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) V ^{2}_{n2}/2 g**

where M=Q_{b}/Q

where

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

V_{n2} = Q/A_{n2}

A_{n2} =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 = {V ^{2}/17.88 + 0.01524} x {(A/a) ^{2}– 1}**

__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 bridge**s, 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 = C_{d} L_{eff} (D_{u} + u^{2} /2g)^{3/2 } if h1*D_{d} > 0.25

For **orifice flow** : Q = C_{d} L_{eff} D_{d} √2g. h1* if h1*/D_{d} <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 = (D_{u}-D_{d}).

D_{u} and D_{d} are the upstream and downstream depths measured from the lowest bed level under the bridge taken as datum.