In such cases, design is based on an increased velocity of flow through culvert. The water is allowed to head up at inlet end of culvert to create that velocity. The greater is heading up of water, greater is head causing flow. Hence, greater will be flow velocity and lesser is opening area.

For a purely alluvial stream having a span length (L) equal to regime width (W), Lacey?s regime scour depth is given by R? = 0.473 (Q/f)^1/3.
Silt factor (f) is obtained by equation f = 1.76 d^1/2 where d is average size of particle in mm.

The value of Cd varies with different type of bridge openings.

The linear waterway of a bridge across a purely alluvial stream is equal to its regime width as given by Lacey.
W = L = 4.75 Q^1/2 = 4.75 x 60 = 285 m.

The afflux for non-erodible beds may be easily computed by using Molesworth empirical formula given as-
h = [V²/17.88 + 0.01524] [(A/a)² ? 1] Where, h = afflux in meters, V = velocity in an unobstructed stream in m/sec, A = unobstructed sectional area of stream in sq.m and a = obstructed reduced c/s area of stream at bridge site.

When bridge span is less than 8 m, it is called Culvert Bridge. The minor bridge has a span length in between 8 m and 30 m and Major bridge have a span range of about 30 to 120 m. Long span bridges have a span length of more than 120 m.

When afflux is less than 1/4 D/s depth, re is no effect on discharge or on U/s depth due to formation of standing wave. The discharge is only dependent upon U/s depth and is independent of D/s depth. It is applicable only when afflux is more than 1/4 of D/s.

The stream is contracted so as to keep span length (L) lesser than regime width (W) for quasi-alluvial stream. The normal scour depth (D) is given by-
D = D? (W?/L)^0.61 where W? = natural unobstructed width of stream and D? = scour depth in quasi-alluvial stream having L=W?.

The factor of safety for single-span structure on a straight reach of stream is generally taken as 1.5 and is taken as 2.0 for multi-span structures.
Maximum scour depth = 1.5 x 5 = 7.5 m.

It is done by U/s wing walls or training works so as to make it equal to regime width and bridge may n be spanned across it. This contraction of stream up to regime width leads to economy since bridge length is reduced.