Wilson's Deposition Velocity

[paulboshoff]

One of the methods used to determine deposition/settling velocity in slurry pumping applications is to use Wilson's nomograph which relates deposition velocity to pipe diameter, "average" particle size (normally d50) and specific gravity of the solids being pumped. If anyone is familiar with this nomograph, they will no that the original equations describing the nomograph were converted into the nomograph at a time when personal computers were not so common. Can anyone assist in supplying the actual equations that were used to develop the nomograph so that I can incorporate these into a spreadsheet? This would remove the need to continually read off values from the nomograph manually.

Thanks in anticipation.

 

[bulkhandling]

In the book Slurry Transport Using Centrifugal Pumps co-authored by Wilson, Addie and Clift, the following formula is given:

(Vsm)max/(2gD(Ss-Sf)^1/2=(0.018/f)^0.13

f is friction factor for fluid alone. V. Matousek recommends f=0.55 for most solids.

This formula does not give exactly the same results as you get from the nomograph since the formula was developed later.

The formula and the nomograph do not include the effect of slurry concentration. Wilson has given the method for the correction based on concentration. This method is a bit too much for writing out here.

 

[bulkhandling]

Continue the above post.

This formula (Vsm)max/(2gD(Ss-Sf))^1/2=(0.018/f)^0.13 is just for large pipe, and particles near Murphian size, he regards the particle size does not influence the Vsm.

In 1992 Wilson proposed another formula which is not included in the 1992 version of the book Slurry Transport Using Centrifugal Pumps:

Vsm=8.8*(f*(Ss-Sf)/0.66)^0.55*D^0.7*d50^1.75/(d50^2+0.11*D^0.7)

Again, f is the friction factor between solids and pipe wall.
d50 is the average particle size, D is the pipe ID.
Ss and Sf are SG of solids and fluid respectively.

This formula still does nopt give the same result as the nomograph and I've not heard the comparison by the author yet (I do not have the newer version of the book than 1992)