fluid_mechanics

C wr
1
10.6 Rapidly Varied Flow 563
where C wr is the rectangular weir coefficient. From dimensional analysis arguments, it is expected
that C wr is a function of Reynolds number 1viscous effects2, Weber number 1surface tension
effects2, and HP w 1geometry2. In most practical situations, the Reynolds and Weber number
effects are negligible, and the following correlation, shown in the figure in the margin, can be
used 1Refs. 4, 72:
0
0 1
C wr 0.611 0.075 a H P w
b
(10.31)
H/P w
V10.13 Triangular
weir
C wr
More precise values of can be found in the literature, if needed 1Refs. 3, 142.
The triangular sharp-crested weir is often used for flow measurements, particularly for
measuring flowrates over a wide range of values. For small flowrates, the head, H, for a rectangular
weir would be very small and the flowrate could not be measured accurately. However, with the
triangular weir, the flow width decreases as H decreases so that even for small flowrates, reasonable
heads are developed. Accurate results can be obtained over a wide range of Q.
The triangular weir equation can be obtained from Eq. 10.27 by using
/ 21H h2 tan a u 2 b
where u is the angle of the V-notch 1see Figs. 10.19 and 10.202. After carrying out the integration
and again neglecting the upstream velocity 1V 2 12g H2, we obtain
Q 8
15 tan au 2 b 12g H 5 2
An experimentally determined triangular weir coefficient, C wt , is used to account for the real-world
effects neglected in the analysis so that
Q C wt 8 15 tan au 2 b 12g H 5 2
(10.32)
V10.14 Low-head
dam
C wt
Typical values of for triangular weirs are in the range of 0.58 to 0.62, as is shown in Fig. 10.21.
Note that although C wt and u are dimensionless, the value of C wt is given as a function of the
weir head, H, which is a dimensional quantity. Although using dimensional parameters is not
recommended 1see the dimensional analysis discussion in Chapter 72, such parameters are often
used for open-channel flow.
0.66
θ = 20°
0.64
0.62
45°
60°
C wt 90°
0.60
0.58
0.56
Minimum C wt for all θ
0 0.2 0.4 0.6 0.8 1.0
H, ft
F I G U R E 10.21 Weir coefficient
for triangular sharp-crested weirs (Ref. 10).