fluid_mechanics

10.6 Rapidly Varied Flow 565
However, since V we find that V 2 2 V c 1gy c 2 12 ,
c gy c so that we obtain
The broad-crested
weir is governed by
critical flow across
the weir block.
or
Thus, the flowrate is
or
H y c y c
2
y c 2H 3
Q by 2 V 2 by c V c by c 1gy c 2 1 2 b 1g y 3 2
c
Q b 1g a 2 3 b 32
H 3 2
Again an empirical weir coefficient is used to account for the various real-world effects not included
in the above simplified analysis. That is
1
Q C wb b 1g a 2 3 b 32
H 3 2
(10.33)
C wb
0
0 1
H/P w
where approximate values of C wb , the broad-crested weir coefficient shown in the figure in the
margin, can be obtained from the equation 1Ref. 62
C wb 1.125 a 1 H P 1 2
w
b
(10.34)
2 HP w
E XAMPLE 10.8
Sharp-Crested and Broad-Crested Weirs
GIVEN Water flows in a rectangular channel of width b 2 m
with flowrates between Q m 3 and Q max 0.60 m 3 min 0.02 s
s.
This flowrate is to be measured by using either 1a2 a rectangular
sharp-crested weir, 1b2 a triangular sharp-crested weir with
u 90°, or 1c2 a broad-crested weir. In all cases the bottom of the
flow area over the weir is a distance P w 1 m above the channel
bottom.
FIND Plot a graph of Q Q1H2 for each weir and comment
on which weir would be best for this application.
SOLUTION
(a) For the rectangular weir with P w 1 m, Eqs. 10.30 and
10.31 give
0.6
Rectangular
Q max = 0.60
Q C wr 2 3 12g bH3 2
a0.611 0.075 H P w
b 2 3 12g bH3 2
0.4
Broad-crested
Thus,
Q, m 3 /s
Q 10.611 0.075H2 2 3 2219.81 m s 2 2 12 m2 H 3 2
0.2
or
Triangular
Q 5.9110.611 0.075H2H 3 2
(1)
Q min = 0.02
where H and Q are in meters and m 3 s, respectively. The results
from Eq. 1 are plotted in Fig. E10.8.
0
0 0.2 0.4 0.6
0.8
H, m
F I G U R E E10.8