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this is a picture from my textbook, Resnick halliday

I have a few questions:

  1. At any point inside a fluid like a gas, the net force is zero although the pressure is not. If this is true it should mean that if I place a surface( with no thickness) at some point in the fluid, there will be no net force on it. Am I wrong here?
  2. Why in the book does it say that there is a net average force on the front and back surface of the cylindrical volume element they have considered? As the volume element enters the high-pressure region don't both sides of the front face experience equal and opposite force so the net force is zero and same applies the rear face, so why is there an average force? ( Right bottom of the image I provided shows that they have considered a net force on each of the two faces and also in the first paragraph they state it explicitly.)
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  • $\begingroup$ In the 2nd question, isn't there a pressure gradient due to "moving air"? $\endgroup$ – Samuel Weir Mar 30 '19 at 0:07
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In the first case, you are doing a force balance on an interface that has no mass; the pressure on one side of the interface is the same as the pressure on the other side of the interface; so there is no net force on it.

In the case of the cylindrical slug of fluid, you are doing a force balance on the slug of fluid, and not on an interface. When you do a force balance on a slug of fluid (or any other body for that matter), you only include the forces acting on the slug or body, not the reaction forces that it exerts on adjacent bodies. So you only include the pressure forces from the side of the interface away from the fluid slug, not the (reaction) pressure forces exerted by the fluid on its side of the interface.

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  • $\begingroup$ I understand that if I consider a certain solid volume one must only consider the forces acting on it's surface from outside. But if you read the text in the image i provided they say the net average force on the trialing surface is pA, but this surface was out side the high pressure region and there was no pressure gradient across this surface and also the pressure on both sides of the surface was p, so force on two sides of this surface are equal and opposite, so how is there a net force? $\endgroup$ – Lucifer Mar 30 '19 at 3:56
  • $\begingroup$ They are not determining the net force on the surface. They are determining the net force on the slug of fluid. The force exerted on the slug by the fluid behind it is +pA. The force exerted on the slug by the fluid ahead of it is $-(p+\Delta p)A$. So the net force exerted on the slug is $-A\Delta p$. The pressure is changing with distance along the pipe. $\endgroup$ – Chet Miller Mar 30 '19 at 12:09
  • $\begingroup$ I understand it now $\endgroup$ – Lucifer Mar 30 '19 at 12:49

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