Question 80: Properties of Matter

Question

A fully loaded boeing aircraft has a mass of $$5.4	imes10^5$$ 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 $$ho$$ 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. ($$\mathrm{g=10~m/s^2}$$)

Accepted Answer

Velocity of aircraft = 1050 km/h = 300 m/s
Now, weight of aircraft = $$\Delta PA$$
$$\Delta P = {{5.4 	imes {{10}^5} 	imes g} \over {500}} = 10800$$ $$\mathrm{Pa}$$
From Bernoulli's principle
$$\Delta P = {1 \over 2}ho \left[ {V_{upper}^2 - V_{lower}^2} ight]$$
$$10800 = {1 \over 2} 	imes 1.2 	imes V_{lower}^2\left[ {{{\left( {{{{V_{upper}}} \over {{V_{lower}}}}} ight)}^2} - 1} ight]$$
$${\left( {{{{V_{upper}}} \over {{V_{lower}}}}} ight)^2} = 1 + {{10800 	imes 2} \over {1.2 	imes {{(300)}^2}}} = 1.2$$
$${{{V_{upper}}} \over {{V_{lower}}}} = 1.096$$
$$\Rightarrow$$ Fractional increases = 9.6%

Answer

16

Answer

8

Answer

6

Answer

10

Properties of Matter

Choose the correct answer: