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Maximum solids flow rate for vacuum system

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BruceTheEngineer

Chemical
Joined
Jul 19, 2017
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17
Location
NL
So I have this vacuum blower that's designed to run at 150 CFM and vacuum air at 12" Hg through a 2 1/2" line. I'm trying to figure out the best way to go about it. Because I can calculate the velocity of the air in the line, I was going to try to rearrange the saltation velocity formula to solve for mass flow rate
V_gs=[(w_s*〖10〗^δ)/(A*p_f )*(√(g*D))^χ ]^((1/(χ+1)) )
to
w_s=(V_gs^(χ+1)*A*p_f)/(〖10〗^δ*〖√(g*D)〗^χ )

But the mass flow rate I get is 133,177 lbs/hr which is not right. The formula I got from here
Then I was going to use the method of calculating pressure loss along the elbows and straight runs of piping and try to determine the maximum solids flow rate that would allow me not to lose all my pressure (starting with 12" Hg equals 5.89 psi and calculating like a pressure drop) that I found here I wanted to make sure this was the right way to go.

Here's the link to the Excel spreadsheet where I tried to use the saltation velocity to calculate the max flow rate of solids
 
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