Handbook of Civil Engineering Calculations

Using Table 1, the number of centrifuges recommended for a 4.0 Mgd (15,410 m

3

/d)

waste water treatment facility is one operational + one spare for a total of two centrifuges.

2. Find the sludge feed rate required
   If the dewatering facility is operated 4 h/d, 7 d/wk, then the sludge feed rate is

Sludge Feed Rate - (6,230 gal/day)/[(4 h/d)(60/min/h)]

= 26 gal/min (1.64 L/s)

Although a 4 h/d operation is below that recommended in Table 1, the sludge feed rate

of 26 gal/min (1.64 L/s) is adequate for the size of centrifuge usually found at a treatment

facility of this capacity. A longer operational day would be necessary if the dewatering fa-

cilities were operated only 5 days per week, or during extended period of peak flow and

solids loading.

Assume a feed sludge specific gravity of 1.03. The sludge feed in Ib/h is calculated us-

ing the following equation:

w= W(p)(s.gQ(%solids)(60min/h)

7.48 gal/ft^3

Ws = Weight flow rate of sludge feed, Ib/h (kg/h)

V = Volume flow rate of sludge feed, gal/min (L/s)

s.g. = specific gravity of sludge

% solids = percent solids expressed as a decimal

p = density of water, 62.4 Ib/ft^3 (994.6 kg/m^3 )

Using values obtained above, the sludge feed in Ib/h is:

r (26 gal/min)(62.4 Ib/ft

3

Iy = )(l .03)(0.05)(60 min/h)

7.48 gal/ft^3

= 670 Ib/h of dry solids (304.2 kg/h)

3. Compute the solids capture
   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 possible to calculate percent recovery without
   determining total mass of any of the streams. The equation for percent solids recovery is

/ C 5 \r F-CC 1

*=1(wV bm /L c~cHcs~ccJ

where R = Recovery, percent solids
C 5 = Cake solids, percent solids (25%)
F = Feed solids, percent solids (5%)
Cc = Centrate solids, percent solids (0.3%)

Therefore, using values defined previously: