View Full Version : How can pressure and velocity be inversely related in fluid flow as per bernoullie?

Dec 20, 2010, 02:52 AM
We know Force F is directly proportional to pressure and to change in velocity w.r.t to time as per Newton 2nd law then how can pressure and velocity can be inversely proportional during fluid flow

Dec 20, 2010, 07:44 PM
You're right that force is directly proportional to pressure, and to acceleration, when dealing with Newtonian mechanics (like for ballistics or things running into each other and transferring momentum, etc). If you were to observe at fluid at the microscopic level, looking at the trajectories and collisions and momenta of all the molecules that make it up, you'd find that Newton's laws are upheld.

However, it's not practical to model a fluid as a massive group of individual molecules. Instead, fluid dynamics is used to describe the macroscopic behavior of entire systems of molecules. Rather than keeping track of every single molecule, fluid dynamics can be used to describe their average behavior, with parameters like temperature, pressure, or mean velocity.

So why would fluids have completely opposite behavior from solids w.r.t. the relationship between pressure and velocity? They don't! As a matter of fact, if you're talking about a fluid flowing into or striking an object, it will exert a force or pressure in much the same way as if it was solid. For example, if you stick a paddle in a fast-flowing river, the water will exert force on the paddle. The faster the current is moving, the more force it will exert. This is exactly analogous to Newton's laws.

So what's this whole pressure and velocity are inversely proportional thing? That's when the fluid is flowing parallel to an object, not against it! There's not really an analog to this in Newtonian mechanics, because if two objects happen to travel past each other without hitting, there's no effect. They just pass right on by and go merrily about their separate ways.

In the case of fluid flow, however, just because the fluid is traveling parallel to an object on average, that doesn't mean that every single molecule in the fluid is traveling in the same direction. Quite the contrary, there are still many, many molecules that strike the surface of the object and impart some of their momentum onto it. As I'm sure you know, the average force of all these molecules over a unit area is called pressure. The faster the fluid flows, however, the higher the proportion of the total energy that's directed parallel to the surface, rather than perpendicular. The net result is that faster parallel velocity of the fluid means less of the molecules' inertia is directed toward the object, so the pressure on the object decreases. This phenomenon was first described by Bernoulli, and is the principle by which airplanes fly, among many, many other things.

There's a pretty decent intuitive explanation of Bernoulli's Principle here (http://home.earthlink.net/~mmc1919/venturi_discuss_nomath.html), along with a link to a more advanced discussion deriving the principle using conservation of energy.

I hope that helps!

Anwar Ansari
Jun 25, 2012, 02:23 AM
Pressure and velocity are inversely proportional.
As ,
assuming flow to be constant , if we reduce the area then velocity has to increase to accommodate constant flow. From this it is clear that if area reduces then velocity increases. Now take an example

suppose P1- 5.0 bar and V1 - 2.0 m/s in pipe and suddenly pipe connverges and let P2 - ? And velocity V2- 3 m/s as we know that velocity has to increase to accommodate the flow as discussed above. From bernoullis equation you will find that pressure P2 come out to be approx. 2.5 bar.That is with increase in velocity pressure got decrease.

Jan 1, 2013, 03:32 PM
@ jcaron2:- Your description is simply outstanding. Clearly proves that you have understood the concept very well.

Feb 5, 2013, 09:54 PM
What is the effect of magnetic field on fluid flow through porous medium if conductive fluid is injected from one side of it?