$[$NOTE: THIS PROBLEM HAS BEEN SELECTED FOR HANDMARKING IN ADDITION TO MOBIUS GRADING$]$

Part A:

A study is being conducted on scour associated with transverse standing waves $($i$.$e$.$ those perpendicular to the direction of flow$)$ around obstacles in a

channel such as jettys, bridge piers and vegetation on flood plains. In the worst case scenario the local scour around bridge piers and abutments can destroy

bridges, or seriously impact stability and safety.

In the study the impact of piers in a canal is being studied. A model $($scale $1$:$13)$ is built of the system where the velocity is $0\mathrm{.}7\frac{m}{s}$ and a wave of $2\mathrm{.}5cm$ in

height is formed.

Determine the following for the prototype.

$($i$)$ The velocity of the prototype.

$($ii$)$ The wave height for the prototype.

Part B:

The effect of scour can also be seen in spillways where piers are used to separate openings. Consider a model of a spillway which is constructed at a

$1$:$25$ scale that is operated with a flow of $0\mathrm{.}05\frac{m^3}{s}.$ As part of the testing a particle's movement via a specified route is timed as taking $1$ minutes.

Determine the following for the prototype.

$($i$)$ The flow rate.

$($ii$)$ The time taken for a similiar particle to travel in the protoype in seconds.