When the sluice gate $G$ in Fig. $6-4a$ is in the open position, water flows out from under the gate at a depth of $2$ ft $.$ If the gate is $5$ ft wide, determine the resultant horizontal force that must be applied by its supports to hold the gate in place. Assume the channel behind the gate maintains a constant depth of $10$ ft $.$

Figure $6-4$

$($a$)$