Question

The construction of a flat rectangular roof (6.17 m × 5.92 m) allows it to withstand a maximum net outward force of 2.00 × 104 N. The density of the air is 1.29 kg/m3. At what wind speed will this roof blow outward?

Answer 1

Answer:

$v_2=29.13\ m/s$

Explanation:

It is given that,

Dimension of the rectangular roof, (6.17 m × 5.92 m)

The maximum net outward force, $F=2\times 10^4\ N$

The density of air, $\rho=1.29\ kg/m^3$

The Bernoulli equation is used to find wind speed of this roof blow outward. It is given by :

$P_1+\dfrac{1}{2}\rho v_1^2=P_2+\dfrac{1}{2}\rho v_2^2$

Here, $v_1=0$ (since air inside the roof is not moving)

$v_2=\sqrt{\dfrac{2(P_1-P_2)}{\rho}}$

Since, $F=(P_1-P_2)A$

$v_2=\sqrt{\dfrac{2F}{\rho A}}$

$v_2=\sqrt{\dfrac{2\times 2\times 10^4}{1.29\times 6.17\times 5.92 }}$

$v_2=29.13\ m/s$

So, the wind speed of  this roof blow outward is 29.13 m/s. Hence, this is the required solution.