Pressure - Velocity relation in fluids

Whats this?? No takers still??
Where are all the brilliant Mechanical, Aeronautical, Piping Engineers??

Come on guys, I am awaiting a good explaination on the topic started. So get started.

Its not the velocity of fluids. Its the volume and pressure relation. I think you'r looking for BOYLE's law. Its an ideal gas law- applicable to all fluids- liquids and gases. Though it has certain limitations for liquids. Try to google for more info.

The velocity and area have a relation too- for calculating the Flow rate of the fluid through a conduit. Here's a simple explanation, you with me?

Force = Pressure x Area

also,

Force = Mass x Acceleration

where,

Acceleration = dv/dt, ie rate of change of Velocity.

So,

Force = M x dv/dt = P x A

Now for a particular fluid- the Mass of the fluid will remain constant.

Hence,

P x A ~ dv/dt

or

(P x A) x dv/dt = constant.

I think this is the relation you are looking for.

Boyle's law

Pressure x Volume = Constant.

Constant flowrate-
Area x Velocity = Constant flowrate.

Hope this helps you out.

Thanks for answering Ron.

But its not the BOYLES LAW that I am looking for.

We can mathematically derive the relation for pressure, area and change in velocity of the fluid. The constant flowrate equation is also true, but what I am looking for is the Physical interpretation of it ie WHY or rather WHAT CAUSES the pressure to change when velocity increases; or WHY or HOW does velocity adjust its value when the Area reduces.

I am looking for that WHY.

What causes the Pressure to change when the velocity increases//

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I fail to understand your question. What do you want?

You want me to explain it in molecular level? or do you want me to explain, it fromt he start?

Please explain.

I have clearly mentioned in the question that I am looking for the REASON what causes the Pressure to reduce when velocity increases( or we increase it by external means).
The formulae always give the relation part of a phenomena between the parameters involved, but they dont clarify HOW it happens.

The graphical link you gave is about Pressure-Area-Force relation, which I am not looking for. Its Pressure- Velocity relation I am interested in , rather the reason for their inter-relation.

If youwant to explain it on Molecular level, go ahead with it, not only me but many other CEans will also benefit from it.

I hope I've made my question clear.

Hi rohan,

When velocity increases flow pressure decreases due increase in pressure drop due to velocity,

if you calculate pressure drop using Darcy's Weisbach formula

Hf=pressure drop = fLV^2 / ( 2*g*D)

where f = Darcy's friction factor
L= Length of pipe
V= velocity of flow
D= Diameter of Pipe

if you observe above equation it is very much clear that if velocity increases pressure drop also increase and hence your flow pressure reduce.

The Relation given above is for the FRICTIONAL HEAD LOSS due to internal pipe surface.
The Darcys formula gives the relation between the Head Loss due to Friction in the flowing fluid wrt Flow Velocity, coefficient of friction, dia. of conduit.
This is NOT what I was looking for.
I want to know the reason WHY PRESSURE DROPS WHEN VELOCITY INCREASES.

for a liquid flowing in a pipe the pressure is exerted by the liquid on the pipe. As the velocity is low there is more interaction between liquid and the pipe reasulting more amount of force on the pipe by the liquid, as the velocity is more, the attractive forces between liquid molecules is more, reasulting less force on the pipe, reasulting less pressure.
The above explanation is what i think as a logic for your questions, try to analise it.

okay sir
you know that fluids flows only when there is pressure difference. if there is no pressure difference, no flow. this is a general fact of science as per analogy current flows from high potential to low potential water flows from high altitude to low altitude similarly when there is a pressure difference in horizontal pipe then flow occurs and the velocity is depend on pressure difference.
if not satisfied
ask.........

The above explaination is not what I was looking for.

All Brilliant Mechanical Engineers on CE, come on , I am waiting for the correct theory and explaination behind this Inverse relation between Pressure and Velocity in the Fluid Flow.

So please get going and explain this.

It's a mechanical problem. The pressure and volume are restricted by the diameter of the channel; there's a nearly constant cross-section, for a small length of overall pipe + fluid (volume).

Assume the pipe has a constant unchanging diameter. The flow is a volume with momentum along a section of pipe (unit length); the pressure is across the pipe's diameter (the pipe 'absorbs' pressure). If the pipe is rigid material, pressure is reflected back to the fluid, perpendicular to the flow. The flow is either because the pipe is angled "downhill" or because of a feed pressure (pumping action).
Things are more complicated if the pipe is elastic (like arteries and blood vessels are), so let's stick with a fixed width container...
(well, consider that blood pressure is regulated by vasodilation - the muscles in the veins dilate and contract to maintain a safe pressure, so that the circulatory system absorbs pressure, as above, or lowers and raises it. A rigid pipe can't do this, so the flow does. Flow is what 'absorbs' the pressure against the walls of the channel a fluid is flowing "against", the reduction in pressure in the fluid is because it's moving and so carries the pressure along the walls, essentially lowering the normal force).

The relation to Boyle's law is: pressure and volume are always constant for a fixed diameter flow; PV is constant for a fixed temperature in a gas = fixed tension or normal pressure (perpendicular to the container walls) in a fluid.
Molecules flow in bulk along the pipe, so there is negligible nonlinearity in large flows (Avogadrian numbers of molecules).

Also, there's a related flow phenomenon in electric charge and electron mobility. Charging a capacitor is essentially "immediate" (ok, it takes a small amount of time, but relative to the discharge rate, it's instantanteous). This is a volume of electric charge, "statically" collected on the surface of a conductor (even though the electrons are inside the metal).
Charge "pressure" against the surface, causes the electrons to flow out of the capacitor, as if a pressure is causing the flow (it is causing the flow, it's called a voltage difference). This is exactly mechanically same as what happens when you fill a container with water, and drain it using a gravity-fed pipe.

Alrighty?

@ Skipper : In the first place Thank you for responding to the question and commenting on it.

There are certain things which I do not agree upon.

The pressue exerted by a Fluid is essentially due to the Height Of the Water Column and the External Pressure if any. And according to the Pascals Law it is exerted equally in all the directions.

And the Pressure exerted by the fluid always acts along the Normal to the flow or the container boundary. So the Flow is not ABSORBING any pressure but is in fact exerting it. You can at the most say that the Newtons Third Law applies here as far as the walls are concerned.

Secondly, what is the theory behind ' Reduction in pressure is because the flow carries the pressure along the walls and so Normal Force reduces' ?? On what basis can this be explained.

The Pressure Velocity Relation I was talking about equally holds TRUE for a flow through a Convergent or Divergent Nozzle attatched to a pipe, where the Pressure DROPS as the Velocity of the fluid Increases as it flows through the Converging Nozzle and vice versa in a Divergent one.

I was seekling an answer to what exatly happens on the Molecular Level which bring about this conversion in the relation between the pressure and velocity.

Thirdly, the Boyles Law gives the relation only essentially betwen te Pressure and VOLUME of a fluid and not the Velocity. Also it is applicable to Static fluids and not flows. So it is not relevant here.

Fourthly, it is a known fact that we need a Potential Difference for the flow of any Physical Quantity (like heat, current, fluidflow) across any two points. We do not need this in the Pressure Velocity Relation here.

So the question still remains unsolved. Can you all please think a little further and try to explain this phenomena.

Rohan@ Skipper : In the first place Thank you for responding to the question and commenting on it.

There are certain things which I do not agree upon.

The pressure exerted by a Fluid is essentially due to the Height Of the Water Column and the External Pressure if any. And according to the Pascals Law it is exerted equally in all the directions.

Yes, in a closed pipe (assume it's full) the pressure is either because of a larger volume (at a greater height, say) 'forcing' the flow through the pipe, or equivalently because of a pump.

And the Pressure exerted by the fluid always acts along the Normal to the flow or the container boundary. So the Flow is not ABSORBING any pressure but is in fact exerting it. You can at the most say that the Newtons Third Law applies here as far as the walls are concerned.

Yep. That's what I say above; the container or pipe has a normal reaction to the pressure, in the flow. The reaction is the absorbance (say by expanding) of flow momentum. If the container is inflexible, the normal shear force is perpendicular to the flow.

Secondly, what is the theory behind ' Reduction in pressure is because the flow carries the pressure along the walls and so Normal Force reduces' ?? On what basis can this be explained.

The pressure is not actually lowered in the fluid, but the normal restoring force at the container wall is less, because of transverse flow (consider that if there is no flow, pressure is maximum at at the walls); fluids are incompressible so the fluid pressure is constant, the flow rate then determines how the stress against the walls, is translated by momentum. The "flow pressure" is not the fluid (internal) pressure, it's the potential 'pushing' the fluid along.

The Pressure Velocity Relation I was talking about equally holds TRUE for a flow through a Convergent or Divergent Nozzle attatched to a pipe, where the Pressure DROPS as the Velocity of the fluid Increases as it flows through the Converging Nozzle and vice versa in a Divergent one.
I was seekling an answer to what exatly happens on the Molecular Level which bring about this conversion in the relation between the pressure and velocity.

Thirdly, the Boyles Law gives the relation only essentially betwen te Pressure and VOLUME of a fluid and not the Velocity. Also it is applicable to Static fluids and not flows. So it is not relevant here.

Fourthly, it is a known fact that we need a Potential Difference for the flow of any Physical Quantity (like heat, current, fluidflow) across any two points. We do not need this in the Pressure Velocity Relation here.

So the question still remains unsolved. Can you all please think a little further and try to explain this phenomena.

Pressure variations are because of the reasons stated - the smaller the cross-section the less fluid there is to translate the pressure into momentum = higher nozzle pressure of fluid per volume.

Molecular versions have to account for the individual dynamics of each molecule; molecules have a shape, a distributed charge and 3 kinds of motion. Friction is very complicated (in fact, it isn't well-understood at all, like the gas laws and bulk flows are).

It's much easier to deal with a macroscopic amount of matter, as a bulk material. The relevance of Boyle's law is that it's a general formulation of pressure/volume, which relate to density/flow.
The potential difference you say is needed for flow, is equivalent to pressure. So if you're talking about "potential", the easiest potential to see, is the potential in a volume of water at a height h. This is equivalent to a volume of heat, at a temperature T, and to a volume of charge at a voltage V.
Gas/Liquid pressure is equivalent to temperature (heat potential) and voltage; as long as you use a general form of 'flow" in each case, a "transport", this is gas/liquid, heat, and charge flow, respectively.

The reaction is the absorbance (say by expanding) of flow momentum. If the container is inflexible, the normal shear force is perpendicular to the flow.

The expansion or Flexibility of the container has got nothing to do with the Normal Reaction. Thre Reaction would still remain the same no matter how flexible or elastic the pipe is.

The pressure is not actually lowered in the fluid, but the normal restoring force at the container wall is less, because of transverse flow (consider that if there is no flow, pressure is maximum at at the walls); fluids are incompressible so the fluid pressure is constant, the flow rate then determines how the stress against the walls, is translated by momentum. The "flow pressure" is not the fluid (internal) pressure, it's the potential 'pushing' the fluid along.

The Normal Restoring force also remains the same no matter how much the flow velocity is.

Incompressibility means that there is no volume change in the fluid on application of pressure. It does not mean that pressure remains constant.

What do you mean exactly by stress/pressure being translated by momentum

Pressure variations are because of the reasons stated - the smaller the cross-section the less fluid there is to translate the pressure into momentum = higher nozzle pressure of fluid per volume

You have stated the Opposite of what the situation is; ie for smaller c/s in a convergent nozzle the pressure is LOW and the Velocity is HIGH and not the otherway round as you have stated above.

Or do you mean to say that the pressure acting on the fluid is the same but the volume of the fluid is less at a smaller c/s.

You have not made yourself clear. So if what I infer from your above quote is actually what you wanted to convey, then it must be the Force acting from an external source pushing the fluid causing flow and not the pressure as you have stated.

Is this what you meant to say :
( pressure = force/area) so MORE force acting on the SAME C/S AREA, so there are LESSER molecules to move , hence HIGHER Velocity.

The rise in velocity aspect can be explained by this but again the Drop in pressure remains unexplained ie in reality the pressure at that c/s of the pipe is REDUCED when the velocity increases.

This is even what I used to think earlier, but it did not answer my query about reduction in pressure. So I always wondered why.

Pressure variations are because of the reasons stated - the smaller the cross-section the less fluid there is to translate the pressure into momentum = higher nozzle pressure of fluid per volume.
OTE]

Thus the higher nozzle pressure thing you stated appears in contrast to the actual situation.

In reality the pressure does show LOWERED when it is measured at the higher velocity areas ie where c/s is lesser. This is what is troubling me.The reason for this is not mentioned clearly. Would you mind shedding some light on that.

So if you're talking about "potential", the easiest potential to see, is the potential in a volume of water at a height h. This is equivalent to a volume of heat, at a temperature T, and to a volume of charge at a voltage V.

What i meant to suggest was we do not need to discuss the potential difference for the pressure velocity relation.

It is nice to have an open discussion on this topic and I thank you for showing interest. I will be happy if we can continue with it, as it is an active discussion over a topic which allows to see a problem with different views and varying ideas which will help to better and clear understanding of the topic

Looking forward for many such interactions. Please do clarify your precise view in the above post of yours. I hope to find an answer for this question.

The expansion or Flexibility of the container has got nothing to do with the Normal Reaction. Thre Reaction would still remain the same no matter how flexible or elastic the pipe is.

How come? If you fill a balloon with water it reacts to the pressure by expanding; you can't expand a rigid container which is why they usually have open ends if you want them to be pipes. A pipe that was flexible would absorb flow until it reached a limit and either became rigid or burst under pressure. Fluid pressure is constant.
The pressure in a pipe is against the wall. The pressure in the flow is because of the bulk momentum in a unit volume, and because the pipe doesn't expand under pressure. The flow 'bends' the normal reaction from perpendicular to the flow, since a molecule in contact with the wall that gets a push toward the center, is moving sideways; shear is translated = the fluid flow is shear from the normal stress. The flow carries the stress at the walls away, as fluid shear.

You have stated the Opposite of what the situation is; ie for smaller c/s in a convergent nozzle the pressure is LOW and the Velocity is HIGH and not the otherway round as you have stated above.

The pressure outside the nozzle is lower than the flow pressure inside.
The velocity is the flow pressure, the fluid's internal pressure is constant.

If fluid pressure is constant, velocity of volume (flow) is the equivalent of pressure in gases.

To recap: pressure in a gas is density*temperature/volume; pressure in a fluid is density*velocity/volume; in electricity it's density*charge/volume.
There is one other thing: fluids flow faster in the center than along the edges, there's a flow gradient, so since flow in fluids = pressure in gases it looks like a pressure gradient. However a standing fluid pressure (flow velocity = 0) is because of the mass potential; flow potential is different (think about how a gas has the same mass independent of temperature).

The pressure in the flow is because of the bulk momentum in a unit volume, and because the pipe doesn't expand under pressure. The flow 'bends' the normal reaction from perpendicular to the flow, since a molecule in contact with the wall that gets a push toward the center, is moving sideways; shear is translated = the fluid flow is shear from the normal stress. The flow carries the stress at the walls away, as fluid shear.

How can the flow bend the direction of the Normal reaction? How can the flow CARRY the stress?

The shear in a fluid is continous between its layers and betweeen the boundary layer and the contact surface.

Is there any known source of physics theory explaining it. I would like to know about it atleast read it once.

The pressure outside the nozzle is lower than the flow pressure inside.
The velocity is the flow pressure, the fluid's internal pressure is constant.

The Velocity of flow and the pressure are two seperate parameters. And the fluids pressure cannot remain constant during a varying diameter or c/s flow or when velocity changes.

Then what would you say about all the fluid machines, equipments where the Higher velocity from a fluid is converted to higher pressure energy to get a greater pressure output from a high velocity flow.

The perfect example of this is the INVOLUTE chamber of the Centrifugal Pump, which is a tube/chamber of continously increasing cross sectional area. The increasing area reduces the velocity head and goes on inceasing the pressure head instead.

How would your theory explain this.

Rohan_sKThe Velocity of flow and the pressure are two seperate parameters. And the fluids pressure cannot remain constant during a varying diameter or c/s flow or when velocity changes.

??
I think you're "keeping" the notion of gas pressure and applying it to pressure of a fluid. Try this thought experiment: take 1 bucket and make a hole in the side, near the base. Start slowly filling the bucket; if the fill rate is low, water flows out the hole and the level of water in the bucket is maintained, at the same height (fluid volume and surface pressure).

If you increase the fill rate the level in the bucket goes up, and passes the outflow rate. Pressure at the outlet is determined by the surface area of the water in the bucket, the higher it goes the higher the outflow rate. Flow pressure at the hole equals surface pressure (cross-section of container). The forces normal to the inner surface of the bucket, all pointing inwards, 'react' to the pressure by 'expelling' water from the hole. Flow out of the hole is the water 'reacting' to these forces.

Shear is not constant in fluids, e.g. water has vorticity which is nonlinear; water can move by rotating (gases do too).

Shear in laminar flows is linear, relative to vortical flow which isn't. Stress at the inside walls of the container is "absorbed" into shear by the fluid motion. Flow is slower at the edges, because there is more friction and interaction, the flow is almost linear near the center, less linear near the walls.
The centrally-directed flow 'pulls' the outer fluid along, translating normal stress into shear velocity.

If the bucket has no hole there's still the same pressures from the bucket and the surface; there's no overall flow but molecules are still subject to normal forces; the shear in a "static" fluid sums to zero = no bulk momentum.

Flow and pressure are more general than volume or density.
A gas has a volume which can vary, a liquid doesn't.
Gas pressure varies with a static volume of gas and a varying container volume, fluid pressure is static for a given fluid volume, flow varies and liquid flow is equivalent to gas pressure.
Gas flowing down a pipe has two kinds of pressure, the gas pressure which varies and the flow rate (which also varies locally, like a fluid's), which is determined by both pressures and the cross section. Liquid flowing down a pipe has only one kind of pressure, the flow rate/velocity.

p.s. the forces normal to the container, pointing directly inward don't "change direction" they always point away from the walls to the center. The fluid is translating, so the fluid "bends" not the normal force. A molecule in contact with a wall will reflect or bounce inwards, as it translates in a general direction along the flow (assuming the walls are smooth).

Here's a bender: (Physics exam) 1. Relate the partial pressure of a thin inert gas, that is converted into plasma by an oscillating electric field inside a glass container to bulk flow momentum and velocity; formulate an expression for bulk flow of charge in the plasma and outwards into the environment... In what sense is there a liquid flow-pressure? Explain your answer.
(I have a paper from a textile researcher, of all places, that does an analysis using Gauss's and Faraday's equations, if you want a peek)

Skipper, you have not spoken about the Centrifugal Pump Involute Casing, and the change of velocity head to pressure head there, yet.

??
I think you're "keeping" the notion of gas pressure and applying it to pressure of a fluid.

The flow of gases is a compressible flow. And I very well understand the difference between Compressible and Incompressible flow concepts.
And I am strictly speaking about the Incompresible flows in liquids.

If you increase the fill rate the level in the bucket goes up, and passes the outflow rate. Pressure at the outlet is determined by the surface area of the water in the bucket, the higher it goes the higher the outflow rate. Flow pressure at the hole equals surface pressure (cross-section of container).

The pressure of water at any level would simply be the Height of Water Column, and the pressure is same for the same height and is equally tramsmitted in all directions( this the beauty of hydraulics).

The forces normal to the inner surface of the bucket, all pointing inwards, 'react' to the pressure by 'expelling' water from the hole. Flow out of the hole is the water 'reacting' to these forces.

And the Outflow rate is not the function of surface area, but simply the height of the water column above the hole. Higher the water column higher the pressure.

It is only the pressure acting at the particular height which causes the water to flow out as soon as it finds an opening and the constrain is removed ( the hole in this case). There is nothing as reacting to the forces, the pressure is equal in ALL directions ( it is not unidirectional as any other stresses are, thats Pascals Law).

Shear is not constant in fluids, e.g. water has vorticity which is nonlinear; water can move by rotating (gases do too).

Shear in laminar flows is linear, relative to vortical flow which isn't

I have never said that the shear is constant. I have clearly said that the Shear force is acting CONTINOUSLY between two adjacent layers of a fluid, and this continous shear is what distinguishes fluids from solids.

And yes you are right, shear does exsist between the layers of water in a Vortex flow too.

Stress at the inside walls of the container is "absorbed" into shear by the fluid motion. Flow is slower at the edges, because there is more friction and interaction, the flow is almost linear near the center, less linear near the walls.

It is correct that the flow is slower at the edges due to friction between the fluid molecules in immediate contact with the surface, and this is exactly what causes the VELOCITY PROFILE in the fluid flow where the velocity is maximum at the center line of flow and lowest at the edges.

But there is nothing such as absorbing of the stresses being absorbed into shear. The flow is by the virtue of the driving force and the shear is merely the resistance to flow.

The centrally-directed flow 'pulls' the outer fluid along, translating normal stress into shear velocity

It is not the inner flow which pulls the outer fluid, but in fact the nature of the velocity profile is itself dictated by the friction between the outer molecules, and the velocity goes on increasing from outside to inside as the friction goes on reducing towards the centre.

If the bucket has no hole there's still the same pressures from the bucket and the surface; there's no overall flow but molecules are still subject to normal forces; the shear in a "static" fluid sums to zero = no bulk momentum.

Correct, there is no shear in a static fluid, except Brownian Motion in molecules.

Gas flowing down a pipe has two kinds of pressure, the gas pressure which varies and the flow rate (which also varies locally, like a fluid's), which is determined by both pressures and the cross section. Liquid flowing down a pipe has only one kind of pressure, the flow rate/velocity.

It is wrong in saying that the flow rate is the pressure in a liquid flow. No, dont confuse in it, Pressure is a different entity and Velocity of flow is a different entity in any fluid flow.

The fluid is translating, so the fluid "bends" not the normal force. A molecule in contact with a wall will reflect or bounce inwards, as it translates in a general direction along the flow (assuming the walls are smooth).

The fluid molecule does not bend or reflect inwards. It is not this way that the flow progresses. It is the driving force ( column pressure or some other external power sorce like a pump or piston pushing or fluid already having some motion) that causes the flow.

The driving force ives the molecules the energy to overcome the shear force between the surface material and themselves and continue to flow. The flow is always in a straight line in case of a laminar flow.

For analogy, you can consider the example of a projectile which when fired in a straight horizontal direction with sufficient velocity, maintains its straight path until it has enough energy left to overcome the gravitational force acting downwards. It will bend down or change direction only after the gravity becomes dominant on the velocity in horizontal direction.
The same happens with the fluid particles in a flow, they are continously pwered by the driving force from behind, ehich keeps them in straight motion.


And I will like to read the reasearch paper you mentioned regarding the Gauss and Faradays equations. Seems interesting. Would you mind mailing them to me, ofcourse if you dont have a problem in sharing it. I will be thankful if you can email them to me.

And regarding the experiment you mentioned , I need to first get information on the topic and study and understand it first., then i will certainly comment on it. can you just give some more details on it so we can have a better idea.

Well, I've tried; you appear to be disagreeing in some respects, and agreeing in others.

As you say there's a distribution of the flow velocity across a fluid with momentum (I called this a gradient).
And, it is true that the flow absorbs the normal forces at the walls - the walls absorb some momentum in the fluid, if the restoring force is linear then the walls return this momentum to the fluid as a normal force. Pressure for a gas is as you say, because of compressibility. Then what is the pressure in a flow of fluid? In a standing fluid the pressure is because of the exposed surface, I mentioned that the bucket has walls too, that react to the pressure (the total pressure on the fluid is the surface pressure plus the container "pressure" or the normal forces, at the container walls).

I'm fairly sure flow pressure is equivalent to gas pressure (as long as the fluid has momentum and the gas doesn't). "Flow" is dependent on bulk properties of matter, electric current is the flow of charge in conductors, electron pressure increases with electron density. Therefore pressure in capacitors is charge pressure or density per volume, equivalent to the pressure in a static volume of gas, or a fixed rate of liquid flow.

A static fluid's pressure depends entirely on the volume of fluid and the surface area, given that the pressure from the walls is constant.

A gas with momentum will change its pressure, this is essentially what happens when a fluid flows, but since fluids do not compress, the drop is entirely a function of the flow rate -> fluid pressure is bulk flow.
This extends to solids, a solid with momentum has a flow-velocity/pressure as well. Note: this is a general extension of the idea of "pressure", "volume" is constant for solids and liquids, so there's a direct relation between gas and liquid pressure.

Why do I insist that pressure from fluid flow is equivalent to a non-moving gas volume? Because fluids that don't flow have a fixed volume and pressure. A gas not flowing has a fixed relation to temperature, a fluid will not react to temperature until BP is reached. So the potential flow in a fixed volume of gas depends on gas pressure in a fixed volume and on the temperature of the gas. Potential flow in a fluid with a fixed volume depends on the height of the fluid. So gas pressure = fluid pressure when the gas is at fixed temp and pressure, and the fluid is at a fixed height; density and gravitational potential are the real drivers but gases 'escape' by expanding = lowering pressure. A fluid 'escapes' by gaining momentum = apparent pressure drop; but, a fluid always has a density dependent pressure.
Density is the key here: a liquid has the same density at different pressures (depths), a gas's density varies at different pressures and temperatures.

I didn't say that molecules bend, fluid motion is the "bend".

p.s. dang that paper has gone missing, after all. If you want to look into plasmas it's somewhat advanced theory. Check out the Lorentz force and flow in plasmas (try wikipedia); you generally don't look at plasma physics until 3rd year or grad level, btw. If you're good at math, no worries I guess.

After a think about all the confusing language, I suppose a simple way to visualise the pressure and density thing, is as follows:

In a cylinder with a piston, some liquid water is in the cylinder, trapped by the piston. If the air is pumped out, and the cylinder stood upright, then the water is frozen.
After freezing, the piston is moved so the ice is stuck to it but not to the cylinder.

Then the water is melted, then vaporised.

When solid, liquid or gas the water has the same molecular mass, but flow and pressure are different material properties. Compress the water when it's a vapor and you have to push against the expansion the heat gives the gas.
Liquid and solid flow are 'compressed' by being denser, but the molecular densities are very similar so liquid flow is translation of density-volume, equivalent to a solid with momentum.

Compressing a gas is equivalent to pumping fluid.

Any logical discussion goes smooth if we agree to disagree, after all its a platform to share diverse views about any topic.

Anyways, coming to the point, whatever you have said about gases and gaseous flow, its pressure , volume etc. is true and I share the same opinion.

But again when it comes to fluids( liquids to be precise), I differ a bit. The case of a flow where you suggest that the pressure drop is an appearent phenomena

The pressure is not actually lowered in the fluid, but the normal restoring force at the container wall is less, because of transverse flow (consider that if there is no flow, pressure is maximum at at the walls); fluids are incompressible so the fluid pressure is constant, the flow rate then determines how the stress against the walls, is translated by momentum. The "flow pressure" is not the fluid (internal) pressure, it's the potential 'pushing' the fluid along.

The pressure in a pipe is against the wall. The pressure in the flow is because of the bulk momentum in a unit volume, and because the pipe doesn't expand under pressure. The flow 'bends' the normal reaction from perpendicular to the flow, since a molecule in contact with the wall that gets a push toward the center, is moving sideways; shear is translated = the fluid flow is shear from the normal stress. The flow carries the stress at the walls away, as fluid shear.

I am quite sure of the fact that the pressure in a flow and the velocity of flow are two different and distinct parameters which cannot be confused to be the same.

About the bending of the normal reaction, I would say that the flow cannot 'bend' the normal reaction as such whatever be the flow velocity.

The normal reaction at any point on the surface of the pipe is due to the pressure of the fluid ( both column pressure and any external driving source). This pressure is always transmitted equally in all directions by any individual molecule by the virtue of the pascals law.

Thus the reaction by the pipe surface is always normal to the molecule in contact, irrespective of its position in the pipe ( above or below the center line).

The flow which is energised by some external means has the potential to overcome the resistance between the molecule in contact with the surface of the pipe which is the shear force we speak about.
The molecules have the energy supplied by the external source (pupming)
to surpass this shear and continue to move in the direction of flow.

By no means does the normal reaction get bend in this process. Normal reaction very well exsists by the virtue of pressure or weight of the water column.

To make it clear, just take the example of any solid which moves on the ground with certain velocity V, weight W and friction f along a straight line. Then irrespective of the magnitude of the velocity V, the normal reaction R will always remain to have the same value throughout the motion and will act in the directin normal to the surface of contact. The velocity or motion of the solid cannot influence its direction in any way. It cant bend the normal reaction due to velocity or friction which acts as a shear force between the solid and the ground.

This is applicable to the fluid flow where the flow velocity and the shear cannot bend the normal reaction in any way. The normal reaction always exsists in the same direction and same magnitude on the molecules in contact to the surface.

And as you said that the flow pressure is the flowrate, then the pressure must increase with the increase in the velocity which is not what is happening. Instead the pressure reduces with the increase in velocity of flow both for a constant diameter pipe or in a convergent nozzle with reducing area.

This is what needs to be clarified. The rest regarding the pressure of gases depending on the volume and the tempreature and density aspects are very much true.

Try this: A gas is "ruled" by the gas law PV = nRT. This relates pressure-volume to a density-temperature product (a compression/expansion to a "packing energy").

Look at the general formulation of Einstein's GR field eqns: G(uv) = 8*pi*T(uv), this relates a mass-energy product to a stress energy (closest packing of "energy" in spacetime). The density on the right has a geometric scale factor 8*pi - if the velocity of the flow is limited by c = 1, the largest diameter "pipe" that energy density can flow in, or the highest density energy can be compressed to, for a given diameter (of the mass-energy product G(uv)). Imagine that the universe is really a gas of free metallic "particles", with a pressure-volume G(uv), and a density-temperature product.

😀

To get the hang of pressure in a fluid start with a closed container like a cylinder with fluid in it. If the fluid is motionless the normal pressure = fluid internal pressure (densities are at equal "packing", for the solid walls and the fluid). In motion, the fluid will transform normal force (constant at the walls, or nearly so, this depends on the material being linearly "solid") as it moves. This is the shear velocity which varies across an area of the container - if you give the piston an impulse the fluid will spread along the bottom of the cylinder in a nonlinear way, when it's a gas it just compresses. Therefore normal wall pressure is translated by the fluid flow, and transformed into gas pressure (if the fluid is in a gas phase).

Assume the earth and moon are particles (of metal); the moon has a constant momentum (or very nearly) around the earth. The flow relation here is that the pressure of the container (gravity) keeps the "gas molecules" translating in a constant volume (orbital momentum). Density-temperature is a no-brainer; both bodies have a gravitational density g(x) where x is a member of {earth, moon} and a temperature which depends on the local energy density (and the permittivity or ability of spacetime to translate the particles along the container).

I think I can explain why pressure decreases in fluid flow. If you force a liquid through an aperture it has to have a higher flow rate, since the volume behind it has a larger cross-section.

Since pressure = rate of flow in a fluid, the PV relation is velocity*volume; the velocity across the flow is differential so that the normal pressure is greatest closest to the walls of the container, and lowest where the flow rate is maximal. Since fluids always have the same intrinsic pressure regardless of flow (they don't compress or expand) then the cross-section determines the velocity*volume relation; since this is equivalent to a density (constant) times a temperature (liquids absorb temperature and stay liquids) the velocity*volume product rules fluid flow.

If you reduce the outflow cross-section and maintain the flow rate, then the velocity must increase. The pressure drop is relative to the normal container pressure, or since the flow is maximal furthest from the walls, this is where the relative pressure drop is largest, in the center where fluid is translating at a maximum.

And, with a solid sliding under "linear" frictional forces - this is approximate and only works out if friction is assumed linear. This is not the case with high pressures and small volumes where friction is decidedly nonlinear (it depends on polarity and the 'chemical' cross-section interacting as two surfaces, how wet the surfaces are, molecular shapes, a lot of things).

Finally after all the lengthy discussion I have reached to a convincing explaination for the Pressure-Volume changes in a fluid flow.

The idea is very simple and needs the understanding of just a few basic principles of Fluid Dynamics and Statics.

The first is the PASCALS LAW which states that the pressure at any piont in the fluid is the measure of the height of the column above it and the density of the fluid and acts equally in all directions.

Therefore,

p( elevation) = (rho)(g)(h)

where, rho = density, g = acceleration due to gravity, h = height of column of fluid above the point.


The main concept is expalined by the BERNOULLI'S EQUATION which is based on the LAW OF CONSERVATION OF ENERGY.

The BERNOULLI EQUATION states that the Total energy content of the fluid in motion remains the same for a streamline and is the sum of the Static Pressure Energy, the Flow Kinetic Energy and the potential Energy due to Elevation.

Therefore,

E(total) = P(total) = P(s) + 1/2(rho)(v^2) + (rho)(g)(h)

where, P(s) = static pressure, v = velocity of flow, h = elevation , rho = density of fluid.

And the Energy is considered per unit volume of the fluid.


The approach of the Bernoulli equation is based on the Energy concept rather than the Mechanics outlook.

The Pressure in the fluid is considered as the total energy that the fluid beholds. Any fluid will have energy or pressure due to one or all of the above mentioned three factors namely the static pressure or the kinetic energy due to velocity or the pressure due to elevation.

Static Pressure : It is the pressure exerted on the fluid by any external source and is maximum when the fluid is at rest and is the count of the pressure due to potential.

Kinetic Pressure : It is the pressure due to the velocity of flow ie the kinetic energy of the fluid.

Elevation Pressure : It is the pressure due to the weight of the fluid above datum elevation.

Thus when the fluid flows under influence of some external energy source, it has energy in terms of total pressure comprising of the three components mentioned above.

Thus when the fluid flows it has some kinetic energy of flow and if the elevation is considered negligible, then the factors affecting thre flow are the static pressure and the kinetic pressure. As mentioned above the static pressure is maximum at rest and as the flow initiates the part of the energy is converted to kinetic energy of flow or dynamic pressure.

The conversion takes place due to the Law Of Conservation Of Energy, which implies that the total energy of a system always remains constant and can be only transformed from one form to another.

Thus when the area of flow reduces, then due to the Law Of Conseravtion Of Mass, the velocity of the fluid must increase in the reduced area so as to maintain the flow rate.

Hence, A1.V1 = A2.V2

Hence to provide for this rise in velocity the part of energy of the static pressure acts on a smaller area and thus increases the velocity. The energy expended in this rise in velocity is a part of the static pressure energy which acordingly reduces to maintain the total energy content of the fluid adhereing to the Law Of Conservation Of Energy.

Thus there is a mutual conversion between the static pressure and the dynamic pressure to maintain the equality of the total pressure or energy of the fluid.

The same is true when the area of flow increases and the velocity must reduce according to the Law Of Conservation Of Mass. The kinetic energy goes on reducing and the pressure energy inturn goes on increasing thus maintaining the Conservation Of Energy of the fluid.

The Pressure and Velocity conversion is thus governed by the basic laws of mass and energy conservation which are the basis of fluid dynamics.

You have given a mathematical solution to the initial query. but let us take an example:
Let us consider a nozzle, like in a common garden pipe, and we put a pressure measuring device obstructing the outlet flow. now pressure is measured by Force/area. So as the cross section decreases the area of the flow is also less. So the pressure must increase.
Also logically when we constrict the flow of a pipe the pressure exerted on our hand also increases if we try to obstruct the flow.

But Bernoulli's expression and the explanation you provided proves it otherwise.

Can you please explain this to me.

The static pressure is the average Kinetic energy of the rapidly colliding molecules of a liquid on the inner walls of container or this is the push which is experienced by the wall of container due to the impact of molecules.
Now see, what happens when the velocity of the fluid is increased....
The colliding particles/molecules of fluid gets a velocity and therefore they have a forward momentum and because of this momentum they strikes with the inner walls of the pipe with very acute angles and therefore less KE is transferred to the walls and hence a less pressure is experienced by the inner walls of pipe.

The static pressure is the average Kinetic energy of the rapidly colliding molecules of a liquid on the inner walls of container or this is the push which is experienced by the wall of container due to the impact of molecules.
Now see, what happens when the velocity of the fluid is increased....
The colliding particles/molecules of fluid gets a velocity and therefore they have a forward momentum and because of this momentum they strikes with the inner walls of the pipe with very acute angles and therefore less KE is transferred to the walls and hence a less pressure is experienced by the inner walls of pipe.

Just think about energy, is only an energy balance, if the fluid increase the speed then it increase the kinetic energy, so for the balance work well the pressure should decrease to decrease the potential energy.
Sorry about my english, i hope i helped. 😒

@bharatbhushan i get your point in the sense that you are calculating the pressure inside the pipe. but in the SFEE, the pressure velocity relation which is given is that of outside the pipe

whenever fluid flows in pipe it is considered to have two type of mechnical energy
1)kinetic
2)potential
which is said to be in form of
1)velocity head
2)pressure head
3)elevation head
4) (-)head loss
now scince there is no energy dissipering thanks to Mr einstine who told energy s conserved
and if elevation head ,head loss are constant then velocity head and pressure head are interrelated as
(pressure head)+(velocity head)=const
or else you can say scince energy is conserve
now science velocity represent kinetic energy ;were as pressure represent potential energy and science mechinical energy remians const
therefore
(velocity)+(pressure)=const

Read about nozzles. It will clear most of the concepts relating to comressible and non compressible fluids and therfore how changes in area affect changes in velocity and therfore a pressure drop.

Can you guys help me how to solve the Flow rate if i have 1 inch pipe with a 30 psi pressure,... actually my problem is how to get the velocity... i have some reference but its a simulation factor.. if i will use the given formula Q=Velocity x Area where velocity is equal to Square root of 2 x gravity x Height the result is too big

example 2inch pipe has a 20 m/sec velocity resulting on 600 GPM based on the formula but on the actual 2" can only have maximum of 250 - 300 gpm @ 30 to 40 PSI.. i hope some one could help me correct the formula im using thanks !!

If we examine Bernoulli's theorem, We have:

P + pgh + 1/2 pv^2 = K = Constant

In certain height, We have:
pgh = K' = Constant
1/2 p = a = Constant

Thus We have:
P + K' + av^2 = K

==> P + av^2 = K" = Constant

==> So P is inversely proportional to v. 😀

😎so for what you are waiting . .. . .😁
just go to charusat.blogspot.com

this is not the exact answer of pressure and velocity dear..............

OK...ITS LIKE THIS...WE KNOW BERNOULLI'S THEOREM IS ---------> (derived from) ----(v^2)/2 + p/(roh) = constant ...................now notice that the right hand side value is constant ! so it means that whatever be the change ...the complete value of the the formula must always be a constant......so from the LHS suppose velocity increases ..then in order to maintain the constant value on the RHS...the other values such as pressure must decrease ! and thats it ! 😀

CE Rookie,
Use the Formula V = RPM (of motor) * D (Diameter of Pump Impeler)/229
This will give you the velocity of the fluid leaving the pump.
Hope it helps.

When velocity increases, flow becomes more uniform. Pressure in a line is as a resut of the forces acting on the walls - basics
As flow becomes more uniform, there is less turbulence as particles are now forced to travel in the direction of the flow which is normal to the pipe and not perpendicular (toward the wall of the pipe).
Hope it helps you in some way. I know everyone is trying their best here.

Rohan_sKI want to know the reason WHY PRESSURE DROPS WHEN VELOCITY INCREASES.

This is a consequence of the First Law of Thermodynamics about conservation of energy. When a fluid is flowing in a closed system the total energy at any cross section is a constant. This consists of potential energy, kinetic energy, and pressure. In a horizontal pipe the potential energy is constant. If velocity increases (kinetic energy increases) pressure has to reduce correspondingly to keep the total constant. Bernoulli's theorem is based on this.

If there is a friction loss, this appears as heat.

Hi Rohan,

Bernoulli has well explained this phenomenon.







There are lota examples on this... For more info. just google it bro...
@ll da best

If we could recall the mass continuity equation
Q = AV
we could see that pressure and velocity has no direct relationship. for a varying area it changes. lets say if in a flow the area is decreasing the velocity will increase to maintain the flow, at the same time the pressure will decrease.
Another example is of a football. There is a pressure inside it but no flow. Moreover, we can increase the pressure but the velocity and flow will not increase.

Rohan_sKIt is a known fact that as the velocity of a fluid increases the pressure decreases accordingly.
It can be easily explained for a varying diameter pipe.
But for a constant diameter pipe, how can we theoretically explain the decrease in pressure with an increase in flow velocity of the fluid.
Can anyone explain why this pressure - velocity varaition occurs, lets develop the fundamental concepts.

using Power formula
P = Fd/t (P- power, F- force, t- time)
speed = d/t, is velocity
P = FS
p= F/A (p - pressure F- force, A- Area)
to get pressure formula from power formula
F = P/S
p = F/A
so, p= PxA/S
therefore the higher speed, the lesser the pressure..

This is only I can share I hope it helps..

BERNOULLI'S PRINCIPLE

Its because of Bernoulli's principle which states 'the total energy of a flowing fluid is constant'. So when the kinetic head arises due to the increase in velocity, the pressure head has to get decreased in order to keep the total head constant as the static head is not going to change if we keep the distances of points of interest same from the datum.

whenever a fluid flowing through a convergent -divergent pipe all other properties are same except pressure,velocity,density(compressible fluid)
according to Bernoullies eqn
Px/£g +Vx^2/2*g+Zx= Py/£g +Vy ^2/2*g+Zy+Hl
where Hl :head loss.
Z:distance of head from datum

Hey guys..i ve been reading the entire discussion but still unable to figure out were we are heading towards......if we say that the increase in velocity causes the drop in pressure say in case of a fire hose nozzle....

the simple reason is that energy can neither be nor be destroyed. whenever there is a flow in pipe then there are three kind of energies - kinetic energy, pressure energy, potential energy.
kinetic energy is because of velocity of fluid.
pressure energy is because of pressure exerted by fluid.
potential energy is because of height.

All of these energies are mentioned in bernoulli's theorem.

now consider that the area of cross-section of pipe decreases and and at same level- according to continuity, if area decreases than velocity increases means kinetic energy increases and as energy can neither be nor be destroyed but only converted from one from to another, so in order to compensate the effect of increased kinetic energy, the pressure enregy decreases means pressure and vice-versa according to the situation.

that's it, this is the main reason that with the increase in velocity pressure decreases and vice-versa....

i hope its clear to you , if not feel free to ask.😀

Hey Rogan ...very valid point U ve raised and uve discussing your topic with my fellow mates as well and it was really surprising to see the top guns amongst thee group were not able to clearly come up with the reason to justify your question...in the end I would say...ur point is valid enough ..wat happens during the fluid flow which causes this change in presuure or drop as U mentioned duue to the increase in the velocity due to the reduced croseection ..even I am untreated to know wat happens T the microscopic level....

I case of nozzle the area of crossection decrease and presuure -f/a....so pressure should increase then...y its the recess then according to continuity and bernauliis...please come up with something sensible and logical people....stop giving theoritical views..be practical..😉

MOD EDIT : Post Merged.

You have to think according to the situation. Consider a tank with high pressure, if we open the tap means water flows with high velocity and eventually after sometime the velocity will start to reduce because of pressure is decreasing accordingly. Velocity and pressure is directly proportional.

If you're looking for a simple reason why, then:

In an incompressible fluid, it is because of the conservation of internal energy. That is as simple as it can get. Bernoulli's equation is what we are looking at here.

The explanation given by #-Link-Snipped-# that when area is reduced velocity increases and to increase this velocity some energy is required which is obtained from static pressure energy...thus as area reduces velocity increases and pressure is reduced....and there is mutual conversion of static pressure and dynamic pressure ..thus even the law of conservation of energy is followed and total energy of flowing fluid which is sum of static pressure and dynamic pressure(if elevation is neglected) remains constant ...thus pressure also remains constant as he mentioned that pressure is the summation of energies of flowing fluid.....so even though static pressure energy is converted to kinetic energy(increased velocity) but total energy remains constant thus pressure is constant and is not reduced even though velocity increases with decrease in area......


someone please explain how pressure and velocity are inversely proportional in a flowing fluid

The concept is simple.Just assume a bunch of molecules.now if the pressure is increased the tend to get compressed it means that their chances for displacement also decreases and so does the velocity also.and viceversa if pressure decreases they are free to move and so velocity increases

Rohan_sKIt is a known fact that as the velocity of a fluid increases the pressure decreases accordingly.
It can be easily explained for a varying diameter pipe.
But for a constant diameter pipe, how can we theoretically explain the decrease in pressure with an increase in flow velocity of the fluid.
Can anyone explain why this pressure - velocity varaition occurs, lets develop the fundamental concepts.

Since the velocity is increasing and from Bernoulli's equation the pressure decreases in any kind of pipe neglecting friction. Let us take a small length of the flow say dx and since the cross section of the pipe is same at every point which implies the amount of liquid in a given volume say dx*A=V depends on the velocity at the chosen dx. If the velocity is low the amount of liquid(molecules) will be high in the volume V and the pressure will be high due to high inter-molecular forces and vice versa when velocity is high, there will be less no of liquid molecules and the inter-molecular forces will be less and hence low pressure.

The static pressure is the average Kinetic energy of the rapidly colliding molecules of a liquid on the inner walls of container or this is the push which is experienced by the wall of container due to the impact of molecules.
Now see, what happens when the velocity of the fluid is increased....
The colliding particles/molecules of fluid gets a velocity and therefore they have a forward momentum and because of this momentum they strikes with the inner walls of the pipe with very acute angles and therefore less KE is transferred to the walls and hence a less pressure is experienced by the inner walls of pipe.

It may be worthwhile to revisit the original post.
Quote: But for a constant diameter pipe, how can we theoretically explain the decrease in pressure with an increase in flow velocity of the fluid. Endquote
The assumption is incorrect. For a constant dia pipe any increase in flow leads to an increase in pressure, which is due to pipe friction.
This can be used to check this:
#-Link-Snipped-#

simply apply bernoulis equation

The answer is very analogous to the situation....
assume person # is applying force as effort to move a huge block"B" ( moving a huge block is possible by overcoming friction and inertial resistance[or accelerational resistance] ) upto a velocity (say 50mph))
as when the block is at rest the force effort is maximum
as the block starts picking velocity force effort decreases..
as the block reaches 50mph the effort minimizes (..upto the level mandate for overcoming friction)
similarly
assume a situation in which a horizontal pipe is there (let it be filled with water initially for simplification) of whose one end is closed and other is fixed to a pump #.
now, let the pump # is applying pressure effort to move water (here moving means overcoming viscosity, overcoming pressure effort applied from other side {since the pipe is closed there is 0 pressure effort or pressure one the other side} upto the velocity (say 50 mph)
now as soon as the closed end is opened to (vaccum of atmospheric pressure) the water starts moving in pipe.
when the water was still the pressure effort was maximum and it reached to minimum when the water reached at 50 mph ( upto a level required for overcoming viscosity and the pressure from other side). The VISCOSITY here is analogous to friction here.
I haven't seen any description done here of viscosity before ( I accept that i haven't read out every description before).... so i am describing it a little bit.
the resistance (of the perpendicular pressure applied on the walls by fluid) generates viscosity. viscosity varies with velocity of flow, dia of pipe, and longitudinal area of pipe (not cross sectional area)
viscous force,

here, A- longitudinal area
u- velocity of flow at the center of cross section of pipe
y- radius of pipe
μ- coefficient of viscosity of fluid
the, coeficient depend upon the nature of flow, type of fluid, compressability etc.
there is friction also present in pipe which acts only at outermost layer of water inside pipe but inside that outer most layer there are infinite layers of water of approx. zero width whose flow is governed by viscosity. thus the flow of liquid is layered which is governed by viscosity.

Nagesh Ranjanviscosity varies with velocity of flow, dia of pipe, and longitudinal area of pipe

Viscosity of a Newtonian fluid is invariant at a constant temperature. None of the above affect it. One can get a better handle on viscosity here:
<a href="https://physics.info/viscosity/" target="_blank" rel="nofollow noopener noreferrer">Viscosity – The Physics Hypertextbook</a>

Rohan_sKThe Relation given above is for the FRICTIONAL HEAD LOSS due to internal pipe surface.
The Darcys formula gives the relation between the Head Loss due to Friction in the flowing fluid wrt Flow Velocity, coefficient of friction, dia. of conduit.
This is NOT what I was looking for.
I want to know the reason WHY PRESSURE DROPS WHEN VELOCITY INCREASES.

For me the above formula explains clearly... the Velocity square is directly proportional to the drop in pressure. That answers your question