Calculating Force using Bernoulli's equation

Question

I am working on the following physics problem and I am confused as to why, according to the textbook, the pressure inside the house is not taken into account. This is not a problem for credit it is just a problem in the textbook that I am using to study for the exam

"Every few years, winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s (about 100 mi/h) when the jet stream descends during early spring. Approximately what is the force due to the Bernoulli effect on a roof having an area of ? Typical air density in Boulder is , and the corresponding atmospheric pressure is . (Bernoulli’s principle as stated in the text assumes laminar flow. Using the principle here produces only an approximate result, because there is significant turbulence.)" (College Physics; Paul Peter Urone and Roger Henrichs).

This is what I did to solve the equation:

P1+1/2pv1^2=P2+1/2pV2^2

F=PA

P1=?

p=1.14kg/m^3

v1=45m/s

v2=0

A=220m^2

F=?

P2=8.89x10^4 N/m^2

P1+1/2(1.14)(45)^2=8.89x10^4+1/2(1.14)(0)^2

P1+1154.25=8.89x10^4

P1=8.89x10^4-1154.25

P1=87745.75

F=881145.75(220)

F=19304065

Answer 1

Before the winds arrive, it is assumed that the air pressure inside the house is equal to the air pressure outside of the house. As the winds begin, the pressure difference is what causes a net upwards force on the roof. The inside pressure of the house is presumably atmospheric pressure, and the outside pressure becomes lower due to the speed of the winds.

Answer 2

Hi Amanda G.,

You're going to have to learn how to find the best form for laws, to be efficient! In the case of flat flow across a planar surface, that's ΔP = (1/2)ρv^2

where v = wind speed, ρ = air density, and ΔP is the pressure difference, which applies across your entire roof.

(Only use the "whole nine yards" equation form when you need to, e.g. with a compressible fluid flowing through a constriction.) You can find such things by Googling the general term (as images) and then looking for your particular case;

for that particular form, see https://www.chegg.com/homework-help/questions-and-answers/5-simple-form-bernoulli-s-equation-ap-24-density-v-velocity-calculated-difference-p-measur-q24259653

-- Cheers, -- Mr. d.