# Faster fluids have a lower pressure?

1. Sep 23, 2006

### freswood

I'm doing an assignment on helicopter flight, and I'm a little confused about the Bernoulli principle. He said that if a pipe is bigger at the beginning and smaller at the end, the fluid travelling through the end of the pipe would have a lower pressure.

This seems counter-intuitive. I would have thought that there would be more pressure on the fluid thats "squeezed in together". I don't think I fully understand the concept of pressure.

Can anyone explain this in layman's terms because my knowledge of physics is very basic. Thanks for your help

2. Sep 23, 2006

### FunkyDwarf

yeh this one is kinda tricky. the way i think of it is the fluid has less time to 'sit there' and exert pressure on the walls of the tube.

3. Sep 23, 2006

### rcgldr

Note the helicopter peforms work on the air, accelerating it downwards (and circularly). This is a different case than the fluid in a pipe case, since the pipe peforms no work on the fluid.

The pipe example is using an ideal non-compressable fluid. In this situation, the amount of mass flowing across any cross section of the pipe is constant. There's some type of force - pressure being applied to cause the fluid to flow in the first place. Since the mass flowing across any cross section is constant, and the fluid is not compressable, the fluid has to be traveling faster in the thinner part of the pipe for the mass flow to equal the mass flow of the fluid in the thicker part of the pipe. In order for the fluid to be traveling faster, it has to accelerate as it transitions from the thicker part to the thinner part. The only reason it would accelerate is due to a pressure differential, so therefore the pressure in the thinner part of the tube must be lower than the pressure in the thicker part.

Even in the case of a realistic fluid, the smaller tube section has a lower pressure. There are syphons that you connect to a faucet, that rely on the venturi effect, using a flow of water through a narrowed pipe to draw another stream of water perpendicular into the narrowed pipe section; you can find one of these at an aquarium supply store. Carburetors work on the same principle.

Another explanation of the Bernoulli principle and air is that the total energy of a volume of air is conserved as long as there is no work done on the volume of air. The total energy of the air consists of it's kinetic energy (which is relative to a frame of reference), it's pressure, and it's temperature. For aerodynamics, the temperature component is ignored to simplify things. So if the kinetic energy of the air is increased without doing work, then the pressure of the air is decreased.

As I first pointed out, a wing performs work on the air, accelerating the air downwards (for a lift reactive force), and forwards (for a drag reactive force). With a typical, efficient, wing, most of the acceleration is downwards and only a bit forwards, resulting in a good lift to drag ratio. Some high end gliders have a 60 to 1 glide ratio.

Last edited: Sep 23, 2006
4. Sep 23, 2006

### arildno

It is crucial to remember that Bernoulli's principle is only valid in the comparison of velocity&pressure at two different points ON THE SAME STREAMLINE for stationary flow.
Since the flow is stationary, it follows that the particle paths coincide with the fluid streamlines.

Thus, as Jeff Reid said, if a particular particle has gained mechanical energy from one point to another (say, either kinetic energy or gravitational potential energy), then (for the inviscid fluid) the only force capable of doing this is that one associated with the pressure difference between the two points.

If two points are NOT connected by a streamline (or the flow being non-stationary), we cannot, in general, set up a principle akin to Bernoulli's principle, and thus we cannot conclude that "greater speed" means "lower pressure).

In the special case of potential flow (or its generalized version (still only a special case of inviscid flow!) called Clebsch flow) we are, however, able to derive a relation between the dynamic&kinematic quantities akin to Bernoulli's principle valid for non-stationary flow and holding between points not necesssarily connected by streamlines.

5. Sep 23, 2006

### Staff: Mentor

It is important to remember that there are two kinds of pressure at work here: static and velocity pressure. If the total pressure is constant and the velocity pressure goes up (as the velocity goes up), the static pressure must go down.

6. Sep 23, 2006

### sdemjanenko

its the same principle as what makes an airplane fly. The distance air must flow over the wing in greater than below, and since stiller air can give more of a perpendicular pressure, it outforces the pressure down from air flowing over at a higher speed and creates lift.

7. Sep 23, 2006

### rcgldr

This is "hump" theory, and it's not true. The hump can be on the bottom, as with this NASA lifting body, with a shape similar to a cone sliced in half, then smoothed out.

m2f2.jpg

lifting bodies web page

In the case of a wing, the total pressure is not constant, since any solid object passing through the air performs work on the air, changing the kinetic energy. Regarding the components of kinetic energy and velocity of air in the direction of travel (drag), the kinetic energy and velocity are decreased with respect to the object's frame of reference, and increased with respect to the air's frame of reference. The components perpendicular to the direction of travel (lift / downforce) are the same for both frames of reference.

Last edited: Sep 23, 2006
8. Sep 23, 2006

### rcgldr

Last edited: Sep 23, 2006
9. Sep 23, 2006

### freswood

Thanks everyone, I think I see what you mean.

My textbook says that work IS done. "In order to increase the velocity of the fluid, work must be done on the fluid travelling through the pipe to increase its kinetic energy. This can only occur if the pressure of the fluid entering the pipe is greater than the pressure of the fluid leaving the pipe."

10. Sep 23, 2006

### rcgldr

Work is being done by whatever is causing the fluid to flow through the pipe, but the narrowing pipe doesn't peform work on the fluid. It's converting some of the potential energy, pressure, into kinetic energy, the total energy is conserved, so there's no net work being done.

Last edited: Sep 24, 2006
11. Sep 23, 2006

### the_force

Hey

So, is it the same as a basic rocket? Wide pipe dwells down to a bottle neck and stores up evergy then released out the other end?

12. Sep 24, 2006

### rcgldr

The main purpose of a rocket nozzle is to maximize the velocity of the exhaust gases. On large rockets, the nozzle can be moved to control the rockets path. The amount of pressure reduction due to the narrowing of the nozzle is very little compared to the pressure differential between inside the engine and outside past the nozzle, which is the atmosphere or space.

13. Sep 24, 2006

### zoobyshoe

I think it's worth highlighting the fact that the drop in pressure described by Bernoulli concerns the internal pressure of the fluid in the smaller section of pipe. It exerts less pressure on the walls of the pipe than the fluid in the larger section exerts on the walls of the pipe.

The pressure that the accelerated stream of fluid might exert on something against which it's directed as it exits the small end of the pipe has increased in terms of psi, hasn't it? The same force has been concentrated into a smaller area.

14. Sep 24, 2006

### arildno

Hmm..as for the rocket nozzle shape, we cannot ignore the fact that the exhaust gas is COMPRESSIBLE. Thus, although we may state a variant of Bernoulli's principle valid for the gas, the additional factor of compressibility must be taken into account, compared to the liquid case.

15. Sep 24, 2006

### Chronos

The volume of fluid flow is constant, only the velocity changes. This is a simple f=ma thing. Under constant force, the fluid velocity increases as the nozzle size decreases. Picture a tank with a pinhole leak in the bottom. The water in the tank is virtually at rest, water passing through the pinhole has a measurable velocity.

16. Sep 26, 2006

### ken

Bernoulli principle is way too weak an effect to explain filght.
It's just a simple easy way to explain it to school kids.

Ken

17. Sep 27, 2006

### rcgldr

Not in a rocket, the gases are expanding due to heat. The mass of flow is constant (ignoring the very small amount of mass converted into energy).

It would be simpler still and more accurate to explain that wings just deflect air downwards, but because air is drawn towards low pressure and away from high pressure areas, that more air is drawn over a wing than below so most of the downwards deflection (acceleraion) occurs from above a typical wing.

18. Sep 27, 2006

### Clausius2

Just only to clarify, as Arildno said, the flow in a rocket nozzle is SUPERSONIC, and actually the conversion of pressure energy into kinetic energy is exactly in the opposite way of this thread is describing. Therefore, in the wide part of the divergent nozzle the flow is less pressurized than in the throat, even though the velocity there is higher.

19. Sep 27, 2006

### Cyrus

Interesante. I have not dealt with flows in the supersonic regime before.

Last edited: Sep 27, 2006
20. Dec 23, 2010

### ZerO LifT

when the velocity increases the pressure decreases , and vice versa , in such a manner that their product is constant along the same stream line

i.e : P x V = cons.
along a stream line : P1 x V1 = P2 x V2 = P3 x V3 = cons.
where : 1 , 2 , 3 are three arbitrary points at the same streamline.

21. Dec 24, 2010

### cjl

This isn't true.

The static pressure varies such that the total pressure remains constant. In other words:

$$P + 1/2 \rho v^2 = cons$$

EDIT: also, wow this is an old thread...