A large concrete gravity dam has five $(5)$ radial gates installed on its central spillway sectionto control releases from the dam. Figure $1$ provides a simplified side view of the dam walland radial gates. The central section of the dam wall has the following dimensions and properties: Maximum water depth above dam spillway crest, z at Full Supply Level with gates closed $=8$ metres. The specific weight of concrete dam wall, $=23\mathrm{.}5$ kN$/$m$^3.$ The vertical height of the dam wall, H $=130$ metres. Dam crest width $($B$-$C$)=9$ metres. The angle of the spillway with the horizontal base, is $60$ degree. Internal angle at the upstream toe, is $85$ degree. Depth of water downstream of the dam wall is $0$ metre. Radial gate radius is $10$ metres, and Length of each radial gate is $15$ metres. The following calculations need to be undertaken:Part $1.$ For the maximum water height at full supply level, calculate the complete vector of the resultant force on the central section of the dam wall per metre length,as it would pass through the dam base, with respect to the downstream toe $($D$).$ Account for the hydrostatic thrust force on the upstream $($A$-$B$)$ face of the dam,pore pressure on the base $($A$-$D$)$ and the weight of the dam wall. The weight of the radial gate and gate supporting structure can be ignored. Assume the radial gates are fully closed and there is no water on the spillway.Part $2.$ For the maximum water height, calculate the resultant force of the water on a single radial gate. Clearly identify the magnitude, direction and line of the actionof the resultant force.Figure $1$: Side view of the concrete dam wall and radial gates. $($Not to scale$)$