Question

During a hurricane, the atmospheric pressure inside a house may blow off the roof because of the reduced pressure outside. If air (density 1.293 kg/m3) is blowing laminarly over the roof of a house at a speed of 128 km/hr, what is the pressure difference between the inside and the outside of the house

Answer 1

817.5 Pa

Step-by-step explanation:

From Bernoulli's equation, considering thst there is no height difference then

P1+½d(v1)²=P2+½d(v2)²

P1-P2=½d(v2²-v1²)

∆P=½d(v2²-v1²)

Where P represent pressure, d is density and v is velocity. Subscripts 1 and 2 represent inside and outside. ∆P is tge change in pressure

Given the speed at roof top as 128 km/h, we convert it to m/s as follows

128*1000/3600=35.555555555555=35.56 m/s

Velocity at the bottom of roof is 0 m/s

Density is given as 1.293 kg/m³

∆P=½*1.293*(35.56²-0)=817.5 Pa