# How to determine the velocity of a gust of air caused by a falling object

• Micah Tate
In summary, Dave states that the wind velocity experienced would be based on the wind force imposed on the building due to the gust of air displaced by the roof falling. The approach used would be to study video of previous implosions to determine the velocity of air expelled.
Micah Tate
Summary: I am looking to determine the velocity of a the gust of air normal to a falling object. Say if you to be standing next to an open frame building with a flat roof then take away all the columns and let the roof free fall. What kind of wind velocity would you experience.

I am looking to determine the velocity of a the gust of air normal to a falling object. Say if you to be standing next to an open frame building with a flat roof then take away all the columns and let the roof free fall. What kind of wind velocity would you experience.

Welcome to PF.

Do you mean the air displaced by the falling object?

Yes I assume it would be similar to the displacement of air say if you were fanning yourself with a piece of paper. I am just not sure how to calculate it.

To be more clear we have a structure near a open frame building that is being imploded. We want to determine what king of wind force if any is imposed on the structure due to the gust caused my the air displaced by the roof falling.

This is going to have to be a pretty idealized scenario, that only loosely applies to a real-world situation.
The variables are legion - and some are chaotic in nature.

For just one example, in a real-world scenario, the roof will not fall straight down. The resultant air movement will be unevenly distributed around the perimeter.

I suspect the model you will end up with is a piston displacing a volume of gas from a cylinder at a certain rate of acceleration*.

*there's another variable: the acceleration will be affected by non-linear wind resistance
Roof falls die to gravity, but ground causes air cushioning. As air rushes out, cushioning decreases.

russ_watters
@DaveC426913 I agree and the roof is actually imploding so that the middle folds in on itself. Though it seems that assuming that the roof is flat and staying parallel to the ground would cause the most drag intern displacing a larger amount of air. I am just trying to get a high level wind velocity result.

Micah Tate said:
@DaveC426913...the roof is actually imploding so that the middle folds in on itself...
I wasn't even thinking of that. I was just thinking that it's aerodynamically unstable, even over such a short distance. It will tilt as it falls, directing the air preferentially.

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I imagine that there must be studies, perhaps even wind tunnel results of a blunt object in a moving stream of air (like in the picture). The streamlines are indicative of air movement normal to the motion. I don't have any such studies, but other PF members may.

But Dave's comment might be more relevant than the OP's question.
DaveC426913 said:
I suspect the model you will end up with is a piston displacing a volume of gas from a cylinder at a certain rate of acceleration*.

If you consider the volume of air in the building before implosion. All that air needs to be expelled. Simplify, saying that it is all expelled horizontally. Then guess that it is expelled only in the final N seconds of collapse. The orifice is the average vertical surface area of the building in the last N seconds. From that, you could calculate an air velocity. That is very crude, but given all the complications crude is perhaps the best you could do.

A completely different approach is to study video of previous implosions. Frame-by-frame analysis should reveal the velocity of air being expelled. Reasonably, the velocity varies with time and with height above ground. You probably want to search for the worst case velocity. In that approach you observe, not calculate.

sophiecentaur
Doppler shift (of sound - SODAR) works well for many applications and it's nicely non-contact.

It should have a dependency on both the mass and density of the roof.

Micah Tate said:
To be more clear we have a structure near a open frame building that is being imploded. We want to determine what king of wind force if any is imposed on the structure due to the gust caused my the air displaced by the roof falling.
There is no simple analytical solution to this. Air immediately adjacent to the building will move down at the speed of the building and air in the building will be expelled bellows-style and the velocity will decrease with distance. I don't think the flow field can be predicted reliably except with CFD analysis.

Thanks for all the Replies, they decided not to implode the building but rather jack the roof down. If any of you ever happen across any papers on something along the lines of this and think of this thread please post it. I am still interested in what the effects would be.

berkeman

## 1. What is the formula for calculating the velocity of a gust of air caused by a falling object?

The formula for calculating the velocity of a gust of air caused by a falling object is v = √(2gh), where v is the velocity, g is the acceleration due to gravity (9.8 m/s²), and h is the height from which the object fell.

## 2. How do you measure the height from which the object fell?

The height from which the object fell can be measured using a measuring tape or ruler. Alternatively, if the object fell from a known height, this value can be used in the velocity formula.

## 3. Does the shape or weight of the falling object affect the velocity of the gust of air?

Yes, the shape and weight of the falling object can affect the velocity of the gust of air. Objects with a larger surface area or higher weight will experience more air resistance and therefore have a lower velocity compared to smaller or lighter objects.

## 4. Can the velocity of the gust of air be accurately determined without advanced equipment?

Yes, the velocity of the gust of air can be accurately determined using basic equipment such as a stopwatch and measuring tools. However, more advanced equipment such as an anemometer can provide more precise measurements.

## 5. How can the velocity of the gust of air be used in scientific research?

The velocity of the gust of air can be used in various scientific research, such as studying the effects of air resistance on falling objects or analyzing the aerodynamics of different shapes and weights. It can also be used in weather forecasting and predicting the impact of air turbulence on aircrafts.

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