CIVIL ENGINEERING FORMULAS

370 CHAPTER THIRTEEN

The sludge feed rate for the dewatering facility is

(13.35)

And the sludge weight flow rate is

(13.36)

Wsweight flow rate of sludge feed, lb/h (kg/h)

Vvolume flow rate of sludge feed, gal/min (L/s)

s.g.specific gravity of sludge

% solids percent solids expressed as a decimal

density of water, 62.4 lb/ft^3 (994.6 kg/m^3 )

Since the solids exiting the centrifuge are split between the centrate and the
cake, it is necessary to use a recovery formula to determine solids capture.
Recovery is the mass of solids in the cake divided by the mass of solids in the
feed. If the solids content of the feed, centrate, and cake are measured, it is pos-
sible to calculate percent recovery without determining total mass of any of the
streams. The equation for percent solids recovery is

(13.37)

where Rrecovery, percent solids
Cscake solids, percent solids (25%)
Ffeed solids, percent solids (5%)
Cccentrate solids, percent solids (0.3%)

The dewatered sludge (cake) discharge rate is

Cake discharge rate (lb/h) dry solids (sludge feed rate, lb/h)(solids recovery)

(13.38)

R (^100) 
Cs
F
FCc
CsCc
Ws
(V)(p)(s.g.)(% solids)(60 min/h)
7.48 gal/ft^3
Sludge feed rate 
gal/day of digested sludge
operating h/day, 7 days/week (60 min/h)
TABLE 13.1 Facility Capacity and Number of Centrifuges
Facility size, Dewatering Centrifuges operating 
Mgd (m^3 /d) operation, h/d Spare @ gal/min (L/s)
2 (7570) 7 1 1 @ 25 (1.58)
5 (18,930) 7.5 1 1 @ 50 (3.16)
20 (75,700) 15 2 1 @ 50 (3.16)
50 (189,250) 22 2 1 @ 75 (4.73)
100 (378,500) 22 3 2 @ 100 (6.31)
250 (946,250) 22 4 2 @ 200 (12.62)
(Design Manual for Dewatering Municipal Wastewater Sludges, U.S. EPA)