Fluids Mechanics Problem

• St3ph3n
In summary, the conversation is about calculating the required horizontal force to open a 1.5m-diameter floodgate hinged at the top and placed vertically in a reservoir, with a sub-atmospheric pressure of -5m on the outflow pipe. The force and depth of the force acting on the reservoir side of the gate are calculated, and the next step is to sum the moments about the hinge to find the required force. The moment of the water pressure and slight vacuum on the other side are opposed by the force of the gate multiplied by its diameter, resulting in one unknown force to 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 = ρghgA to calculate the magnitude of the force acting on the outside of the gate

hp = [(IG)/(hgA)]+hg 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 :)

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.