What is Pressure and surface tension in fluids

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Today I was speaking with a professor and he asked me, regarding fluids, what is pressure. I said force per unit area acting normal to a surface. He then asked what I meant by surface. I wasn't really sure how to respond.

He also asked me what surface tension was. I said it is a force per unit length between molecules, like a cohesive force and that if we are given a square surface, surface tension acts to pull the sides of the square, ultimately minimizing surface energy.

He then said the explanation he was looking for referred to cuts through a control volume, and whether pressure and surface tension depended on such cuts. Can someone finesse all of what I've said, whether I'm right or wrong, and explain the cuts he was referring to?
 
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I'm not a fluid specialist (as are @Chestermiller and @boneh3ad), but I think that the point the professor was trying to get you to see is that pressure exists everywhere inside a fluid, while your answer involved a surface.
 
Yeah, I was thinking he might have been looking for the surface to be real or virtual, located anywhere in the fluid and spun in all 3 axes, thus providing pressure at every point and in all directions.
 
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Any ideas anyone? If not I'll stop posting on this thread.
 
joshmccraney said:
Any ideas anyone? If not I'll stop posting on this thread.
Huh? You posted this thread three weeks ago and got some responses. Did you not see them?
 
Yea sorry, I totally missed the above two comments. Thanks!