How to determine duct sizes from calculated pressure drops? 1

[oaskar]

I'm trying to redesign a pneumatic transport system, so I know that the optimum velocity to move my product is 5000 fpm and i know our production rates, my question is how do i know if the current duct sizes are suitable for the new air volume that i assumed

 

[yedwa]

Oaskar,

In pipe flow you only need two know of these three and then its its easy to calculate the third one.

Flow, head and diameter.

In this case i assume you have the head (pressure loss or you know what head your fan or compressor can develop).

The procedure is:

1) Calculate this constant a=ev/Q
e-pipe roughness
v-viscocity of the fluid (kinematic)
Q-is the flow rate
should be around 1.0*10^(-11) (order of magnitude)

2)calculate this constant B=[128*g*H*Q^3/(pi^3*L*v^5)]^0.5
g-gravitational constant 32.2 (or 9.81 if you are working SI)
H-head in ft
Q-flow rate
pi-3.142
L-length of duct
v-once again the viscocity of fluid (kinematic)

should get B~ 1.0*10^12 (order of magnitude)

3)now using the two constants you may calculate the Reynolds number using

Re^2.5=-2.0*log[pi*a*Re/14.8+(2.51*Re^1.5)/B]

there lots programs out to solve this equation ees, mathcad excel solver etc or a good calculator like HP 48g or a TI 92.

4) From the Reynolds number calculate the diameter directly using d=4*Q/(pi*v*Re)..

Hope this helps..



Yedwa

 

[oaskar]

yedwa,
Does this apply to pneumatic transport of dry products(pellets) too??

 

[yedwa]

Oaskar,

The method presented above applies to any type of fluid. For dry products like pellets the only important thing the non-settling velocity that you can calculate easily by using the Stokes formula:

Vs=(Rs-Rm)gd^2/u
where Vs-settling velocity
Rs- is the density of the pellet
Rm- is the density of fluid medium
g-is the gravitational constant
d-is the diameter of the pellet
u-is the dynamic visocity of the fluid medium

And make sure that your design velocity does not drop below this velocity.

This kind of flow is not slurry so basic equation like these apply.

So you are good to go..

Yedwa