Question

A mud cup is placed under one cone of a hydrocyclone unit being used to process an unweighted mud.Twenty seconds were required to collect 1 qt of ejected slurry having a density of 20 lbm/gal.Compute the mass of solids and water being ejected by the cone per hour.(Answer: 852 lbm/hr and 47.6 lbm/hr)

Answer 1

Density of water = 8.33 lbm/gal

Average Density of slurry ejected = 20 lbm/gal

Average density = density of solid x mass fraction of solid + density of water x mass fraction of water

Average density = density of solid x mass fraction of solid + density of water x (1 - mass fraction of solid)

20 = 21.7 x mass fraction of solid + 8.33(1 - mass fraction of solid)

mass fraction of solid = (20 - 8.33)/(21.7 - 8.33)

= 0.8728

Rejected slurry flow rate = 1 qt / 20s

Mass of solid

= (0.8728) x (1 qt / 20s) x (1gal/4qt) x (21.7lbm/gal) x (3600s/hr)

= 852.34 lbm/hr

Mass of water ejected

= (1 - 0.8728) x (1 qt / 20s) x (1gal/4qt) x (8.33lbm/gal) x (3600s/hr)

= 47.68 lbm/hr