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Streamline Flow

An aeroplane ...

Question

An aeroplane is passing through an air tunnel. The velocity of air is 70 m/s and 63 m/s respectively at its upper surface of wing and lower surface of wing. Find out the lifting force. Given that total wing area is $2.5 m^{2}$ and air density is $1.3 k g / m^{3}$ .

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Solution

Given $v_{2} = 70 m s^{- 1}; v_{1} = 63 m s^{- 1}$ ;
$p = 1.3 k g m^{3}, F = ? A = 2.5 m^{2}$

$∴$ From Bernoulli's theorem

$P_{1} + \frac{1}{2} p v_{1}^{2} = P_{2} + \frac{1}{2} p v_{2}^{2}$

$∴ P_{1} - P_{2} = \frac{1}{2} p v_{2}^{2} - \frac{1}{2} p v_{1}^{2} = \frac{1}{2} p (v_{2}^{2} - v_{1}^{2})$

or $Δ P = \frac{1}{2} \times 1.3 (v^{2} + v^{2}) (v^{2} - v^{2})$

$= \frac{1.3}{2} (70 + 63) (70 - 63)$

$= \frac{1.3}{2} \times 133 \times 7$

or $Δ P = 605.15 N m^{- 2}$

$∴$ Lifting force $F = Δ P A = 605.15 \times 2.5 = 11512.875$
or $F = 1.5 \times 10^{3} N$

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