# Pressure - Velocity relation in fluids

Discussion in 'Mechanical | Automobile | Aeronautics' started by Rohan_sK, May 31, 2009.

1. ### skipper Apprentice

Engineering Discipline:
Computer Science
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.

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2. ### Rohan_sK Apprentice

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

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.

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3. ### skipper Apprentice

Engineering Discipline:
Computer Science
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).

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4. ### skipper Apprentice

Engineering Discipline:
Computer Science
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).

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5. ### Rohan_sK Apprentice

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.

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6. ### donarundas Newbie

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.

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7. ### bharatbhushan198 Newbie

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.

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8. ### bharatbhushan198 Newbie

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.

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9. ### juma1987 Apprentice

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.

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10. ### donarundas Newbie

@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

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11. ### shubhrajeet tiwa Apprentice

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
now scince there is no energy dissipering thanks to Mr einstine who told energy s conserved
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

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12. ### rpower Apprentice

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.

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13. ### amici_mike Apprentice

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 !!

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14. ### pdpax Newbie

Engineering Discipline:
Aerospace
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.

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15. ### emmawotson Apprentice

Engineering Discipline:
Mechanical
so for what you are waiting . .. . .
just go to charusat.blogspot.com

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16. ### sexy_engineer Apprentice

Engineering Discipline:
Mechanical
this is not the exact answer of pressure and velocity dear..............

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17. ### Crysis Recore Newbie

Engineering Discipline:
Chemical
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 !

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18. ### CE Designer Ace

Engineering Discipline:
Mechanical
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.

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19. ### CE Designer Ace

Engineering Discipline:
Mechanical
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.

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20. ### A.V.Ramani Guru

Engineering Discipline:
Biomedical
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.

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