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This is a question from a study guide for a military officer exam:

I have fluid flowing through an elbow in a pipe (the elbow is in the shape of an upside down and backwards "J") and the flow goes from south to north to east. If holes are drilled at the upper left outside part of the bend and the lower right inside part of the bend, at which point will pressure be lower? Please see attached image for a picture of the question.

When I have thought about this problem, I keep coming back to pressure being transmitted equally to all parts of a fluid, so I don't understand how the pressure can be different at one of the holes. The book gives the answer as the inside bend which I can force myself to accept since I can picture the fluid attempting to go straight to the outside bend hole and thus hitting that part harder, but I don't really understand it.

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  • $\begingroup$ Would this have anything to do with centripetal acceleration? $\endgroup$
    – atheo8
    Aug 12, 2014 at 16:47
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    $\begingroup$ Actually I take back my earlier comment. After some Googling it appears the pressure is dominated by inertial terms. It's higher on the outside of the bend because that's where the liquid is being forced inwards. See this article and this paper. Note that in figure 2 the inside of the pipe is to the right. $\endgroup$ Aug 12, 2014 at 17:00
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    $\begingroup$ For the close voters, this question seems to me to be as close to a conceptual question as we can get and still be borderline homework. I'd prefer that we leave it open. $\endgroup$ Aug 12, 2014 at 18:08
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    $\begingroup$ A way to think about it is a water slide having curves. Obviously the water will rise up on the outside of each curve (as will the child enjoying the ride). Another thought: isn't this the way those infamous gas centrifuges work? $\endgroup$ Aug 12, 2014 at 18:50
  • $\begingroup$ You have all been very helpful. Thank you all for your inputs. $\endgroup$
    – atheo8
    Aug 16, 2014 at 14:28

3 Answers 3

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When a pipe is bent the outside curve - what would be the longest path through the curve - has the highest pressure and the lowest speed. The inside curve - the shortest path through the curve - has the lowest pressure and the highest speed. In short, when the path of a fluid in steady-state flow bends, the pressure on the outside of the bend is always higher than the pressure on the inside of the bend.

The pressure would be lower on the lower right inside point of the bend.

I could no view that attached image; however, I hope that helped.

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If you imagine the bend portion of the pipe to be a part of a circle, it becomes apparent that there is centripetal force present. As the water travels through the bend, there is a centripetal force that acts inwards towards the centre of the "circle". There must be a reactionary force to this which acts in the opposite direction, in other words the outer wall of the pipe. This reactionary force upon the area of the outer wall causes a higher pressure.

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The same answer as above, but I also happened to have analysis results for this question. Hope this helps, enter image description here

The above image is velocity contour of the cross section of the pipe. Below Image is for Pressure enter image description here

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