Question

A wind blows at the speed of 30m/s across a 175m² flat roof of a house. 

a) What is the pressure difference between the inside of the house and the outside of the house just above the roof? (Assume that the air pressure inside the house is atmospheric pressure)

b) What is the force on the roof due to the pressure difference?

Answer 1

a) Let's write the Bernoulli's equation:

$$P_1+\dfrac{1}{2}\rho v_1^2=P_2+\dfrac{1}{2}\rho v_2^2,$$ $$P_1+0=P_2+\dfrac{1}{2}\rho v_2^2,$$ $$P_1-P_2=\Delta P=\dfrac{1}{2}\rho v_2^2,$$ $$\Delta P=\dfrac{1}{2}\cdot1.2\ \dfrac{kg}{m^3}\cdot(30\ \dfrac{m}{s})^2=540\ Pa.$$

b) By the definition of the pressure, we have:

$$\Delta P=\dfrac{F}{A},$$ $$F=\Delta PA=540\ Pa\cdot175\ m^2=9.45\cdot10^4\ N.$$