Mechanical Properties of Fluids - Result Question 8

8. A wind with speed $40 m / s$ 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 atmosphere pressure, the force exterted by the wind on the roof and the direction of the force will be $(\rho _{\text{air }}=1.2 kg / m^{3})$

[2015]

(a) $4.8 \times 10^{5} N$, upwards

(b) $2.4 \times 10^{5} N$, upwards

(c) $2.4 \times 10^{5} N$, downwards

(d) $4.8 \times 10^{5} N$, downwards

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Answer:

Correct Answer: 8. (b)

Solution:

  1. (b) According to Bernoulli’s theorem,

$P+ _2^{1} \rho v^{2}=P_0+0$

So, $\Delta P=\frac{1}{2} \rho v^{2}$

$F=\Delta PA=\frac{1}{2} \rho v^{2} A$

$=\frac{1}{2} \times 1.2 \times 40 \times 40 \times 250$

$=2.4 \times 10^{5} N$ (upwards)