Question $2$

a$)$ A reservoir is designed such that at its base is a culvert $1\mathrm{.}25$ m in diameter that is closed

by a circular gate of the same diameter. The gate can open by rotating about its

horizontal diameter to allow water to flow through the culvert from the reservoir when

water level in the reservoir reaches a certain height.

i$)$ Show that the turning moment on the gate is independent of the depth of water in

the reservoir if the gate is completely immersed, and

ii$)$ find the value of this moment.