Consider a sluice gate across a $2-$m wide rectangular channel.

a$)$ Compute the magnitude of the force required to hold the gate when it is closed and the water depth behind

the gate is $1\mathrm{.}21$ m$.$

b$)$ When the gate is open, the upstream and downstream water depths are, respectively, $1\mathrm{.}20$ m and $0\mathrm{.}13$ m$.$

$($i$)$ Neglecting the head loss, compute the discharge of flow in the channel, $($ii$)$ determine the Froude

numbers and types of flows upstream and downstream, and $($iii$)$ the force required to hold the gate in

place.