Page 403 - Civil Engineering Formulas

330 CHAPTER TWELVE

Water surface

H

P

FIGURE 12.25 Weir not sharp crested.

Sharp-crested weirs are useful only as a means of measuring flowing water.
In contrast, weirs not sharp crested are commonly incorporated into hydraulic
structures as control or regulation devices, with measurement of flow as their
secondary function.

FLOW OVER WEIRS

Rectangular Weir

The Francis formula for the discharge of a sharp-crested rectangular weir hav-
ing a length b greater than 3h is
b nh 3/2 3/2
Q 3.33 10 [(h h 0 ) h 0 ] (12.125)

3
3
where Q discharge over weir, ft /s (m /s)
b length of weir, ft (m)
h vertical distance from level of crest of weir to water surface at point
unaffected by weir drawdown (head on weir), ft (m)
n number of end contractions (0, 1, or 2)
2
0
h head of velocity of approach [equal to v 0 /2g c , where v 0 velocity of
approach, (ft/s) (m/s)], ft (m)
2
2
g 32.2 (lb mass) (ft)/(lb force) (s )(m/s )
c
If the sides of the weir are coincident with the sides of the approach channel,
the weir is considered to be suppressed, and n 0. If both sides of the weir are
far enough removed from the sides of the approach channel to permit free lat-
eral approach of water, the weir is considered to be contracted, and n 2. If
one side is suppressed and one is contracted, n 1.
Triangular Weir
The discharge of triangular weirs with notch angles of 30°, 60°, and 90° is
given by the formulas in Table 12.2.