Hydraulic Structures: Fourth Edition

Worked Example 10.3

Establish the stage (headwater level)–discharge relationship for a concrete
rectangular box culvert, using the following data: width1.2 m;
height0.6 m; length30 m; slope1 in 1000; Manning’s n0.013;
square-edged entrance conditions; free jet outlet flow; range of head water
level for investigation0–3 m; neglect the velocity of approach.

Solution

1. H/D1.2. For H0.6 m, free flow open-channel conditions prevail.
   Referring to Fig. 10.6 and assuming that a steep slope entry gives
   entrance control, i.e. the depth at the inlet is critical, for H0.2 m,
   ignoring entry loss yc(2/3)0.20.133 m and Vc1.142 m s^1. This
   gives the critical slope (Vn)^2 /R4/30.004 24. Therefore the slope of
   the culvert is mild and hence subcritical flow analysis gives the
   following results:

Q1.2y 0 [1.2y 0 /(1.2 2 y 0 )]2/3(0.001)1/2/0.013

2.92y 0 [1.2y 0 /(1.2 2 y 0 )]2/3; (i)

CULVERTS, BRIDGES AND DIPS 443

Table 10.6 Range of values of Cfor free flow over the embankment

Type of surface Range of h/L Range of C

Paved surface 0.15 1.68
0.20 1.69
0.25 1.70
Gravel surface 0.15 1.63
0.20 1.66
0.25 1.69
0.30 1.70

Table 10.7 Correction factor, f(non-modular flows)

Type of surface Range of hd/s/H f

Paved surface 0.8 1.0
0.9 0.93
0.95 0.8
0.99 0.5
Gravel surface 0.75 1.0
0.8 0.98
0.9 0.88
0.95 0.68
0.98 0.50