CIVIL ENGINEERING FORMULAS

HYDRAULICS AND WATERWORKS FORMULAS 317

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,

(12.71)

The velocity can be determined from the Manning equation:

(12.72)

By substituting this into

(12.73)

whereHhead on entrance measured from bottom of culvert, ft (m)
Keentrance-loss coefficient
Sslope of energy grade line, which for culverts is assumed to equal
slope of bottom of culvert
Rhydraulic radius of culvert, ft (m)
dnnormal depth of flow, ft (m)

H(1Ke)

2.2

2 gn^2

SR4/3dn

V^2 

2.2SR4/3

n^2

HKe

V^2

2 g



V^2

2 g

dn

H

Entrance loss plus velocity head

Water

surface dc

dn dn D

S

V^2

2 g

(1 + Ke)

FIGURE 12.14 Open-channel flow occurs in a culvert with free discharge

and normal depth dngreater than the critical depth dcwhen the entrance is

unsubmerged or slightly submerged. Discharge depends on head H, loss at

entrance, and slope of culvert.