How can the required force to open the gate be calculated?

[St3ph3n]

Hi, I need help with a fluid mechanics question:

A 1.5m-diameter floodgate placed vertically is 6m below the water level at it's
highest point. The gate is hinged at the top and opens into the
reservoir. Calculate the required horizontal force applied at the bottom of the gate
in order to open it when the pressure on the other side of the gate in the outflow
pipe is sub-atmospheric at -5m gauge pressure head.

The equations I used are:

F = ρgh_gA to calculate the magnitude of the force acting on the outside of the gate

h_p = [(I_G)/(h_gA)]+h_g to calculate at what depth the force acts.

I am able to calculate the force acting on the reservoir side of the gate to be 34.65KN and also where it acts to be 4.51m, using the above equations. After that however I'm lost. I know I probably have to take moments around the hinge using the above data to eventually calculate the required force but I'm not quite sure as how to go about that.

Any help would be greatly appreciated :)

 

[LawrenceC]

Like you said, sum the moments about the hinge. A moment(torque) is force times distance. On one side you have the water pressure. It's moment about the hinge is its force multiplied by the distance the center of pressure is from the hinge. Because there is a slight vacuum on the other side, the vacuum also contributes to the moment in that direction. These moments are opposed by a force you are to calculate that it is represented by the force multiplied by the diameter. When equated there is one unknown, namely, the force you seek.