Thread: Bernoulli Principle

I have a question about the Bernoulli Principle. The principle states that for an increase in speed of a fluid, a decrease in pressure occurs. Every website I go to simply states what the theorem is but doesn't explain why. My question is....Why does the increase in speed give a decrease in pressure?

It makes more intuitive sense if you imagine persistent pressure in a water pipe and then how opening household fixtures reduces the total pressure. You know what happens when you're taking a shower and some jerk uses the sink. Both sink and shower share this common supply and when the water in that pipe flows faster (to feed two outlets) the pressure drops.

OK, what you said makes sense, but I still don't feel like I completely understand it. I feel like you have just described (or given an example of) the principle in action, but not an explanation of why that decrease in pressure occurred.

Thanks

It's perhaps a little unconventional again but I could imagine very well the flowing liquid applying a drag on the inner surface of the hose or tube all way round while flowing. The same as with such a finger trap.

On a molecular level, the static pressure is an expression of the averaged momentum of molecules striking the container. If a molecule strikes the wall perpendicularly, then say its contribution to pressure is 1.0. If it stikes at an angle of 30 degress its contribution is 1 x cos30, or 0.866.

If the fluid starts moving in one direction the average angle of incidence increases, let’s say to 45 degrees so the cosine decreases to 0.707 and this is reflected in the reduced static pressure.

This is off the top of my head, and it’s my conjecture as to the answer to an interesting question. It may well be wrong.

Molecular analogy: Riot police holding back a crowd. Now, there is pressure in the crowd. Imagine you've wound up in front for some reason. Suppose the police start walking backward. Suppose they turn and run. You may not wish to chase the police at this stage but it's your inertia vs. the crowd's inertia.

This all assumes an open system. Bernoulli principle does too. No pressure change inside a bike tire when you spin it.

But a crowd is analagous to a compressible fluid (gas) since the people (molecules) spread apart when they start to run. Bernoulli's original derivation was for liquids (incompressible), where molecules don't spread out when accelerated. Thus your analogy doesn't actually explain the effect in a liquid.

I think Bunbury has the right explanation on a molecular level.
The Wikipedia article
http://en.wikipedia.org/wiki/Bernoulli%27s_principle
Says

Bernoulli's principle is equivalent to the principle of conservation of energy. This states that in a steady flow the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy and potential energy remain constant.

If that doesn't help, maybe you could think of a tank of water, which has a certain amount of potential energy. If you punch a hole near the bottom of the tank, a stream of water runs out at zero (gage) pressure. The potential energy is converted to kinetic and the water loses pressure.

And you don't need an open system to demonstrate the Bernoulli principle.

Take a closed pipe with a constriction and a fluid flowing through it. At the point of the constriction the fluid will have a greater speed and a lower pressure.

Originally Posted by SteveC

I have a question about the Bernoulli Principle. The principle states that for an increase in speed of a fluid, a decrease in pressure occurs. Every website I go to simply states what the theorem is but doesn't explain why. My question is....Why does the increase in speed give a decrease in pressure?

This used to be a well known principle. It was used in the older kerosene lanterns, to inject a stream of kerosene into the throiated cloth bag.

It is also a dangerous accident. If you have a container of gasoline and the gasoline has other substances in it, that either contain water or are known to pick up water from the atmosphere. Substances like alcohols, either dry gas or some other chemical now used. Also oils may pick up water, especially when contaminated by salts, or chemicals.

When a container of gasoline like this has a very small opening in it. Like a pin hole. If the fumes that are escaping the tank are lit. This tiny hole allows for high velocity two way travel in and out of the tank. If the tank is sturdy, it can cause an explosion that most would not believe. Because it creates a laser like beam that disassembles the chemicals in the tank. Resulting in super heat and pressure within.

If it is a flimsy tank it will probably just pop the tank violently, and spill the ignited fuel all over.

People used to lose their fingers while putting down the Formica on the old rounded Formica tops, using the old style lanterns, when the fuel would become contaminated with water.

Some night spear fishermen as well have probably run into this too. I used to use "White Water" brand kerosene to go spear fishing at night. We knew not to use it, if it was contaminated, old, or was in a rusted can.

There is always a danger of those lanterns blowing up. Because on a humid day the tank can continuously suck in gases that have mixed with outside air. Even on a dry day this could occur. Especially if oxygen content is high.


Take a look at this video, and the effect of water upon hot aromatic hydrocarbons.

http://www.Rockwelder.com/WMV/KitchenOilFire.wmv

Water is 8:1 by weight oxygen over hydrogen.

I have experimented with aromatic hydrocarbons and you can see that without oxygen even when hot, they only create a yellow flame.

http://www.Rockwelder.com/WMV/hydrocarbonburn.wmv


http://www.Rockwelder.com/Explosives/pipepock.wmv

These are the individual frames from the pop.









Sincerely,


William McCormick

William, what in Pan's name does any of this have to do with the OP? You just can't help yourself, can you?

Originally Posted by Janus

And you don't need an open system to demonstrate the Bernoulli principle.

Take a closed pipe with a constriction and a fluid flowing through it. At the point of the constriction the fluid will have a greater speed and a lower pressure.

That's the ideal demo.

...but the pipe is open at either end of the Principle, or fluid wouldn't be flowing. Systems are only closed theoretically, where convenient to imagine them so.

Originally Posted by KALSTER

William, what in Pan's name does any of this have to do with the OP? You just can't help yourself, can you?

Who's Pan?

But more important, what I was discussing is a common misunderstanding of that principle.

I think if more individuals understood this I would be helping myself.

This effect is also used in refrigeration. The reduction of pressure on the outlet side of a narrow venturi, or as we call it in refrigeration the expansion valve, creates the cooling effect in the evaporator coils of the system.

You can also use standard 90 psi air pressure to freeze below freezing, and heat above cherry red, a venturi, that on one side, gets hot, and on the other side it gets cold.

What I was talking about though with the gas tanks and pin holes. Or lanterns and torches is a real issue, that is not taught in college. Or understood in most cases. I know I have worked with college engineers. And only those engineers that have worked in garage mechanic type places would understand this.

I was talking to a compressor shop owner and friend of mine. And he went out to a shop just recently and almost got into a quarrel with someone. Because my compressor friend knew exactly why the fellow at the high pressure paint ball shops tank blew up.

The fellow at the paint ball shop did not like why it blew up. And protested that he had been filling tanks like that for years. And the compressor shop owner told him that he had been very lucky for years. The fellow got angry. Because he no longer liked where he worked or his misunderstanding of oxygen under high pressure. Even if it is in the form of CO2, there is oxygen ready to react. And Carbon ready to burn.

The fellow said that he had been filling this tank that blew and that it had CO2 in it previously. He said he was filling them with high pressure air, without vacuuming them out. And had been for years and never had a problem. He had all the right filters and oil removal stuff in his pumping system. But the tanks he was filling were old CO2 tanks and evidently they do not like the rather sudden high pressure. Or slight oil contamination in the lines on the valve.

There is also a massive amount of heat released when you first pressurize the line. And a massive amount of cooling as the fluid enters the venturi. This can add to the rather violent effects. Even the carbon in CO2 can detonate and release massive metal melting heat.

Also ARC can occur between such different temperatures in close proximity. An actual electrical arc can occur, when electrons are so abundant on the hot side and so scarce on the cold side. This can lead to the cold side creating an arc against the flow of electrons from the hot side.

High pressure gases are a mean business.



Sincerely,


William McCormick

Originally Posted by Pong

...but the pipe is open at either end of the Principle, or fluid wouldn't be flowing. Systems are only closed theoretically, where convenient to imagine them so.

Well, we often pump water around in a closed loop, and the Bernoulli principle does apply wherever there is a flow restriction or a change to the pipe size.

Originally Posted by Harold14370

Originally Posted by Pong

...but the pipe is open at either end of the Principle, or fluid wouldn't be flowing. Systems are only closed theoretically, where convenient to imagine them so.

Well, we often pump water around in a closed loop, and the Bernoulli principle does apply wherever there is a flow restriction or a change to the pipe size.

I'm being dogmatic and difficult. I'll stop.

The Bernoulli principle is built on the laws of conservation of energy and momentum. It says that the total work done on the fluid is constant, and therefore takes the form:



is called the dynamic pressure, and represents the kinetic energy of the fluid due to the actual external forces acting on it i.e. the flow.

is the gravitational potential energy, taking into account any change in height of the flow.

P is the static pressure and represents the pressure of the fluid excluding the kinetic energy due to the actual flow i.e. the dynamic pressure. For example, for a flow through a pipe, the static pressure would be the pressure felt over the wall of the pipe. Even though the fluid is flowing parallel to it, and therefore is not contributing any kinetic energy from the flow (dynamic pressure), it still does contribute some kinetic energy as static pressure, just like a canister of pressurized gas.


It's accurate for incompressible streamlined flow, but applies intuitively to other flows too.

If the velocity increases, the dynamic pressure increases, and for a constant height, this must mean that the static pressure has to decrease since the energy must remain constant. The Venturi meter and Pitot-static tube both use this effect to measure the velocity of a fluid (An airplanes airspeed for example):

http://en.wikipedia.org/wiki/Pitot_tube
http://en.wikipedia.org/wiki/Venturi_meter

This effect is also used in refrigeration.

That would be the Joule-Thompson effect not the Bernoulli principle.

Bunbury's explanation made sense to me on a molecular level. If all the particles in a pipe are traveling through it very quickly in one direction, none will be imparting significant forces on the side of the pipe. If the particles are not flowing (but still under some pressure) more will hit the outside of the pipe perpendicularly. Grazing the side of a pipe (happens with a rapid flow) will definetly impart less force on the pipes walls because the particles are going through it, not smacking into it.

That sounds like a pretty solid explanation to me concerning pipes, however, if we try to visualize what happens with an airplane wing, i get confused because the air is not constricted inside a pipe.

My hypothesis concerning airplane wings would be that when the air particles encounter the curved top surface, they get whipped through faster, and in the process, spread out. The spreading out would be the only thing that could contribute to lower pressure. Thats all I can think of with that situation.

The Bernoulli equation isn't directly applicable to lift over a wing. The principle has some intuitive meaning in one factor of lift generation....that is the air over the top of the wing moves at a faster velocity (see longer path explanation) than the air going under, so that the static pressure over the lower surface is greater than that over the upper surface. But also, downwash contributes greatly towards lift being generated, forcing fluid downwards as it leaves the wing.

The bernoulli principle provides some good insight into fluid dynamics, and in a few cases the equation can be accurately used, but most of the time, analysing things like lift on an aircraft wing is alot more complicated, due to the large number of variables. The bernoulli equation is by no means the 'be all and end all' of fluid dynamics laws.

In case you are looking into some aerodynamics, most analysis now is done by CFD simulations, or pre-tested airfoil sections and data are available from NACA.

Originally Posted by bit4bit

The Bernoulli equation isn't directly applicable to lift over a wing. The principle has some intuitive meaning in one factor of lift generation....that is the air over the top of the wing moves at a faster velocity (see longer path explanation) than the air going under, so that the static pressure over the lower surface is greater than that over the upper surface. But also, downwash contributes greatly towards lift being generated, forcing fluid downwards as it leaves the wing.
...
In case you are looking into some aerodynamics, most analysis now is done by CFD simulations, or pre-tested airfoil sections and data are available from NACA.

Yeah, I don't recall the exact numbers, but as I recall the vast majority of "lift" on an airplane wing comes from downwash, NOT the Bernoulli effect. The Bernoulli effect contributes to lift a little, but it's relatively trivial.

Which is why airplanes can fly with wings that are perfectly symmetrical on the top and bottom, or fly while upside down - something that wouldn't make sense based on the simple "the air goes faster over the top of the wing than the bottom, so you get Bernoulli lift" explanation for flight that you usually see in popular sources.

Edit: And actually if you think about it, the normal Bernoulli explanation for flight doesn't really seem to make physical sense from a perspective of conservation of momentum, because if the air is exerting a net lift on the plane upward, then the plane must also be exerting a net downward pressure on the air around it, which MUST deflect air downward...something that the Bernoulli explanation for flight doesn't seem to consider.

Right, but the Bernoulli principle certainly does play a part. Measurements of flow velocities/pressures in wind tunnel tests (using Pitot-static tubes) have shown that for asymmetric airfoils, wind velocity is faster over the longer (upper) surface of the wing than the shorter lower surface. This leads to there being more pressure on the lower than the upper, and there is a resultant upwards force (well some backwards force too, drag).

Bernoullis equation would not be accurate to predict this force though. The main reason being that the flow will most likely be compressible, having density variations, though there is a compressible version too. Even so, you then have viscosity, thermal properties, and turbulence to take into account.

The Newtonian explanation is actually also true, but is not the whole picture. Downwash happens because of a centrifugal force at the forward end of the wing forces air up into air above, and creates a region of higher pressure. This upwards deflection causes a low pressure at the rear of the wing, and so fluid travels from higher to lower pressure. Newtonian mechanics applies, because this downward momentum of the air gives a reactive upwards force to the wing.

The angle of attack also makes a hugh difference to the lift co-efficient of an airfoil, generally increasing it with increasing angle, up until a stall angle.

Edit: And actually if you think about it, the normal Bernoulli explanation for flight doesn't really seem to make physical sense from a perspective of conservation of momentum, because if the air is exerting a net lift on the plane upward, then the plane must also be exerting a net downward pressure on the air around it, which MUST deflect air downward...something that the Bernoulli explanation for flight doesn't seem to consider.

The Bernoulli explanation still makes sense intuitively, you have to think of it in terms of lower and higher pressures on either side of the wing. Particles collide with the wing in elastic collisions, and so momentum is still conserved. There is simply more collisions below than above. In fact thats another part of the Newtonian explanation, that particles literally hit the bottom of the wing, and bounce off downwards imparting momentum in doing so, which to some extent is true, but not a satisfactory explanation by itself. I think this type of analysis becomes more useful at really high Mach numbers, like in space shuttle re-entry.

The Navier-stokes equation is the most acuurate model we have of fluid flow, but is still not 100% complete due to things like turbulence, which is one of the big open questions in physics.

Originally Posted by Bunbury

This effect is also used in refrigeration.

That would be the Joule-Thompson effect not the Bernoulli principle.

I would not claim to know what colleges call these things.

However what I am talking about, is the same thing in both cases. Call it what you will. The same principle is in effect.

You put a small block up against a pressurized flow, and leave only a small venturi.

With just fluid loops you will get reduced pressure and higher velocity.

With systems that pump fluids that can evaporate, and the venturi is small enough, this effect that reduces pressure also causes the liquid to evaporate.

Sincerely,


William McCormick

Originally Posted by bit4bit

The Bernoulli principle is built on the laws of conservation of energy and momentum. It says that the total work done on the fluid is constant, and therefore takes the form:



is called the dynamic pressure, and represents the kinetic energy of the fluid due to the actual external forces acting on it i.e. the flow.

is the gravitational potential energy, taking into account any change in height of the flow.

P is the static pressure and represents the pressure of the fluid excluding the kinetic energy due to the actual flow i.e. the dynamic pressure. For example, for a flow through a pipe, the static pressure would be the pressure felt over the wall of the pipe. Even though the fluid is flowing parallel to it, and therefore is not contributing any kinetic energy from the flow (dynamic pressure), it still does contribute some kinetic energy as static pressure, just like a canister of pressurized gas.


It's accurate for incompressible streamlined flow, but applies intuitively to other flows too.

If the velocity increases, the dynamic pressure increases, and for a constant height, this must mean that the static pressure has to decrease since the energy must remain constant. The Venturi meter and Pitot-static tube both use this effect to measure the velocity of a fluid (An airplanes airspeed for example):

http://en.wikipedia.org/wiki/Pitot_tube
http://en.wikipedia.org/wiki/Venturi_meter

I am not much on the theories of conservation of energy.

In a closed loop, you can cavitate, as you change pressure to the venturi. By closing valves suddenly or opening valves suddenly. I know you mentioned streamline flow. However in life when calculating for a system this is never the case.

A small air bubble in a capillarity tube could increase the velocity towards the end of the tube and injure someone.

As you increase the length of the small tube eventually it will drip out of the end. And increase the pressure back at the venturi. The slowing is due to friction within the pipe.

So all this is relative to the exact system in question.

The big pipe small pipe is really interesting.

The big pipe is moving slow because it is moving a large volume. The small pipe or pipes that cut off the flow of the large pipe with a restriction, or venturi, are moving a low volume of fluid. Since the pressure is there, at the main pipe. The fluid flows faster in the smaller pipes, but only if the small pipe raises the pressure of the main pipe before the venturi.

If you take a bunch of smaller pipes, with the exact same volume as the larger pipe, the fluid speed will be equal in both the little and big pipes. Maybe a bit slower in the smaller pipes, if done independently.

You are actually getting into dead head pressure.

It is all relative.



Sincerely,


William McCormick

Your taking a shower and the shower curtian keeps coming toward you. Why? With the shower off the fluid pressure is pushing equally in all directions. Now we turn the shower on. The shower being on causes an unbalance in fluid pressure, and because the fluid on the inside is moving downward it is lessly moving against the shower curtain. The fluid pressure on the outside is still pushing equally in all directions, but now it has more pressure toward the curtain than the fluid pressure on the inside of the shower can hold back. As a result the shower curtain comes toward you in the shower.

Originally Posted by Raymond K

Your taking a shower and the shower curtian keeps coming toward you. Why? With the shower off the fluid pressure is pushing equally in all directions. Now we turn the shower on. The shower being on causes an unbalance in fluid pressure, and because the fluid on the inside is moving downward it is lessly moving against the shower curtain. The fluid pressure on the outside is still pushing equally in all directions, but now it has more pressure toward the curtain than the fluid pressure on the inside of the shower can hold back. As a result the shower curtain comes toward you in the shower.

I do not have shower curtains. Could you detail that explanation a little better?

I would suspect that the steam rising would create a negative pressure in the closed in area.


Sincerely,


William McCormick

Originally Posted by William McCormick

Originally Posted by Raymond K

Your taking a shower and the shower curtian keeps coming toward you. Why? With the shower off the fluid pressure is pushing equally in all directions. Now we turn the shower on. The shower being on causes an unbalance in fluid pressure, and because the fluid on the inside is moving downward it is lessly moving against the shower curtain. The fluid pressure on the outside is still pushing equally in all directions, but now it has more pressure toward the curtain than the fluid pressure on the inside of the shower can hold back. As a result the shower curtain comes toward you in the shower.

I do not have shower curtains. Could you detail that explanation a little better?

I would suspect that the steam rising would create a negative pressure in the closed in area.


Sincerely,


William McCormick

Ahh but in that case it woulden't work with cold water, which it does.

Originally Posted by Raymond K

Originally Posted by William McCormick

Originally Posted by Raymond K

Your taking a shower and the shower curtian keeps coming toward you. Why? With the shower off the fluid pressure is pushing equally in all directions. Now we turn the shower on. The shower being on causes an unbalance in fluid pressure, and because the fluid on the inside is moving downward it is lessly moving against the shower curtain. The fluid pressure on the outside is still pushing equally in all directions, but now it has more pressure toward the curtain than the fluid pressure on the inside of the shower can hold back. As a result the shower curtain comes toward you in the shower.

I do not have shower curtains. Could you detail that explanation a little better?

I would suspect that the steam rising would create a negative pressure in the closed in area.


Sincerely,


William McCormick

Ahh but in that case it woulden't work with cold water, which it does.

Are you saying that by spraying the shower curtain, on one side that it moves into the spray. Or that at some point later it moves into the spray.

If the shower depresses the curtain into an arc, then yes the fluid will try to leave the surface of the curtain upon reaching the end of the arc. And fluid capillarity will pull the curtain after the arc.

However that is another principle in my opinion.


ARC without out added power, can take an incoming flow of material and alter its path without much loss of velocity. However there will be some loss of velocity.

Years ago I built an impeller that was used with a similar design, on a prototype F-14 airplane. The actual impeller was a quarter circle. Or 90 degrees of a circle. This impeller is very interesting because once fluids or air move into the impeller, they perpetuate the impeller. Not totally. However enough so that increasing the speed of the impeller creates a neat almost unbelievable curve in output power compared to input power.

It uses velocity to hurl the air or fluid from the impeller at a faster rate then it is input. Creating a vacuum that sucks in air or fluid that then drives the impeller.






At the time there was some fear that other countries might use this to create a fleet of planes that would not need refueling. That could swipe at America from anywhere. So they cancelled the project.

In my opinion there was a fleet of George Washington rabbles at home that would have made a deposit in Washington DC for lack of Satisfaction from our servants.

Sincerely,


William McCormick

Originally Posted by William McCormick

Originally Posted by Raymond K

Originally Posted by William McCormick

Originally Posted by Raymond K

Your taking a shower and the shower curtian keeps coming toward you. Why? With the shower off the fluid pressure is pushing equally in all directions. Now we turn the shower on. The shower being on causes an unbalance in fluid pressure, and because the fluid on the inside is moving downward it is lessly moving against the shower curtain. The fluid pressure on the outside is still pushing equally in all directions, but now it has more pressure toward the curtain than the fluid pressure on the inside of the shower can hold back. As a result the shower curtain comes toward you in the shower.

I do not have shower curtains. Could you detail that explanation a little better?

I would suspect that the steam rising would create a negative pressure in the closed in area.


Sincerely,


William McCormick

Ahh but in that case it woulden't work with cold water, which it does.

Are you saying that by spraying the shower curtain, on one side that it moves into the spray. Or that at some point later it moves into the spray.

If the shower depresses the curtain into an arc, then yes the fluid will try to leave the surface of the curtain upon reaching the end of the arc. And fluid capillarity will pull the curtain after the arc.

However that is another principle in my opinion.


ARC without out added power, can take an incoming flow of material and alter its path without much loss of velocity. However there will be some loss of velocity.

Years ago I built an impeller that was used with a similar design, on a prototype F-14 airplane. The actual impeller was a quarter circle. Or 90 degrees of a circle. This impeller is very interesting because once fluids or air move into the impeller, they perpetuate the impeller. Not totally. However enough so that increasing the speed of the impeller creates a neat almost unbelievable curve in output power compared to input power.

It uses velocity to hurl the air or fluid from the impeller at a faster rate then it is input. Creating a vacuum that sucks in air or fluid that then drives the impeller.






At the time there was some fear that other countries might use this to create a fleet of planes that would not need refueling. That could swipe at America from anywhere. So they cancelled the project.

In my opinion there was a fleet of George Washington rabbles at home that would have made a deposit in Washington DC for lack of Satisfaction from our servants.

Sincerely,


William McCormick

My overall idea is that when a shower (with cold water) is turned on you have more downward fluid pressure than left, right, up, and down due to the velocity of the fluid in the shower. That would make the shower a low pressure area on the left, right, and upper sides, and a higher pressure area on the bottom side. If we put a big sheet on all four planes of the shower(top, bottom, left-side, right-side) the sheet would bend inward on the left, right, and top sides because they are a low pressure area. The sheet would bent outward on the bottom side because it is a high pressure area.

Originally Posted by Raymond K

My overall idea is that when a shower (with cold water) is turned on you have more downward fluid pressure than left, right, up, and down due to the velocity of the fluid in the shower. That would make the shower a low pressure area on the left, right, and upper sides, and a higher pressure area on the bottom side. If we put a big sheet on all four planes of the shower(top, bottom, left-side, right-side) the sheet would bend inward on the left, right, and top sides because they are a low pressure area. The sheet would bent outward on the bottom side because it is a high pressure area.

Another phenomena that could also cause this is the collegiate cap as I call it.

Years ago in the north east. Someone probably a college professor had an idea for a chimney cap. They created a metal tube that fit over the ceramic stone stack that protrudes the mostly brick chimneys in the area. Then there was a tube of mesh to stop squirrels from getting in and to let the smoke out. And then a cap to keep the rain and squirrels out.

The cap worked amazingly well. It actually increased flow by creating a funnel effect. Or a velocity effect. It helped both fireplaces and oil fired furnaces. Due to this amazing flow dynamic. It is a velocity stack.

I actually created one myself by mistake years ago. With a bonnet for a race boat. To keep water out. It went over the eight pack fuel injector tubes. And the fellow I was working with burnt up a few sets of plugs before he figured it out with a flow bench.

The only problem was that in the winter when a cold front moved in. With oil burners, or dwindling coal, or wood fires, the flow and velocity was so great in a downward flow, that the fumes of the furnace or fireplace were actually forced into the house. They cooled the chimney and kept the flow going in reverse.

I believe now, I understand what you are saying about the curtain. What could be happening is this principle. As the air is moved with the shower spray. It hits the floor of the shower, accelerates to get through the smaller gap between the curtain and floor. Is deposited there outside where it creates higher air pressure and that would cause your curtain moving into the shower as well.

There are many phenomena that could be at work here though.


Sincerely,


William McCormick

The shower being on causes an unbalance in fluid pressure, and because the fluid on the inside is moving downward it is lessly moving against the shower curtain. The fluid pressure on the outside is still pushing equally in all directions, but now it has more pressure toward the curtain than the fluid pressure on the inside of the shower can hold back. As a result the shower curtain comes toward you in the shower.

Raymond,

The way I envisage the shower curtain effect is as follows: As water falls from the shower head it entrains air which flows downward with the water. The water and air separate at the bottom as the water goes down the drain and the air then flows back up the shower curtain and the walls, as it's got nowhere else to go. So what you have is a closed circuit air circulation powered by the falling water, and the air flowing up the curtain produces a lower static pressure so the curtain is pushed in. As you say, a good demonstration of the Bernoulli principle.