# What is fluid pressure?

I cannot understand the concept of fluid pressure.

Consider a liquid molecule at some point inside a liquid vessel. All the other molecules which are in contact with this molecule will exert normal force upon this molecule. So, this liquid molecule experiences zero net force. If there is no force on the liquid molecule, there will be no pressure because

pressure=magnitude of net force on the area/ area of the surface

If the net force is zero, how will a pressure be exerted at all? Then how does the concept of fluid pressure comes into picture?

• More on definition of pressure. – Qmechanic Feb 17 '17 at 7:13
• "If the net force is zero, how will a pressure be exerted at all?" - OK, let's imagine that you're on a field with big, giant football players pushing on you from all sides. You're not moving in any direction because these very huge forces which are squeezing you on all sides all balance out so that the net force on you is zero. Do you understand now how there can be large pressures acting on an object even if the net force on it is zero? – Samuel Weir Feb 17 '17 at 7:30
• That molecule is also pushing all the molecules around it just like they are pushing it. The pressure is like all the molecules being bunched tight. Its like people bwing squeezed in a space. Just like the people around you squeeze into you, you squeeze into the people around you as well. – JMac Feb 17 '17 at 10:50
• Id also like to mention that fluid pressure is a result of intermolecular forces (bonding, etc), not particle collisions like in gases. By nature of the fluid existing on earth, gravity will pull all the particles down, but they really, really dont want to compress so the bonds are stressed, giving rise to pressure due to gravity. Liquid pressure always behaves like a bunch of ultra strong springs - they compress, but they dont want to. But with all molecules looking in any direction for a way to release the potential energy, hence pressure exists in all directions. – Sam Gallagher Mar 20 '18 at 14:15
• If you place a book on a table, the book is experiencing a normal force from the table (a pressure acting over an area). The table is experiencing an equal but opposite firce from the book. But an action-reaction pair does not constitute no net force on either body. When considering force equilibrium on a body, you only include forces acting in that body, not forces that it exerts on other bodies. – Chet Miller Jun 25 '18 at 2:22

Consider a vessel filled with liquid of density d Lets take two points A and B such that A is x distance below the surface and B is x+h below the surface.

Now consider a cylinder of fluid with ends A and B and area of crossection A'.

This cylinder is in equilibrium hence the forces must balance out hence

$A'(Pb - Pa) = mg = A'hdg$ $Pb = Pa + hdg$

That is the pressure difference between the points.

The example that you gave was basically a cylinder of A' = 0 and h = 0 hence the pressure difference was also zero.

You can clearly see that its the force of $mg$ downwards that actually leads to a pressure difference and thus pressure is simply a consequence of gravity on a fluid.

• So, this pressure resulting from mg is called fluid pressure? – Arishta Feb 17 '17 at 5:54
• Yes that is indeed fluid pressure – Rishabh Feb 17 '17 at 5:55
• My textbook says that the fluid pressure is due to the contact forces by the neighbouring particles. How do you explain that? – Arishta Feb 17 '17 at 7:14
• The object in the fluid is EXCLUDING other particles from its volume, and it does this by exerting an equal and opposite force to all incident forces, as Newton's law prescribes. – Whit3rd Feb 17 '17 at 8:12
• @TausifHossain Suppose the incompressible fluid is inside a cylinder and I squeeze down on the fluid with a piston. Do you still think the pressure must be negligible without gravity? Or the incompressible fluid does not fill the container, and I force compressible gas into the container at 1 GPa. – Chet Miller Oct 9 '18 at 23:59