What is the pressure force on the gate at point A?

[Bluestribute]

Homework Statement

The following shows a cross section through a tank with a rectangular sloping gate that is 10 m long and 4 m wide (width is measured into the page). The gate is hinged along its top edge and held closed by a force at its bottom edge at A that acts perpendicular to Gate AB. Friction in the hinge and the weight of the gate can be neglected.

What is the pressure at A?

Homework Equations

?

The Attempt at a Solution

So I had the flu for this and don't quite know where to begin. I know you need to solve for pressure, but the way you do that is very confusing. I know it also involved centroids (I think at least) so I can apply what I'm learning about that (here) once I know what equations and theories to use for water pressure.

 

[haruspex]

The image won't display, and the description doesn't seem to have enough info. Is there liquid in the tank? If so, to what depth? If no liquid, what is providing pressure?

 

[Bluestribute]

That better? Might have been some extension problems (but yes, filled with water, bottom right corner is a straight line through, making essentially a "triangle cut")

 

[haruspex]

That better? Might have been some extension problems (but yes, filled with water, bottom right corner is a straight line through, making essentially a "triangle cut")

Yes, that worked.
Finding the pressure at A is fairly trivial. No need to consider the gate etc., just the tank and the depth of water in it.
Are you sure it's not asking for the force applied to hold the gate shut? Or maybe that's a later part of the question?

 

[Bluestribute]

It is a multi part question with force coming later, yes. But I'm about 50% on finding pressure. I know it involves like γh and stuff, but I can't find anything where someone just up and writes what each number represents and how to use them to find the pressure. So there's always weird dimensions floating around with no explanation as to why.

 

[haruspex]

It is a multi part question with force coming later, yes. But I'm about 50% on finding pressure. I know it involves like γh and stuff, but I can't find anything where someone just up and writes what each number represents and how to use them to find the pressure. So there's always weird dimensions floating around with no explanation as to why.

Then maybe it's best if you post a link to a site that you can't understand and I lead you through it.

 

[Bluestribute]

This problem is actually a practice final I'm working on. That's all the info it gives. I've attached a slide I was looking at too. I understand the 62.4, I understand taking the moment, I understand taking area of something, but there's dimensions thrown in without labels that's confusing me. Like, where do they belong in the equation for water pressure?

 

[nasu]

You should read about hydro-static pressure and then try again the first question.
For the first question you need only the formula for hydro-static pressure.

 

[Bluestribute]

Ok. So, ρgh. This is in meters, so it's (1000)(9.81)(12.5). 1000 kg/m³, gravity constant, and it's 12.5 meters high. Check. Point B (next question) is 73575 N/m². In the calculator it goes.

Question 3 (still finding water pressure so I feel it still fits in this thread),
What is the total hydrostatic force acting on the gate?

 

[Chestermiller]

OK, so now you know the pressure at points A and B, and you can use the same approach to get the pressure at any other location in-between points A and B. You are aware that the pressure acts perpendicular to the gate, correct? With this knowledge, what is the magnitude of the pressure force on the gate, and, in what direction does it act?

Chet