Handbook of Civil Engineering Calculations

Daily Rate: (27,531 lb/wk)/(5 d/wk) = 5506 Ib/d (2499.7 kg/d)

Hourly Rate: (5506 lb/d)/(6 h/d) = 918 Ib/h (416.8 kg/h)

2. Size the belt thickener
   Using the hourly rate of sludge calculated above, and a loading rate of 1,000 Ib/h per me-
   ter of belt width, the size of the belt thickener is:

Belt Width =

918

I^ = 0.918 m (3.01 ft)

1000 Ib/h-m

v

'

Use one belt thickener with a 1.0 m belt width. Note that one identical belt thickener
should be provided as a spare.
The thickened sludge flow rate (S) in gal/day (m
3
/d) and the filtrate flow rate (F) in
gal/day (m
3
/d) are computed by developing solids balance and flow balance equations:
(a) Solids balance equation. Solids in = solids out, which implies that: solids in sludge
feed = solids in thickened sludge + solids in filtrate. Assume the following:

• Sludge feed specific gravity (s.g.) =1.01


• Thickened sludge s.g. = 1.03


• Filtrate s.g. = 1.0


• Suspended solids in filtrate = 900 mg/L = 0.09%

Therefore, the solids balance equation on a daily basis becomes:

5506 Ib = (S 9 gal/day)(8.34 lb/gal)(1.03)(0.05)

+ (F, gal/day)(8.34 lb/gal)(l .O)(0.0009) (1)

5506 Ib/d - 0.4295(5) + 0.0075(F)

(b) Flow balance equation. Flow in = flow out, which implies that: influent sludge
flow rate + washwater flow rate = thickened sludge flow rate + filtrate flow rate. Daily in-
fluent sludge flow rate = (58,000 gal/day)(7/5) - 81,200 gal/day (307.3 m^3 /d).

3. Compute the thickened sludge and filtrate flow rates
   Washwater flow rate is assumed to be 16 gal/min (1.0 L/s). Washwater flow rate varies
   from 12 gal/min (0.757 L/s) to 30 gal/min (1.89 L/s) depending on belt thickener size.
   Therefore, with an operating schedule of 6 h/d (360 min/d) the flow balance equation on a
   daily basis becomes:

81,200 gal/day + (16 gal/min)(360 min/d) - S + F

86,960 gal/day = S + F (2)

Putting (Eq. 1) and (Eq. 2) in matrix format, and solving for thickened sludge flow rate
(S) and filtrate flow rate (F):

[" 0.4295 0.0075 ][" S] f 5506]

L 1 1 J [Fj [86,960J

S = 11,502 gal/day (43.5 m

3

/d) of thickened sludge at 5.0% solids

F= 75,458 gal/day (285.6 m

3

/d) of filtrate