Question

The Bernoulli effect can have important consequences for the design of buildings. For example, wind can blow around a skyscraper at remarkably high speed, creating low pres- sure. The higher atmospheric pressure in the still air inside the buildings can cause windows to pop out. As originally constructed, the John Hancock Building in Boston popped windowpanes that fell many stories to the sidewalk below. (a) Suppose a horizontal wind blows with a speed of 11.2 m/s outside a large pane of plate glass with dimensions 4.00 m 3 1.50 m. Assume the density of the air to be constant at 1.20 kg/m3. The air inside the building is at atmospheric pressure. What is the total force exerted by air on the win- dowpane?

Answer 1

Answer:

9483.26399 N

Explanation:

$\rho$ = Density of air = 1.2 kg/m³

v = Velocity of wind = 11.2 m/s

A = Area = $4\times 31.5\ m^2$

The force on the pane is

$F=\dfrac{1}{2}\rho v^2A\\\Rightarrow F=\dfrac{1}{2}\times 1.2\times 11.2^2\times 4\times 31.5\\\Rightarrow F=9483.26399\ N$

The force on the pane of glass is 9483.26399 N