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

1. Apr 18, 2014

### powerr3

1. The problem statement, all variables and given/known data
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

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

3. 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 Ive done is right. Any help would be great!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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2. Apr 18, 2014

### Staff: Mentor

You should explain the formulas you use.
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?
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?
How did you calculate that?

3. Apr 18, 2014

### SteamKing

Staff Emeritus
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.

4. Apr 18, 2014

### 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!

5. Apr 18, 2014

### powerr3

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

6. Apr 18, 2014

### Staff: Mentor

They are not.
The water goes from 0m depth to 2m depth.
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.

7. Apr 18, 2014

### powerr3

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

8. Apr 18, 2014

### SteamKing

Staff Emeritus
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?