What distance can airborne mining dust travel from a gravel mine operation?

Question:

Answers:
While the answers given previously were terse and unhelpful, they are unfortunately correct. A large number of assumptions must be made in order to answer the question.

Before showing the results of any calculations, I feel it is only fair to mention that the actual amount of dust in the air will vary dramatically from day-to-day and hour-to-hour. While these calculations will show how far specific dust particles can theoretically travel, it is the actual concentration of airborne particles that should be observed. Furthermore, exposure to rock dust at small concentrations is generally deemed acceptable by labour and environmental agencies. A proper air sampling regime should be put in place to determine how often dust is being released and at what concentration. This test should run for a significant period of time to encompass as many temperature and other environmental variables as possible.

In order to calculate how far the dust can travel, the terminal velocity of the particles must be determined. This will allow us to find out how long it will take for the particles to fall from a particular height. Once this period has been determined, the distance which a particle can travel is a function of the wind speed.
(displacement = velocity * time)

Here are my assumptions:

1. The rock has a density of 2.5 g/cc

2. Ambient air pressure and temperature are 100 kPa and 25 degrees Celsius

3. The highest, and most severe, source of dust generation is 5 metres (16') off the ground, such as where a conveyor belt empties onto a stockpile of crushed material.

For anyone interested in double-checking my work, the assumptions above led me to the following parameters, required in order to calculate terminal velocity:

Air Density = 1.174 kg/m^3
Air Viscosity = 1.84E-04 g/cm-s
Gas Mean Free Path = 0.068 μm

Note that the units used for travel distances calculated below vary depending on particle size.

Calculations for 100 μm Particles:
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Dust of this size is well above the median inhalable diameter specified by the EPA. These calculations are included only to show how quickly this size material can fall to the ground.

The terminal velocity of this size of particle is calculated to be 0.573 m/s using the Intermediate Law for Fluid-Particle Forces, in the conditions specified previously.

It will therefore take 8.7 seconds for these particles to fall from a height of 5 metres.

Wind Speed____Travel Distance
5 km/h________12.1 m
10____________24.3
20____________48.5
40____________97.0
60____________145.5
80____________194.0

Calculations for 10 μm Particles:
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Dust of this size is the median inhalable diameter specified by the EPA. “The EPA describes inhalable dust as that size fraction of dust which enters the body, but is trapped in the nose, throat, and upper respiratory tract.” (Quote is from the cited webpage, below)

The terminal velocity of this size of particle is calculated to be 7.53E-03 m/s using Stokes Law for Fluid-Particle Forces, in the conditions specified previously.

It will therefore take 664 seconds for these particles to fall from a height of 5 metres.

Wind Speed____Travel Distance
5 km/h________0.9 km
10____________1.8
20____________3.7
40____________7.4
60____________11.1
80____________14.8

Calculations for 5 μm Particles:
------------------------------.

Dust of this size falls within the respirable dust range as specified by the EPA. “Respirable dust refers to those dust particles that are small enough to penetrate the nose and upper respiratory system and deep into the lungs. Particles that penetrate deep into the respiratory system are generally beyond the body's natural clearance mechanisms of cilia and mucous and are more likely to be retained.” (Quote is from the cited webpage, below)

The terminal velocity of this size of particle is calculated to be 1.91E-03 m/s using Stokes Law for Fluid-Particle Forces, in the conditions specified previously.

It will therefore take 2,612 seconds for these particles to fall from a height of 5 metres.

Wind Speed____Travel Distance
5 km/h________3.6 km
10____________7.3
20____________14.5
40____________29.0
60____________43.5
80____________58.1

Conclusion:
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As you can no doubt see, by varying the particle size, wind speed and release height we can show that dust could end up just about anywhere downwind. In reality, the further the dust travels the more diluted it will become due to localized air movements and therefore become less and less harmful.

From a practical point of view, unless you are located particularly close to the dust source (<1 km) and/or are regularly inconvenienced by airborne rock dust, I do not expect that there is any cause for concern.

For more rock dust information see:

http://www.osha.gov/SLTC/silicacrystalline/dust/dust_control_handbook.html

Other Answers:
This depends on the wind velocity and other atmospheric conditions.

whever the wind takes them

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What distance can airborne mining dust travel from a gravel mine operation?

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