For this bridge $5$ piers $($columns$)$ with spread footings are considered. the columns are

evenly spaced along this bridge. Design data are as follows:

$$ No of circular piers $=5$

$$ Diameter of each pier $=2\mathrm{.}5$ m

$$ Approximate height of middle pier $=11$ m

$$ Approximate height of other piers $=$ varies $($should be calculated$)$

$$ Height of spread foundation $=2$ m

$$ Spread foundation base dimensions $=5$m x $5$m

$$ Minimum depth of foundation from the riverbed to the base of footing $=4$ m

To control the local scour around pier foundations, gravel riprap is used. Close to the locationof bridge, the river has a straight reach.

Based on the maximum flow rate $3570\mathrm{.}226887$:

$($a$)$ Find the Area of the river cross section without the $5$ piers.

$($b$)$ Find the Area of the river cross section with $5$ piers.

$($c$)$ Find the average velocity of river during the $100-$year flood without bridge piers.

$($d$)$ Find the average velocity of river during the $100-$year flood with bridge piers.

$($e$)$ Accordingly, find the afflux height and the length of backwater