Page 859 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

814 Appendix D: Fluid Mechanics—Reviews of Selected Topics

D.4.6 TRIANGULAR WEIR 2 For minimum flow,
A triangular weir, often called a ‘‘V-notch’’ weir, is accurate
Q(min, 500 persons)
as a metering device and is cheap. Since the elevation differ-
ence is larger over a given flow range, it is less satisfactory ¼ 278L=person=day 500persons¼ 189,250L=day
than the rectangular weir for water surface elevation control.
¼ 100 gpcd 500 persons ¼ 50,000 gal=day
The flow-head relation is
3
¼ 6,685 ft =day)

8 p ffiffiffiffiffi u 2:5
C VH 2g tan H (D:80) Metric U.S. Customary
Q ¼
15 2
Q ¼ 0:79H 5=2 Q ¼ 1:44H 5=2
189=24=3600 ¼ 0:79H 5=2 6685=24=3600 ¼ 1:44H 5=2
in which H ¼ 0:095 m (9:5 cm) H ¼ 0:31 ft (3:7in:)
3
3
Q is the flow (m =s) or (ft =s)
C VN is the weir coefficient ¼ 0.58 when u ¼ 608, given in
Table D.8 (dimensionless) Discussion
2
2
g is the acceleration of gravity (9.81 m=s ) or (32.2 ft=s ) The tailwater level range from 9.5 to 29 cm should be
acceptable, and so the triangular weir would be the choice
b is the length of weir crest (m) or (ft)
for flow measurement or for the dual role of tailwater
H is the height of water level above weir crest upstream
elevation control and flow measurement. The rectangular
from effect of drawdown (m) or (ft)
weir is the choice if tailwater control is the only function.
u is the angle of notch in triangular weir (degrees)
D.4.7 PROPELLER METERS
For a weir having u ¼ 608, C VN ¼ 0.58, the discharge equation is
for metric units, A propeller meter is simply a propeller placed in a matched
pipe section that is coupled to a flow volume indicator (regis-
ter). Such meters come in a range of sizes from 50 mm (2 in.)
5=2
Q ¼ 0:79H (D:81) to 3 m (120 in.) and are used widely in all kinds of situations
(Huth, 1990). Such meters are accurate to within 2%
and for U.S. Customary units, throughout a 10:1 or 20:1 operating range.
The propeller has three or six blades and rotates in propor-
tion to the velocity in the pipe section. The volume of flow
Q ¼ 1:44H 5=2 (D:82) that has passed the propeller is proportional to the number of
revolutions, i.e.,
Terms are illustrated in Figure D.11b. Usually, a weir with a
V ¼ k(m) n(rev) (D:83)
608 notch is used since the coefficients are usually readily
available from references.
in which
3
V is the volume of flow that has passed the propeller (m )
3
Example D.4 Triangular Weir Head Calculation or (ft )
k(meter) is the coefficient of proportionality to calibrate
3
3
Calculate the head on a 608 triangular weir at Empire for flow meter (m =rev) or (ft =rev)
maximum and minimum flows. n(rev) is the number of revolutions of propeller associated
with volume V (rev)
1. For maximum flow,
Q(max, 1,000 persons) Example D.5 Show the Derivation
of Equation D.83
¼ 3,028 L=person=day 1,000 persons
¼ 3,028,000 L=day The volume of flow which has passed the pipe section,
e.g.,
( ¼ 800 gpcd 1,000 persons ¼ 800,000 gal=day
3
¼ 106,952 ft =day) dV ¼ Q dt
¼ v(pipe) A dt
Metric U.S. Customary
Q ¼ 0:79H 5=2 Q ¼ 1:44H 5=2 ¼ k(meter) rpmŠ A dt
½
3,028=24=3,600 ¼ 0:79H 5=2 106,952=24=3,600 ¼ 1:44H 5=2 ¼ k(meter) dN=dtŠ A dt
H ¼ 0:29 m (29 cm) H ¼ 0:94 ft (11:3in:) ½
V ¼ k(meter) N