# The force of wind blowing on a wall at an angle

• hyperddude
In summary, the conversation discussed the calculation of the magnitude of force on a wall with width w meters and height h meters, when subjected to a wind with velocity v m/s at a 45 degree angle. The collisions of the air molecules with the wall are perfectly elastic and the density of air is 1.2 kg/m^3. The suggested method involved finding the change in momentum, which was calculated to be 1.2\sqrt{2}v^2wh. However, it was pointed out that the mass of the air hitting the wall should actually be 1.2*vwh\sin{45°}, resulting in a force of 1.2v^2wh.
hyperddude

## Homework Statement

Say there is a wall with width $w$ meters and height $h$ meters. There is a wind with velocity v m/s blowing on the wall at a 45 degree angle. The collisions of the air molecules with the wall are perfectly elastic. What is the magnitude of the force on the wall? (The density of air is 1.2 kg/m^3).

## Homework Equations

$Δp = FΔt$ (p is momentum)

## The Attempt at a Solution

In one second, an air particle moves v meters. The area of the wall is wh, so the volume of the air that hits a surface in one second is vwh. The density is 1.2kg/m^3, so the mass would be 1.2*vwh. My next step would be to find the change in velocity, which I think is $v\sin{45°} + v\sin{45°} = \sqrt{2}v$.

So, the change in momentum would be $mv = 1.2\sqrt{2}v^2wh$. The time is 1 second, so the force would be $1.2\sqrt{2}v^2wh$ Newtons. Is my method correct?

hyperddude said:

## Homework Statement

Say there is a wall with width $w$ meters and height $h$ meters. There is a wind with velocity v m/s blowing on the wall at a 45 degree angle. The collisions of the air molecules with the wall are perfectly elastic. What is the magnitude of the force on the wall? (The density of air is 1.2 kg/m^3).

## Homework Equations

$Δp = FΔt$ (p is momentum)

## The Attempt at a Solution

In one second, an air particle moves v meters. The area of the wall is wh, so the volume of the air that hits a surface in one second is vwh. The density is 1.2kg/m^3, so the mass would be 1.2*vwh. My next step would be to find the change in velocity, which I think is $v\sin{45°} + v\sin{45°} = \sqrt{2}v$.

So, the change in momentum would be $mv = 1.2\sqrt{2}v^2wh$. The time is 1 second, so the force would be $1.2\sqrt{2}v^2wh$ Newtons. Is my method correct?

I think you are overestimating the mass of the air hitting the wall. If the wall were directly facing the wind the volume would be vwh. But it's tilted away from the wind, shouldn't it be less? And I think your answer for the change in velocity came out ok, but you should really be doing it by taking the difference of two vectors.

Dick said:
I think you are overestimating the mass of the air hitting the wall. If the wall were directly facing the wind the volume would be vwh. But it's tilted away from the wind, shouldn't it be less?

Oh, good catch. I believe the mass should be $1.2*vwh\sin{45°}$. So the force is $1.2v^2wh$?

I think so.

Thanks!

## 1. How does the angle of the wind affect the force on a wall?

The angle of the wind plays a significant role in determining the force exerted on a wall. The force is directly proportional to the cosine of the angle of incidence, meaning that the force increases as the wind blows more perpendicular to the wall.

## 2. What is the maximum force that wind can exert on a wall?

The maximum force of the wind on a wall depends on several factors such as wind speed, angle of incidence, and the structural integrity of the wall. In general, wind speeds of over 100 mph can exert forces of up to 50 pounds per square foot on a wall.

## 3. How does the shape of the wall affect the force of wind blowing on it at an angle?

The shape of the wall can greatly impact the force of the wind. For example, a curved wall will experience less force than a flat wall due to the wind being able to flow around the curve. Additionally, walls with rounded edges can also experience less force compared to sharp-edged walls.

## 4. Can wind blowing on a wall at an angle cause structural damage?

Yes, wind blowing on a wall at an angle can cause structural damage. If the force of the wind exceeds the structural integrity of the wall, it can lead to cracks, fractures, or even collapse. It is important to consider wind forces when designing and constructing buildings.

## 5. Is it possible for the force of wind blowing on a wall at an angle to change over time?

Yes, the force of wind blowing on a wall at an angle can change over time. Wind speed and direction can fluctuate, causing the force on the wall to vary. Additionally, as a wall ages, its structural integrity may also change, affecting how it withstands wind forces.

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