Question $2$

Figure $2$ shows a control gate in a channel of $3$ m width. The maximum water depth is $6$ m $,$ the same as the gate radius. The water density is $1000k\frac{g}{m^3}.$ The centre of gravity of the water above the gate is shown in the figure as CG$.$ At the maximum water depth,

a$)$ Calculate the horizontal pressure force on the gate.

b$)$ The vertical pressure force on the gate is equal to the weight of $($imaginary$)$ water occupying the space above the gate curvature $($shaded grey area$)$ but acts in the upward direction. Consider the pressure distribution on the curved surface and explain why. Use sketch as appropriate.

c$)$ According to $($b$),$ calculate the vertical pressure force on the gate.

d$)$ Calculate the moments due to the horizontal and vertical forces calculated in $($a$)$ and $($c$)$ above, and thus determine the minimum external torque $($moment$)$ needed to hold the gate in place.

Figure $2.$ For Question $2$

Answers:

a$)529740$N

c$)832112$N

d$)$Horizontal force Fx acts clockwise:Mx$=529740$ x $4=2\mathrm{.}12$MNm

Vertical force Fy acts anti$-$clockwise:My$=-832112$x$2\mathrm{.}55=2\mathrm{.}12$MNm

The net moment$=$Mx$+$My$=0$ no net moment.