Question

A large building shaped like a box is 40 m high with a face that is 6565 m wide. A strong wind blows directly at the face of the​ building, exerting a pressure of 170 N/m2 at the ground and increasing with height according to ​P(y)=170+​2y, where y is the height above the ground. Calculate the total force on the​ building, which is a measure of the resistance that must be included in the design of the building.

Answer 1

`F=55146000 N`

Step-by-step explanation:

Given:

Pressure on the building = 170 N/m²

Pressure function P(y) = 170 + 2y

Consider a small height of the building as dy

the small force (dF) exerted on the height dy will be given as

dF = P(y)×(Area of the building face)

or

dF = (170 + 2y)(6565)dy

or

dF = 170×6565×dy + 2y×6565×dy

dF = 1116050dy + 13130ydy

integerating the function for the whole height of 40 m

`\int\limits^(40)_0 {F} = \int _0^(40)\:\left(\:1116050dy\:+\:13130ydy\right)`

`F = \int _0^(40)1116050dy+\int _0^(40)13130ydy`

`F=\left[1116050y\right]^(40)_0+13130\left[(y^2)/(2)\right]^(40)_0`

`F=44642000+10504000`

`F=55146000 N` ; Total force exerted on the face of the building