A wind with speed 40m s ^ - 1 blows parallel to the roof of a...

A wind with speed

40m{s}^{- 1}

blows parallel to the roof of a house. The area of the roof is

250{m}^{2}

. Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the direction of the force will be :

\left({ρ}_{air} = 1 . 2kg{m}^{- 3}\right)

Options

A $4.8 \times {10}^{5}$ N, downwards
B $4.8 \times {10}^{5}$ N, upwards
C $2.4 \times {10}^{5}$ N, upwards
D $2.4 \times {10}^{5}$ N, downwards

Correct answer

C. $2.4 \times {10}^{5}$ N, upwards

Step-by-step solution

By Bernoulli's equation,

P + \dfrac{1}{2}ρ{v}^{2} = {P}_{0} + 0

{P}_{0} - P = \dfrac{1}{2}ρ{v}^{2}

F = \dfrac{1}{2}ρ{v}^{2}A

= \dfrac{1}{2} \times 1.2 \times {\left(40\right)}^{2} \times 250

= \dfrac{1}{2} \times 1.2 \times 1600 \times 250

= 2.4 \times {10}^{5}

N, upwards

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