How is afflux calculated in bridge design?

The rise in water level upstream of bridge as a result of obstruction to the natural flow caused by the construction of the bridge & its approaches.

Afflux can be estimated by using several empirical equations e.g. IRC:89 (1985) Nagler (1918), Rhebock (1921), Yarnel (1934), Rao (1997) etc.

IRC-SP 13 recommends use of wier /orifice formula for computing flow with known afflux or vice versa. For shallow channels with wide flood planes (as observed in most of the rivers across the bridges on this roadway a rough first approximation of finding afflux can be obtained from the following expression, (Bradley 1970).

h *1 = 3( 1- M) V2n2/2 g

where M=Qb/Q


Qb =is that portion of the total discharge Q in the approach channel within a width equal to the projected length of the bridge

Vn2 = Q/An2

An2 =is the gross area of waterway under the bridge opening below normal stream depth corresponding to design flood discharge.

IRC:5 and 89 recommend use of Molesworth’s equation for computing approximate afflux given below:

  h = {V2/17.88 + 0.01524} x {(A/a) 2– 1}

Afflux at a Bridg

Where, h = afflux in metres

V = is the mean velocity of flow in the river prior to bridge construction i.e.
corresponding to normal HFL

A = Areas of flow section at normal HFL in the approach river section.

a= Areas of flow section under the bridge.

In case of rivers with erodible beds, full afflux as calculated by the formula may not occur.

For minor and medium bridges, weir and orifice formula given in IRC:SP-13 can be used for computing afflux depending on whether the flow under the bridge is choked or free.
For choked weir type flow: Q = Cd Leff (Du + u2 /2g)3/2                                    if h1*Dd > 0.25

For orifice flow :                     Q = Cd Leff Dd √2g. h1*                                  if h1*/Dd <0.25

Where Cd & Co are the coefficients of discharges for weir and orifice type flows respectively.
Cd and Co values are given in the IRC code,

h*1 = afflux = (Du-Dd).

Du and Dd are the upstream and downstream depths measured from the lowest bed level under the bridge taken as datum.


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