# Direction of pressure forces on a control volume (surface)

According to http://www.mne.psu.edu/cimbala/Learning/Fluid/Pressure/pressure_basics.htm, "Pressure always acts inward normal to any surface (even imaginary surfaces as in a control volume).".

Following the above definition and considering a control volume in a tube with water, as shown below, the pressure acts in the opposite direction of the velocity on the right side of the control surface. Could someone please explain why this makes sense? If you were to place your hand on this end of the control surface, you would certainly say that the water pushes your hand to the right, right?

I have also seen an explanation for this. On page 31 in Advanced Transport Phenomena: Analysis, Modeling, and Computations by P. A. Ramachandran, it says that "Note that the pressure forces are compressive and act inwards on the control volume." However, I do not understand the logic behind this in my example with water in a tube. To me, the pressure is trying to expand the control volume on the right side of the control surface and is trying to compress it on the left side.

It's a good question . I also got confused when i studied it in fluid mechanics and static tube . I think you will get the answer if you visit https://en.wikipedia.org/wiki/Pressure#Liquid_pressure the part of (Direction of liquid pressure)

Check Newton's third law: For every action there is an equal and opposite reaction.

You push on the right, and the fluid pushes on you.

Of course, in a control volume, fluid can move across the surface, but there is still equal and opposite pressure on both sides.

Unless there isn't, in which case the fluid accelerates (changes velocity), but you're not talking about that.

• Thanks for your answer @MikeDunlavey, but why is the pressure force acting inward on the control volume? Jun 23, 2015 at 16:31
• @FredikLAa: To help you understand, 1) assume the velocity is 0, and 2) assume the volume is a cylinder with a piston on the right. The fluid is pushing out, and to keep it in place, the piston is pushing in. Then, convince yourself the velocity doesn't matter - i.e. there can be leakage in the left and out the right, and it doesn't change anything. Jun 24, 2015 at 13:40

Are you saying the fluid is pulled on right side and pushed from left side! Pressure is always compressive. The flow is taking place from left to right because compressive pressure on left side is more than that at right.

• Thanks for your answer @imgodsparticle. Could you please elaborate? What causes the "compressive" pressure to act toward the left on the right hand side? Jun 23, 2015 at 16:30