Pressure in Bernoulli's Theorem

Question

I am not sure about what does pressure mean in this theorem.Is it the pressure applied by the pipe when the fluid flows in it or something else?Please explain clearly.

Answer 1

The Bernoulli equation links the pressure at one point on a streamline to anther point on the same streamline with some more parameters included.

If there were no viscous forces and the fluid flowed through a horizontal pipe of constant cross sectional area then the pressure at each point along a streamline would be the same as would the mass flow rate through the tube (conservation of mass with no sources or sinks of fluid within the pipe).

Now imagine a situation were the cross-sectional area of the pipe decreased.
If the mass flow rate through the pipe is to be kept constant throughout the pipe then the fluid needs to travel faster and faster as the cross-sectional area of the pipe decreases.

This means that the fluid must be accelerated and a force is required to do this.
The force is provided by a pressure difference along the streamline with the pressure being larger where the fluid is moving slower.

Your derivation of the Bernoulli equation probably was via the conservation of energy where the work done by the force produced by the pressure difference is equated to the increase in kinetic energy of the fluid.

Answer 2

The pressure can't be applied by a pipe. It means the pressure at that end of the pipe, because the pressure difference across the 2 ends of the pipe is what also helps in moving the fluid through it.

Answer 3

I am not sure what image you have in mind when you say "...pressure applied by the pipe...". You may think of it as pressure exerted by pipe walls normal to flow direction. This pressure is also what is recorded by a pressure gauge fitted on pipe wall such that flow does not directly impinge on the sensing element of the pressure gauge. This pressure goes by the name of "static" pressure, as against another kind called stagnation pressure which is the pressure that would result at a point where flow comes to a halt. (Only static pressure appears in Bernoulli equation as it is usually stated.)

Answer 4

Pressure is not something that exists only at a solid surface. It is present throughout the fluid. The small parcels of flowing fluid press on each other at the hypothetical interfaces between them. It is the same as if there were an actual small thin solid surface placed between them.