50^{2}) [∵ lift = P_{1} - P_{2}]$
or ${v^{2}}_{2} - 2500 = \frac{2000}{1.3}$
or, $v_{2} = 63.55 m / s$

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