CIVIL ENGINEERING FORMULAS

316 CHAPTER TWELVE

From the Bernoulli equation for the entrance and exit, and the Manning
equation for friction loss, the following equation is obtained:

(12.69)

Solution for the velocity of flow yields

(12.70)

whereHelevation difference between headwater and tailwater, ft (m)
Vvelocity in culvert, ft/s (m/s)
gacceleration due to gravity, 32.2 ft/s^2 (9.81 m/s^2 )
Keentrance-loss coefficient
nManning’s roughness coefficient
Llength of culvert, ft (m)
Rhydraulic radius of culvert, ft (m)

The preceding equation can be solved directly because the velocity is the only
unknown.

Culverts on Subcritical Slopes

Critical slope is the slope just sufficient to maintain flow at critical depth.
When the slope is less than critical, the flow is considered subcritical.

V

B

H

(1Ke/2g)(n^2 L /2.21R4/3)

H(1Ke)

V^2

2 g



V^2 n^2 L

2.21R4/3

V^2

2 g

(1 + Ke)

Hydraulic

grade line

H

FIGURE 12.13 With entrance and exit of a culvert submerged, normal pipe

flow occurs. Discharge is independent of slope. The fluid flows under pres-

sure. Discharge may be determined from Bernoulli and Manning equations.