Back Water Curve and Afflux

Consider the flow over a dam. On the upstream side of the dam, the depth of water will be rising. If there had not been any obstruction (such as dam) in the path of flow of water in the channel, the depth of water would have been constant line parallel to the bed of the channel. Due to obstruction. the water level rises and it has maximum depth from the bed at some section.

Let $h_{1}=$ depth of water at the point, where the water starts rising up, and

$h_{2}=$ maximum height of rising water from bed.

Then $\left(h_{2}-h_{1}\right)=$ afflux.

Thus afflux is defined as the maximum increase in water level due to obstruction in the path of flow of water.

The profile of the rising water on the upstream side of the dam is called back water curve.

The distance along the bed of the channel between the section where water starts rising to the section where water is having maximum height is known as length of back water curve.

Expression for the Length of Back Water Curve is

$$L=\frac{E_2-E_1}{i_b-i_e}$$

Where,

$L=$ Length of Back Water Curve

$E_2=h_2+\frac{v_2^2}{2g}$

$E_1=h_1+\frac{v_1^2}{2g}$

$i_b=$ Bed slope

$i_e=$ Energy line slope