A triangular gate is to be installed in the vertical wall of a tank that holds a fluid of density $($r$)=1000$ kg$/$m$3$

$,$ as shown below. The gate has a width $($c$)$ of $1\mathrm{.}5$ metres and a height $($a$)$ of $1\mathrm{.}2$

metres, as shown in the elevation below. The distance $($H$)$ from the top of gate to free surface

of the fluid is $5\mathrm{.}5$ metres.

$($a$)$ Determine the surface area of the triangular gate $($in m$2)$

$($b$)$: Determine the vertical distance $($in metres$)$ from the area centroid of the gate to the free surface

of the fluid.

$($c$)$: Determine the magnitude of the fluid pressure force $($in kilo$-$newtons$)$ acting on the gate.

$($d$)$: State the angle $($in degrees$)$ between the vertical gate and the force.

$($e$)$: Determine the second moment of area $($in m$4)$ of the gate needed to locate the fluid pressure force

relative to the free surface.

$($f$)$: Determine the vertical location $($in meters$)$ of the fluid pressure force below the free surface.

$($g$)$: Determine the minimum moment $($in kN$.$m$)$ that must be applied to open the gate into the fluid

$($assume anticlockwise is positive$).$

ANSWERS:

a$)0\mathrm{.}9000$

b$)6\mathrm{.}300$

c$)55\mathrm{.}62$

d$)90\mathrm{.}00$

e$)0\mathrm{.}0720$

f$)6\mathrm{.}313$

g$)21\mathrm{.}54$

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