# Projectile motion or stokes law

1. Oct 21, 2009

### bif

Its a while since I've done any motion calcs so I'm after some guidance.

I am vertically dropping a range of materials (size 8-20 mm) into a horizontal air stream in a pipe (pipe diammeter d , ~0.3m)

The horizontal air velocity in the pipe is 10 m/s

The particle bulk density ranges from 200-2500 kg/m3

The high bulk density material falls pretty vertical through the horizontal air stream and the low bulk density material get caught in the air and never lands (ie its carried off in the air stream). In between these 2 extremes, the material is deflected a certain distance along the pipe, with the lighter material moving furthest from the drop position in the horizontal plane.

I am trying to model this.
My known variables/constants are particle size, particle density, pipe diameter (ie vertical drop height), pipe velocity, air viscosity and gravity.

My unknowns are time it takes to hit the bottom of the pipe and how far in the horizontal direction has it moved, when the particle lands

Any advice on how I model this fall. Is it projectile motion, or should I be looking to utilise Stokes law, or both??

Thanks

2. Oct 21, 2009

### bif

(I'm new to the forum and think I may have posted this in the wrong area - have just copied and posted here so hope this is correct)

Its a while since I've done any motion calcs so I'm after some guidance.

I am vertically dropping a range of materials (size 8-20 mm) into a horizontal air stream in a pipe (pipe diammeter d , ~0.3m)

The horizontal air velocity in the pipe is 10 m/s

The particle bulk density ranges from 200-2500 kg/m3

The high bulk density material falls pretty vertical through the horizontal air stream and the low bulk density material get caught in the air and never lands (ie its carried off in the air stream). In between these 2 extremes, the material is deflected a certain distance along the pipe, with the lighter material moving furthest from the drop position in the horizontal plane.

I am trying to model this.
My known variables/constants are particle size, particle density, pipe diameter (ie vertical drop height), pipe velocity, air viscosity and gravity.

My unknowns are time it takes to hit the bottom of the pipe and how far in the horizontal direction has it moved, when the particle lands

Any advice on how I model this fall. Is it projectile motion, or should I be looking to utilise Stokes law, or both??

Thanks

3. Oct 21, 2009

### Andy Resnick

Any decent model is going to be entirely too complicated to easily describe here. Here's a simple model, which should provide results to a modest degree of accuracy:

All particles are spherical and of the same size. Model the air stream as constant velocity, constant diameter jet. Make the problem 2-D, with the assumption that all particles fall through the same thickness of the horizontal air stream. The particles undergo free fall the entire time, but while they are in the air stream they are subjected to an additional force F = 6*pi*a*U*nu, where 'a' is the diameter of the particle, 'U' the velocity of the air stream , and 'nu' the kinematic viscosity of air (units of Stokes [St]).

Then it's just simple kinematics.

4. Oct 22, 2009

### bif

Thanks for that Andy,
have managed to do this, but for small low density particles, this doesn't work. I think I need to introduce drag, and terminal velocity, as I know the material l;ess than 5 mm and density of less than 100 kg/m3 with be carried off in the air stream.

How do i include this in my calcs?