A fully loaded boeing aircraft has a mass of $5.4\times10^5$ kg. Its total wing area is 500 m$^2$. It is in level flight with a speed of 1080 km/h. If the density of air $\rho$ is 1.2 kg m$^{-3}$, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be. ($\mathrm{g=10~m/s^2}$)
Solution
<p>Velocity of aircraft = 1050 km/h = 300 m/s</p>
<p>Now, weight of aircraft = $\Delta PA$</p>
<p>$\Delta P = {{5.4 \times {{10}^5} \times g} \over {500}} = 10800$ $\mathrm{Pa}$</p>
<p>From Bernoulli's principle</p>
<p>$\Delta P = {1 \over 2}\rho \left[ {V_{upper}^2 - V_{lower}^2} \right]$</p>
<p>$$10800 = {1 \over 2} \times 1.2 \times V_{lower}^2\left[ {{{\left( {{{{V_{upper}}} \over {{V_{lower}}}}} \right)}^2} - 1} \right]$$</p>
<p>$${\left( {{{{V_{upper}}} \over {{V_{lower}}}}} \right)^2} = 1 + {{10800 \times 2} \over {1.2 \times {{(300)}^2}}} = 1.2$$</p>
<p>${{{V_{upper}}} \over {{V_{lower}}}} = 1.096$</p>
<p>$\Rightarrow$ Fractional increases = 9.6%</p>
About this question
Subject: Physics · Chapter: Properties of Solids and Liquids · Topic: Elasticity
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