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**Particle Fall through the atmosphere**

Lecture #5 Ashfall Class 2009

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**Distance d travelled by an object falling for time t:**

Time t taken for an object to fall distance d: Instantaneous velocity vi of a falling object after elapsed time t: Instantaneous velocity vi of a falling object that has travelled distance d: Average velocity va of an object that has been falling for time t (averaged over time): Average velocity va of a falling object that has travelled distance d (averaged over time): use g = 9.8 m/s² (metres per second squared; which might be thought of as "metres per second, per second”. Assuming SI units, g is measured in metres per second squared, so d must be measured in metres, t in seconds and v in metres per second. air resistance is neglected--- quite inaccurate after only 5 seconds

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Particle Fallout After a very short time, ~4 seconds, particles will reach a terminal velocity in earth's atmosphere, with their gravitational attraction to the earth balanced by air resistance. Small particles have dominant air resistance (fall slowly) while large particles have dominant gravity (fall rapidly).

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Reynolds Number Re Reynolds number is a dimensionless number (i.e. it has no units) that is a measure of the type of flow through a fluid. In the case of falling particles, this describes the way that air flows around the particle. There are three basic types: laminar where Re < 0.4, intermediate where 0.4 < Re < 500, and turbulent where Re > 500.

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**Medium and small pyroclasts Fast-falling Large Pyroclasts**

RN =dvt/ Medium and small pyroclasts Fast-falling Large Pyroclasts D = 1mm D = 1µm .01 cm/s 10 m/s Laminar flow; RN = 10-2 Turbulent flow; RN = 106 RN = 20 RN = 40 RN = 104 Fluid dynamics applies dimensionless analysis of fall of spheres in the atmosphere, which shows that experience with large pyroclasts might not apply to smaller ones which fall much more slowly…

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**Conventional Wisdom: Particle Settling**

Particle Reynolds number, Rep: ratio of inertial force to viscous force per unit mass Rep = Vtd / v Vt = particle terminal fall velocity; d = particle diameter; v = fluid kinematic viscosity Rep : > 500 turbulent 1-500 transitional <1 laminar Drag force: (i) viscous drag (friction between the fluid and the particle surface) (ii) form drag (inertial force caused by the acceleration of fluid around the particle as it falls) From Sparks et al. [1997] particle accelerates due to gravity

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Larger pyroclasts, those >2mm in diameter, fall in a turbulent flow regime (Re> 500) through the atmosphere. Small pyroclasts, <1/16 mm (62 μm or 4 Φ), fall in laminar flow regime (Re<0.4). Intermediate size particles are transitional.

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**Particle Terminal Fall Velocity**

For large particles (Rep > 500) – inertial forces dominate: For small particles (Rep < 1) - viscous forces dominate: d = particle diameter ρp = particle density ρf = fluid density g = acceleration due to gravity Cd = dimensionless drag coefficient ρp = particle density g = acceleration due to gravity d = particle diameter v = kinematic viscosity

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**Fall of spherical particles in earth’s atmosphere**

This diagram shows how fast fine spherical ash particles would fall if they were simple particles. In reality we know that most ash this size falls out in less than 24 hours. Schneider et al., 1999, J Geophys Res

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**Particle Terminal Fall Velocity**

Mean particle size at ~330 km from MSH (Ritzville, WA) was 20 microns; Vt ~ ms-1 100 micron diameter particle has Vt of ~4-7 ms-1

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**Atmospheric Structure**

Environmental parameters determined from the radiosonde sounding taken at Spokane International Airport at 1800 UTC on 18 May 1980.

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Bonadonna et al., 1998

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Bonadonna et al., 1998

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Bonadonna et al., 1998

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Bonadonna et al., 1998

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Bonadonna et al., 1998

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Bonadonna et al., 1998

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Bonadonna et al., 1998

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Bonadonna et al., 1998

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**Figure 2 Typical stereo-pair taken at 8o tilt angle.**

Owen P Mills, MS thesis, Michigan Tech, 2007 Figure 3. Digital elevation map produced from stereo-pair in Figure 2.

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**Augustine ash P Izbekov**

Ash is NOT spherical! Riley et al., 2003

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Riley et al., 2003

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**Rose W I, C M Riley and S Dartevelle, 2003, J Geology, 111:115-124.**

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Riley et al., 2003

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Riley et al., 2003

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Riley et al., 2003

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Riley et al., 2003

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**Rose W I, C M Riley and S Dartevelle, 2003, J Geology, 111:115-124.**

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**Rose W I, C M Riley and S Dartevelle, 2003, J Geology, 111:115-124.**

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Riley et al., 2003

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Lesson 21 Laminar and Turbulent Flow

Lesson 21 Laminar and Turbulent Flow

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