How Do You Calculate Tension in a Gate Retaining Cable with Water Pressure?

[myheadhurts]

hi guys, i have a problem with mechanical principles. ill write the question here but ill also attatch a word doc with a drawing included. i understand that when posting such questions, an attempt at solution is also expected. that's a bit difficult as i can't seem to fathom where to start with it. so i was wondering if i could get a little help with method rather than numbers and answers?? after all, I am going to get more like this so best understand it too :D anyway here goes;

Water is retained in a 1m wide rectangular section channel by a sluice gate that can pivot about its base, as shown below. Determine the tension in the horizontal retaining cable attached to the top of the gate when the depth of the water in the channel is 1.5m the density of water is 1000kgm.

any help with this guys would be greatly appreciated!

 

[schlunk]

First off, let's break it into parts. Would you be able to figure out the tension if instead of water, you had a generic force pushing at the midway point of the gate?

How about if the force was at some other point besides halfway?

Now, could you figure it out if you had two forces pushing at different points?

So from there, your problem really comes into figuring out how much force does the water present to the gate and where. I would suggest taking a sum of the tension created by an infinite number of forces at an infinite number of points from the bottom to the 1.5m mark. That is to say, I would take an integral. The trick is now figuring out what are the forces that I want to integrate... I'll leave that to you.

(Maybe there is a simpler way, but this is what occurs to me at the moment.)

 

[pongo38]

Can you work out the pressure of water at a depth of 1.5 m? Can you sketch the pressure distribution on the gate? Can you work out the water force trying to open the gate? Can you draw a free body diagram of the gate and put on it all the forces acting? Can you make equilibrium statements about your free body diagram?