Pressure, Velocity and Bernoulli's Law

Have a look at http://en.wikipedia.org/wiki/Orifice_plate.

An orifice or reducing in pipe size has an choking effect on the flow in a system. Therefore reducing the pipe size will reduce the flow or require more head / force to overcome the additional impeding / friction loss.

The decrease in pressure due to velocity has found its way into some really nice products.

Bernoulli's law may be more easy to grasp if you think of it in terms of conservation of energy.

Think about a very large diameter pipe with an incompressable non viscous fluid traveling through it. The pipe begins to smoothly decrease in diameter until it is has only one tenth the cross sectional area as it orignally had. It continues for a considerable distance and then begins to increase in diameter smoothly until it is at the original very large diameter.

You can calculate various measures of the energy per unti mass of the fluid prior to the constriction. We will say the pipe is horizontal and that the pipewall is frictionless. Ignore changes in heat for a moment. So just think about the pressure (potential) and the velocity (kinetic).

When the pipe is large the velocity is low and the pressure is high.

As the pipe narrows, the velocity increases.... where does this energy come from? It is a conversion of potential energy measured by the decrease in pressure into the kinetic energy measured by the increase in velocity. So as the pipe narrows, pressure decreases as velocity increases.

Until you reach the smallest diameter, where pressure is the lowest and velocity is the highest.

As the diameter of the pipe begins increasing, the velocity decreases.... where does the energy go? It is seen as an increase in pressure... kinetic to potential.

Hi,

Thank you Benbenben. Your explanation has cleared off the confusion about inverse relation between kinetic energy (Velocity) and Pressure energy. The explanation was superb. But can you tell me what exactly is the relation between velocity and pressure?

If this is the relation:

P₁ + 1/2 r v₂² = P₂ +1/2 r v₂²

then we should not, strictly speaking, say that pressure is inversely proportional to velocity as the nature of the relation is additive, or should we?

Loved the comment at the bottom re inconsistent observations and human intellect providing an explanation, however complicated. That explains conspiracy theorists. Thanks

The following solved example is very interesting and demonstrates the relations between velocity, pressure, flowrate, ... etc. depending on the Energy Equation which derived from Bernoulli's law:

Energy Balance: (P₁/W) + (V₁²/2g) + Z₁ + H_P = (P₂/W) + (V₂²/2g) + Z₂ + ∑H_L

And as you see, there is a such relationship between a variety of parameters, where any change in any parameter can affect on the others. Please see my post 6 of CR4 Thread Selecting Pipe Size, and you can easily see how much the value of velocity depends on a lot of parameters, not only the size of pipe nor the flowrate, ... etc. but also the friction loss in pipe is one of those parameters.

In another discussion regarding converting velocity to pressure, you offered the following equation:

V=[2g(P+Z+Hp)/(fL/D+k+1)]0.5

Can you please list the the components of this equation

Thank you

RD

I am not going to answer your confusion, which others are doing (better than my would be answer0. But wish to show the mistakes in your post:

If P is inversely proportional to V

and F= V*A (which means V= F/A)

Then P is inversely proportional to F/A. This means P is inversely proportioanal to F and directly proportional to A.

This shows that if your statements are analysed properly for constant A, P is inversely proportional to F.

(Am I increasing yoyr confusion?)

That is the very fact that has been confusing me.

We find, as you pointed out, that,

F = v*a

where v is velocity and a is cross-sectional area.

P = f/a and a = f/P

where f is force and a is cross-sectional area.

Substituting,

F = v*f/P.

According to this Flow is inversely proportional to pressure.

But Poiseuille's equation shows that flow is directly proportional to pressure.

P2-P1 = F*R

where R is resistance and R= 8hl/(pi*r^4)

where h is co-efficient of viscosity; l is the length of the tube concerned; r is the radius.

I suspect the confusion is arising as you compare two different effects.

Considering an effectively incompressible fluid.....

Bernoulli is considering a reversible conversion of energy which can be seen as changes between pressure and velocity. This change occurs in either direction.

When you consider the effects of friction/viscosity, there is an irreversible conversion of energy which can be seen as pressure to heat. This occurs effectively exclusively in one direction, that is, from pressure to heat.

Dear!!!!

Pressure is proportional to flow ????? please justify this assumption

Flow is volumetric flow if the same flow passes through large area velocity energy converts in pressure energy and if same flow passes through small area pressure energy transforms in velocity energy. So they are only inversely proportional.

Actually that was not a assumption.

This is the form of Ohm's law as applied to fluids.

V = I*R

where V is potential difference, I is current flow, R is resistance.

From this,

P = F*R

Where P is pressure change, F is flow of fluid, and R is resistance.

Sorry, for me it is not possible to relate flow with current

Dear friend,

A large area can not create any pressure energy.

Potential energy is due to position and pressure energy is stored only when the number of fluid molicules are more than normal in a restricted space.

Dear friend,

1. Pressure: Pressure is created, only and only when the flow is restricted. A free flowing fluid (gas or liquid) can not exert any pressure. Pressure is potential energy stored in the fluid due to its position.

2. Flow: flow is unit *volume* (L x b x h etc.) of a fluid passing from a given point in unit time.

3. Velocity: velocity is the distance travelled by a molicule of the fluid in unit time.

When a pressurised fluid escapes from restriction and finds a free straight path it tends to create suction around it due to the pressure energy converted into kinetic energy causing a partial vaccuum between moving molicules. This means that the more the velocity the more the negative pressure or suction.

I think this will clear your doubts.

Regards.

R S Sahni

Gud Answer shalini.

Clearly understood.

Hi, I think it's very easy to get the idea of how conservation of energy works, you just need to focus alittle bit on the following:

we all know that we have three types of energy allocated within the flow, namely (Kinetic Energy, Static Energy, Potential Energy)

*change in Kinetic Energy will occur wherever a deceleration or acceleration combines the moving fluid (flow). which means that the controlling factor for the K.E. is the velocity. and I guess it's apparent that Kinetic always relates to something moving.

*change in static energy is mainly affected by the drop or rise in pressure. Imagine that there is a body of a known mass on your hand, it will ofcourse generate a force on the area of your hand where it's located which is known as (PRESSURE). I suppose that by now u must have known that when a body moves with the speed that equals the Light speed it will completely lose it's mass and this mass will convert to a pure energy!! so when mass accelerates it starts to change some of it's static energy into Kinetic energy.

*change in potential energy is caused by the gravity and has no deal to do with pressure and velocity as it has it's own characteristics which depends mainly on the altitude and earth gravity. But when it changes it also tends to change the other energy parameters, but none of the other types of energy can make a change in potential energy if there is no change in altitude.

So we conclude that ::

Velocity=Minimum ---------> Pressure=Maximum Value

Velocity=Maximum --------> Pressure=Minimum Value

Well now,

I am pretty much of a dummy on all this stuff but it seems to me that something is missing from your equations (feel free to 'dis' me if you think I'm wrong).

When a fluid (no particular fluid has been specified) comes under pressure, certain changes begin to occur at the molecular level in the fluid itself. Because of the heat generated they (the molecules) will tend (in most fluids) to expand. This should tend to change the dynamics as to their resistance to the forces applied, even if only a little bit and even at simple atmospheric pressure.

As I said, I might be all wet (pun intended) but it seems reasonable to me.

plz explain sir,

i am lot of confused about that point, mainly principle used in Ejector system.

pressure is inversaly proportional to the velocity

according to eq of continuity area and velocity is inversaly proportional to each other

hence area is directly proportional to pressure

Sorry - just had to change the title.

'tis, after all, an engineering forum.

Maybe searching Bernoulli's Principle and/or Bernoulli's Equation (in fluid dynamics), will bring greater clarity.

Not to be confused with; Bernoulli's Theorem (probability), in "law of large numbers". Or Bernoulli's differential equation.