Page 389 - Civil Engineering Formulas

HYDRAULICS AND WATERWORKS FORMULAS 317

Entrance loss plus velocity head
2
(1 + K ) V
e
2g
H
d n d n D Water
surface d c
S

FIGURE 12.14 Open-channel flow occurs in a culvert with free discharge
and normal depth d n greater than the critical depth d c when the entrance is
unsubmerged or slightly submerged. Discharge depends on head H, loss at
entrance, and slope of culvert.

Entrance Submerged or Unsubmerged but Free Exit. For these conditions,
depending on the head, the flow can be either pressure or open channel (Fig. 12.14).
The discharge for the open-channel condition is obtained by writing the
Bernoulli equation for a point just outside the entrance and a point a short dis-
tance downstream from the entrance. Thus,
V 2 V 2
H K e d n (12.71)
2g 2g
The velocity can be determined from the Manning equation:
2.2SR 4/3
2
V (12.72)
n 2
By substituting this into
2.2
H (1 K e ) SR 4/3 d n (12.73)
2gn 2

where H head on entrance measured from bottom of culvert, ft (m)
K entrance-loss coefficient
e
S slope of energy grade line, which for culverts is assumed to equal
slope of bottom of culvert
R hydraulic radius of culvert, ft (m)
d normal depth of flow, ft (m)
n