Page 461 - Water and wastewater engineering

11-34 WATER AND WASTEWATER ENGINEERING

As noted in Figure 11-14 , the flow of backwash water out of the gullet controls the dimen-
sion h. The lowest feasible depth h at the outlet of the gullet is determined by the height of wash
2
water required to overcome the entry headloss into the outlet pipe (0.7 v /2g) plus the velocity
head that is lost in producing the desired velocity in the pipe. The backwash conduit velocity is
generally in the range 1.2 to 2.4 m/s.
The wash water discharge, Q ww , is determined from the backwash rate and the area of the filter.
The solution is iterative. A trial value of b is selected and the dimension H is calculated. Mea-
suring from the bottom of the wash troughs, the depth is checked against one of the criteria noted
above. If the depth is greater than the depth to the bottom of the underdrain, it is too deep. If the bot-
tom of the gullet is above the media, the width may be too large. Depending on the size of the plant,
with smaller plants having smaller gullets, trial widths in the range of 0.4 to 2 m are suggested.

Example 11-7. Determine the gullet dimensions for Ottawa Island’s rapid sand filter. Use
the filter dimensions from Example 11-5 and the backwash rate from Example 11-6 . Assume a
450 mm diameter pipe from the gullet is to carry the wash water at a velocity of 1.8 m/s.

Solution:
a. Estimate the velocity head in the effluent conduit.
v 2 ( 18 m/s). 2
. 017 m
0165 or .
2g 29 81 m/s ). 2
(
b. As shown in Figure 11-14 , estimate the velocity plus entry headloss as
v 2 17 . (18 . m/s ) 2
(17 . ) 2 028 m
.
2g ( 29 81 m/s )
.
c. Calculate h.
(
h diameter of pipe velocity head entrance hheadloss)
.
h 045 m 028 m 0 73 m
.
.
d. From Example 11-5 , assume a value of 0.6 m as a first trial for the width b and estimate
H using Equation 11-20 . Use the wash rate from Example 11-6 to estimate Q ww .
36 m/h( 5 2 m)(. 55 m). 3
Q 0 286 m /. s s
ww
3 600 s/h,
⎡ 2 0 286 m /s) 2 ⎤ / 12
3
( .
⎢
H ( . 2 ⎥
073)
2
2
⎣ ⎢ ( . m/s )( 0.6 m)( 0 73 m)⎥ ⎦
.
6
981
.
.
H 07548 or 0 8 m
This is 0.8 m below the bottom of the wash troughs. Using the depth of the trough from
Example 11-6 , the initial estimate of the bottom elevation of the gullet is then
Depth H depth of trough
08. m 0435. m
.
1235. or about 125 m below the lip of the wash trough