Understanding Bernoulli's Principle

[marwan]

Hey,

I have this experiment i have to do and i have to undnerstand Bernoulli's Principle and it is just not getting to me. I don't understand how the pressure will decrease as the speed increases, or how the pressure will increase if the speed decreases.


Like in the textbook, it says that " if two train are going in opposite directions on close tracks, the tops of the cars tend to lean to lean towards each other. Why would that happen? What do they have to do to make sure the trains don't hit each other?

I just need someone to explain it to me. I really need to ur help, thanks in advance.


Marwan

 

[HallsofIvy]

Not a whole lot to explain- it's a matter of experimental evidence.

One way of thinking about it is this: If a gas is moving very rapidly, then the same amount of gas is spread over a greater area. It's spread more thinly so it has less pressure.

 

[Townsend]

Hey,

I have this experiment i have to do and i have to undnerstand Bernoulli's Principle and it is just not getting to me. I don't understand how the pressure will decrease as the speed increases, or how the pressure will increase if the speed decreases.


Like in the textbook, it says that " if two train are going in opposite directions on close tracks, the tops of the cars tend to lean to lean towards each other. Why would that happen? What do they have to do to make sure the trains don't hit each other?

I just need someone to explain it to me. I really need to ur help, thanks in advance.


Marwan

I think of this in terms of the law of conservation of energy. It is much like when you hold your thumb over the end of a garden hose. The pressure behind your thumb accelerates the water and so it squirts out the end of the hose.

Now let's think about what is really happening in the garden hose example. You have potential energy built up in the hose in the form of pressure. Once that energy is used to accelerate the water it has the form of kinetic energy. If all of the potential energy is used in accelerating the water out of the end of the hose then there is no more pressure.

Lets look at a carburetor venturi to get a better idea of how this principle works in action.

http://abbysenior.com/mechanics/images/fuel.h4.gif

Air enters the venturi of a carburetor when the engine creates a vacuum. The ambient air pressure forces air in the carburetor from above. As you can see the venturi throat squeezes this incoming air forcing it to accelerate the air in order to move the same volume of air at the same rate as it is moving above the throat of the carburetor. This squeezing action is equivalent to you putting your thumb over the end of the hose. As the air is accelerated by the pressure above it some of that pressure is changed from potential energy to kinetic energy. This means that it will have less pressure than slower moving air outside the carburetor.

Now if you can imagine how an airplane wing resembles the shape of the venturi. This is how an airplane wing creates lift. As air is force to move faster over the top section of a wing the pressure above the wing is lower than the pressure below the wing.

http://www.newsandevents.utoronto.ca/bios/askusimages/airflow.gif

As you can see from the cut away section of an airplane wing the length of the upper portion is longer than that of the lower section. That means that air must travel farther to move across the top of the wing than it does for the lower section of the wing.

A really neat experiment you can try for your self will amaze you and your friends and teacher. You can do it a couple of ways depending on what supplies you have at your disposal.

1. For this version you need an smooth plastic funnel a garden hose that works and a smooth rubber or plastic ball. All you have to do is place the small end of the funnel into the hose and make sure it fits snugly. Now turn on the water and make sure you have good volume of water moving through the hose. Now all you have to do is push the ball into the moving stream of water until it sets up inside the funnel. You will start to actually feel the water sucking the ball in. Now remove you hand and behold the power of science! Note that the quality of the ball and funnel have a lot to do with how well this works so if it is not working for you it might be the funnel or ball or both.

2. Same as above but instead of using water we will use air. You need to have an air-compressor available to you that you can use to force air through the small end of the funnel. Then as before push the ball up into the funnel until you start to feel the suction holding the ball in place.

Best of luck

 

[Andrew Mason]

I just need someone to explain it to me. I really need to ur help, thanks in advance.

The key to understanding Bernouilli's principle is conservation of energy and the relationship between pressure and energy.

Pressure of a liquid or gas, P, represents potential energy/volume. PV = potential energy. If energy is conserved (no energy escapes the enclosed space, which is, say, a pipe), then the total potential and kinetic energy of the system cannot change. So PV + KE = Constant.

Now consider pipe full of a fluid or gas of mass M at pressure P flowing with speed v . The energy is determined by:
$$PV + \frac{1}{2}Mv^2 = C$$

The energy per unit volume is ($\rho$ = density):
$$P + \frac{1}{2}\rho v^2 = C$$

Now the substance suddenly passes through a pipe section with smaller diameter. The total energy/unit volume cannot change. In order to maintain the flow rate, the speed has to increase to v', so the substance gains kinetic energy. Now the energy density is:

$$P' + \frac{1}{2}\rho v'^2$$

but because energy is conserved, we know that:

$$P' + \frac{1}{2}\rho v'^2 = P + \frac{1}{2}\rho v^2$$

$$P - P' = \frac{1}{2}\rho (v'^2 - v^2)$$

So, when the speed increases, pressure has to decrease. If it didn't it would have to obtain energy from somewhere, which is contrary to our assumption.

AM