Page 402 - Civil Engineering Formulas

HYDRAULICS AND WATERWORKS FORMULAS 329

T d sin (12.122)
d
D c (1 cos ) (12.123)
2
Flow quantity is then given by

1 3/2
3/2 1/2

2 g r sin 2
Q 2 D c 5/2 (12.124)
1/2
8(sin ) (1 cos ) 5/2
WEIRS

A weir is a barrier in an open channel over which water flows. The edge or sur-
face over which the water flows is called the crest. The overflowing sheet of
water is the nappe.
If the nappe discharges into the air, the weir has free discharge. If the dis-
charge is partly under water, the weir is submerged or drowned.

Types of Weirs
A weir with a sharp upstream corner or edge such that the water springs clear of
the crest is a sharp-crested weir (Fig. 12.24). All other weirs are classed as weirs
not sharp crested. Sharp-crested weirs are classified according to the shape of the
weir opening, such as rectangular weirs, triangular or V-notch weirs, trapezoidal
weirs, and parabolic weirs. Weirs not sharp crested are classified according to the
shape of their cross section, such as broad-crested weirs, triangular weirs, and (as
shown in Fig. 12.25) trapezoidal weirs.
The channel leading up to a weir is the channel of approach. The mean
velocity in this channel is the velocity of approach. The depth of water produc-
ing the discharge is the head.

Water surface

H

P

FIGURE 12.24 Sharp-crested weir.