A plane is in level flight at constant speed ...

Mechanical Properties of Fluids

Question : 27 of 31

Marks: +1, -0

A plane is in level flight at constant speed and each of its two wings has an area of

25\text{ m}^2

. If the speed of the air is

180\text{ km h}^{-1}

over the lower wing and

234\text{ km h}^{-1}

over the upper wing surface, determine the plane’s mass. (Take air density to be

1\text{ kg m}^{-3})

Solution:

Here,

v_{1}=180\text{ km h}^{-1}=50\text{ m s}^{-1},

v_{2}=234\text{ km h}^{-1}=65\text{ m s}^{-1}

area of the each wing,

A = 25\text{ m}^2

and density of air,

r = 1\text{ kg m}^{-3}

According to Bernoulli’s theorem,

P_{1}-P_{2}= \frac{1}{2}\rho(v_{2}^{2}-v_{1}^{2})

= \frac{1}{2}(65^{2}-50^{2})

=862.5\text{ N m}^{-2}

Now, upward lift from both the wings,

F = (P_1 - P_2) \times 2A

= 862.5 \times 2 \times 25\text{ N}

Let M be the mass of the plane. As the plane is in level flight,

F = Mg

M = \frac{F}{g} = \frac{862.5 \times 2 \times 25}{9.8}

=4.4 \times 10^{3}\text{ kg}

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