Force between two gates where they touch in a canal lock.

[powerr3]

Homework Statement

The attached plan view of a pair of lock gates. Each gate is supported on hinges at the edge of the channel. The gates are retaining 2m depth of water on the hatched side. What is the contact force between the gates where they touch in the middle? Density of water = 1000kg/m^3

Homework Equations

Pa = ρgh
Pa=Force/Area
Moment on each hinge = Fv*dh + Fh*dv

The Attempt at a Solution

Pa = ρgh = 19620Pa
F = PA = 94176N
Moment on each hinge = 14.2kNm
Thats all I got. I don't know how to get the contact force, and I'm not sure if what I've done is right. Any help would be great!

 

[mfb]

You should explain the formulas you use.

Moment on each hinge = Fv*dh + Fh*dv

If that is supposed to mean horizontal and vertical, I would not use this approach. Which forces are acting on the gates? In which directions do they point?

Pa = ρgh = 19620Pa

What did you use for h here? Is the pressure the same everywhere? If not, at which point do you have this pressure? Can you get any meaningful force with F=PA then?

Moment on each hinge = 14.2kNm

How did you calculate that?

 

[SteamKing]

If you want to find the contact force where the gates come together, draw a free body diagram of one gate. The contact force must be sufficient to keep the gate in equilibrium.

 

[powerr3]

mfb;
Sorry for the lack of clarity. Yes I do mean Horizontal and Vertical. I chose this method and resolved the force of the water acting on the gate, so the pressure and Force I found in the first two equations is the average acting on the gate.
I used 2m for h as the question wasn't clear whether the gate was fully submerged or not.
I think my approach is wrong in general.

SteamKing:
For equilibrium, the contact force goes towards the meeting point of the gates, but what is my opposite force? More guidance would be life saving!

 

[powerr3]

SteamKing: Is my answer for Force of water correct? and do I apply that to my free body diagram?

 

[mfb]

so the pressure and Force I found in the first two equations is the average acting on the gate.

They are not.

I used 2m for h as the question wasn't clear whether the gate was fully submerged or not.

The water goes from 0m depth to 2m depth.

I think my approach is wrong in general.

I would not split it in horizontal and vertical forces, that just makes calculations more complicated. But torque around the hinges is the right approach.

but what is my opposite force?

The water, of course. No, your answer there is not correct.

 

[powerr3]

mfb: How do I find the Torque when I don't know the applied force (which Is what I am looking for?)

 

[SteamKing]

SteamKing: Is my answer for Force of water correct? and do I apply that to my free body diagram?

You should draw a separate diagram showing of a vertical section of the gate. The pressure you calculated in the OP is the the hydrostatic pressure at a depth of 2 meters. What is the pressure at a depth of 0 m? What's the average pressure on the gate?