# Tension along a curved surface [closed]

I'm curious what the tension in a rope will be when its exposed to a uniform load. Assuming a similar setup to this question what will the tension along the rope/tube be?

• Can you explain what you mean by "differential pressure" on a rope? Is this a hollow pressurized tube? I can't see the connection with the linked question. Please clarify. Jun 30, 2015 at 19:01
• @Floris I mean that there is a pressure difference above the tube and below. like in the question linked. I linked the question as the setup is identical but instead of load I'm looking for Tension Jun 30, 2015 at 19:47

## 1 Answer

When there is a pressure difference across a rope (or a "uniform load" of some kind) then the tension in the rope has to be such that the net force perpendicular to the rope exactly cancels the force. For this, the rope needs to be bent, and the combination of the radius of curvature and the tension gives you the net force according to this diagram (from the link given below):

A full derivation can be found at hundreds of links - for example this one

In a diagram like this, there is a change in tension between A and B - the horizontal component has to be the same, but since the angle changes, the vertical component must change, and so does the total tension. The net vertical force is the difference between the vertical forces on the left and the right.

Without a more detailed description of your problem it is hard to give you a more specific answer.

• Thanks Floris. I think I can figure out the rest from there Jun 30, 2015 at 20:10