How Do You Calculate the Depth in This Hydrostatics Problem?

[ceulmad]

Please HELP! Hydrostatics Problem

Hi,

I am really desperate and need help with the following problem in hydroststics.

take a look at the picture:

http://www.moncton.net/banners/statics.gif

the answer is 0.955 meters. I have no idea how they arrived at that answer. Pleeeease HELP!

THANKS SOOOO MUCH!

 

[radou]

I'm not sure I can help much here, but you should start with calculating the torques of the weight of the gate and the torque of the resulting hydrostatic pressure force around a wisely chosen point.

 

[ceulmad]

I'm not sure I can help much here, but you should start with calculating the torques of the weight of the gate and the torque of the resulting hydrostatic pressure force around a wisely chosen point.

thanks for the advice, I have done that. What point are your referring to?

 

[radou]

thanks for the advice, I have done that. What point are your referring to?

The point where the hinge of the gate is placed wouldn't be a bad idea.

 

[ceulmad]

The point where the hinge of the gate is placed wouldn't be a bad idea.

So fine, I can calculate the Moment about that point for the 4000kg force (4000*9.81*1.6)
but then what?

i realize that there must be a reacting moment pushing in the opposite direction. But at what location?

 

[radou]

i realize that there must be a reacting moment pushing in the opposite direction. But at what location?

The other moment is the one produced by the resulting force of the hydrostatic pressure, as already mentioned. This resultant force acts at the center of the gate and it 'tries' to open the gate. By setting the sum of these moments equal zero with respect to the mentioned point, you are expressing a condition of equilibrium, i.e. you can find a boundary expression for the height h, since the equation includes the hydrostatic pressure.

 

[ceulmad]

The other moment is the one produced by the resulting force of the hydrostatic pressure, as already mentioned. This resultant force acts at the center of the gate and it 'tries' to open the gate. By setting the sum of these moments equal zero with respect to the mentioned point, you are expressing a condition of equilibrium, i.e. you can find a boundary expression for the height h, since the equation includes the hydrostatic pressure.

again, thanks for your help, bu tthis is what i have been doign all along. Its just I can't get 0.955m to be my answer. Can you try to crunch these numbers?

Another ? is why are you saying that the resulting moment is in the center of the gate? The centroid of pressure is 1/3 from the bottom usually?

 

[radou]

Another ? is why are you saying that the resulting moment is in the center of the gate? The centroid of pressure is 1/3 from the bottom usually?

You're right, my mistake.

I'll look at the answer as soon as I find the time.