$5.$ An isosceles triangular plate $3$ m high and $2$ m base is immersed vertically in water in such a way that its apex is below the base and at a distance of $4$ m below the water surface. Find the total pressure and position of the centre of pressure.

$[$Ans$.\backslash (58\mathrm{.}86\backslash$mathrm$\{$kN$\}$ ; $2\mathrm{.}25\backslash$mathrm$\{$~m$\}\backslash )]$

$6.$ A rectangular plate $1$ m wide and $2$ m deep is immersed in water in such a way that its plane surface makes an angle of $\backslash (45^\{\backslash$circ$\}\backslash )$ with the water surface and its centre of gravity lies $5$ m below the water surface. What is the total pressure on the plate and the point where it acts?

$[$Ans$.\backslash (98\mathrm{.}1\backslash$mathrm$\{$kN$\}$: $5\mathrm{.}03\backslash$mathrm$\{$~m$\}\backslash )]$

$7.$ A rectangular plate $2$ m wide and $3$ m deep is immersed in water in such a way that its plane makes an angle of $\backslash (30^\{\backslash$circ$\}\backslash )$ with the water surface and its upper edge is $1\mathrm{.}5$ m below the water surface. Calculate the total pressure and the position of centre of pressure.

$[$Ans$.\backslash (132\mathrm{.}4\backslash$mathrm$\{$kN$\}$ ; $2\mathrm{.}33\backslash$mathrm$\{$~m$\}\backslash )]$

$8.$ A circular plate of $3$ m diameter is immersed in water in such a way that it makes an angle of $\backslash (30^\{\backslash$circ$\}\backslash )$ with the horizontal and $1$ I $1$ m below the water surface. Find the total pressure on the plate and the centre of pressure.

$[$Ans$.\backslash (121\mathrm{.}4\backslash$mathrm$\{$kN$\}$ ; $1\mathrm{.}8\backslash$mathrm$\{$~m$\}\backslash )]$

$9.$ A gate $3$ m wide and $2$ m deep is fitted in a wall having a slope of $\backslash (60^\{\backslash$circ$\}\backslash )$ constructed across a channel. Determine the total pressure on the gate and its position, when the channel is full of water.

$[$Ans$.\backslash (50\mathrm{.}97\backslash$mathrm$\{$kN$\}$ ; $1\mathrm{.}15\backslash$mathrm$\{$~m$\}]\backslash )$