A triangular plate ABC is submerged in water with its plane vertical. The side AB is 4m long and is 6m below the water surface while the vertex C is 2m below the surface. Find the force exerted by the water on one side of the plate (density of water is 1000 kg m^3).

I'm looking at it and all I can think is that the answer is 0? Maybe I'm misinterpreting it?

  • $\begingroup$ I believe what you're thinking is that the plate isn't accelerating, therefore the nett force is nought, which is true. The question specifically asks for the force on one side of the plate, which will be balanced by an opposite force on the other side of the plate, thus yielding the zero nett force you are stuck on. $\endgroup$ Commented Dec 7, 2013 at 6:22

1 Answer 1


The question is asking what is the force exerted by the water on either of the two faces of the plate. The net force will be zero as force on either side sides cancel, so your intuition made sense.

The force on a side comes from water pressure across the triangular surface. The pressure at any point on the triangle depends on the depth of that point. There is a simple formula relating water pressure and depth and you'll find that the density comes in handy. Make sure you sketch a diagram of how the triangle sits in the water.

Once you can work out the pressure at any point on the triangle, to get the overall force you need to use the relationship between force and pressure. You need to think about how to sum up all the varying points of pressure over the area of one side.

Don't forget: As you sink, water pressure rises and so does the "amount of plate" at that depth!

For a sanity check: The answer should be between 100 and 500 kN

  • $\begingroup$ Okay, I don't think i've seen that formula before so I'll have a look for it. My diagram is currently just a traingle vertical under the water, the plane of the triangle is parallel to the force of gravity $\endgroup$
    – Carterini
    Commented Dec 6, 2013 at 22:00
  • $\begingroup$ Sorry, I can't find a decent explanation anywhere. I don't even know what i'm searching for to be honest! $\endgroup$
    – Carterini
    Commented Dec 6, 2013 at 22:13
  • $\begingroup$ Try "water pressure + depth". Probably add "physics" as well to avoid the more useless pages! $\endgroup$
    – ejrb
    Commented Dec 6, 2013 at 22:18
  • $\begingroup$ The thing that's confusing me is that plate seems to have no thickness, so the water won't apply a force on the sides. The faces are also perpendicular to the force the water applies due to it's weight so the force on the face is 0? So where does the force come from? $\endgroup$
    – Carterini
    Commented Dec 6, 2013 at 22:21
  • $\begingroup$ By "sides" it means the triangular faces of the plate, not the edges (I was confused about the wording too!). The weight of the plate does not matter: it could be made out of rock or paper - the force will be the same. $\endgroup$
    – ejrb
    Commented Dec 6, 2013 at 22:26

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