The Concept of Pressure in Bernoulli’s principle

[tasveerk]

Hello,
I am somewhat confused about the concept of pressure in Bernoulli’s principle, which states that velocity and pressure are inversely related. When I think of pressure, I think that there is higher pressure acting on a liquid when a pipe is smaller rather than larger. I would appreciate it if someone could explain what sort of pressure is this principle referring to.
Thanks!

 

[PhysicoRaj]

velocity and pressure are inversely related. When I think of pressure
what sort of pressure is this principle referring to.

Hi,
The pressure is exerted by the constituent molecules of the liquid on the walls of the pipe or other material in it. If the velocity is greater the pressure FROM THE FLOWING FLUID is lesser and vice versa.

 

[rcgldr]

When I think of pressure, I think that there is higher pressure acting on a liquid when a pipe is smaller rather than larger.

This is true in the case where there is a limited power source (as opposed to unlimited) driving the fluid through the pipe, such as the water in a hose from a fully open tap at your home. The pressure in the hose will be greater if the flow is restricted due to some constriction in the hose rather than letting the water nearly freely flowing through an unrestricted hose.

What Bernoulli principle is getting at is what happens to the fluid as it travels through a constriction in a pipe. The mass flow (kilograms per second) through any cross section of the pipe is constant or otherwise mass would be accumulating. Since the mass flow is constant, the velocity of the flow must be greater in narrower sections of the pipe. Since the pipe doesn't generate any forces that increase the fluid's velocity, the only remaining explanation is that a pressure differential within the fluid itself is responsible for the increase in velocity in the narrower sections of a pipe. This in turn means that the pressure in the narrower section of pipe must be less than the wider section of pipe leading into the narrower section of pipe.

Another term used for this reduction of pressure in a narrowing pipe is Venturi effect. It's used in carburetors (for engines that still use these), to assist in drawing fuel into the air stream. Wiki link:

http://en.wikipedia.org/wiki/Venturi_effect

 

[russ_watters]

Part of the confusion here is due to the fact that there is more than one type of pressure and people/articles are often sloppy about which they are referring to. Often when people say "pressure" they are referring to static pressure. But there is also velocity pressure and total pressure. In Bernoulli's equation, when velocity increases, velocity pressure increases and static pressure decreases, while total pressure remains constant.

 

[cmb]

Pressure is a measure of potential energy stored, per unit volume measured in J/m^3.

Now consider what Bernoulli says - all he says is that when a fluid gains kinetic energy it must loose some pressure energy, and/or vice versa, because energy cannot be created or disappeared in a smooth, lossless, fluid flow.

That's all Bernoulli's equation says. It states that the sum of pressure and kinetic energy of a fluid flow remains constant.