A hydro$-$electric power generation facility uses a $300$ ft $.-$high and $700$ ft $.-$wide dam for its

operation. The water depth behind the dam is $280$ ft on a certain day and the local atmospheric

pressure is $14\mathrm{.}7$ psia $.$ Determine the

a$)$ pressure at the entrance to the turbine $($bottom of the dam$)$

b$)$ resultant hydrostatic force acting on the dam wall and its location measured from the free

surface of the water.

The gate $($hinged at B $)$ shown in the figure is used to contain the water in its reservoir. Under the

closed configuration, the gate leans on the floor of the reservoir as shown. The gate is $6$ m wide

$($in the direction perpendicular to the page$)$ and has a mass of $320$ kg $.$ The barometric pressure is

$755$ mm of mercury $.$ If $h_1=0\mathrm{.}6m$ and $h_2=4m,$ determine the minimum force $(F)$

required to open the gate if it is applied at the center as shown.