flow velocity

7/23/2019 Flow Velocity

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Flow velocity

Flow velocity of a fluid is defined as:

A vector field which is used to mathematically describe the motion of a

fluid. The length of the flow velocity vector is the flow speed. The flow

velocity u of a fluid is a vector field

Which gives thevelocity of anelement of fluid at a position and

time .

Flow velocity is a vector quantityused to describe the motion of afluid. It can be easily determined for laminar flow but complex to

determine for turbulent flow.

Why is there a need of techniques for velocity flow

measurement?

Velocity flow measurement techniques allow for the measurement

of total flow by measuring the velocity of the fluid within a fixed area duct

or pipe. The technique uses a measuring probe to determine the velocity

of the fluid in the center portion of the pipe.

It is important to understand that with all fluid flows, there are

boundary layer effects at the interface between the walls of the duct or

pipe and the fluid flowing through it. For this technique to provide

reasonably accurate results, the velocity measurement of the flow must be

made well within the duct, to minimize the effects of the boundary layers.
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For this reason ducts or pipes of small diameter typically do not fair well

with this technique.

The technique also requires that you be in a laminar flow

environment. The results in a turbulent flow area suffer in stability and

accuracy. It is possible to calculate the location where the flow in a pipe

or duct is fully laminar, but for most applications a general rule of thumb

is sufficient. That rule is to make the measurement at least 10 pipe

diameters upstream and 20 pipe diameters downstream of any junction,

elbow or other flow disturbing point in the pipe.

Techniques for measuring the volume flow rate:

There are many techniques for measuring the volume flow rate.

These include:

Turbine meters

Vortex flow meters

Rota meters

Electromagnetic flow meters

Ultrasonic flow meters

These can and are used to measure flow rate in turbulent flows.

They dont tell us anything about the turbulence.


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In a sense, the volume flow rate devices really measure the velocity of the

flow. For the most part, though, they measure the mean velocity of the

fluid.

Techniques for measuring the flow velocity:

For many applications, we want to measure the velocity at a point. In

particular, if were interestedin measuring the local velocityin a

turbulent flow . . .

Here, we have fourchoices:

Pitot tube

Hot-wire anemometry

Laser Doppler anemometry (or velocimetry) (LDV)

Particle image velocimetry (PIV)

Pitot tubeThe Pitot tube is a simple device that allows for the

measurement of the flow pressure in a moving fluid.


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Working of Pitot tube

It works in much the same way as the restriction flow meters

do. The tip brings the fluid moving towards to a stop, so the pressure you

measure there is the stagnation pressure. The pressure along the side of

the tube corresponds (you hope) to the static pressure in the free stream.

You use Bernoullis equation to get the velocity.

By solving we get the following equation:

Now by simply multiply it by the area of the duct to get the total volumeflow.

Advantageous of Pitot tube

The Pitot tube is a simple, inexpensive, and highly reliable

devicesince it has no moving parts.

Requires only a few access holesinto the flow conduit; no wide

open cut needed.

It also causes very small pressure dropand usually does not

disturb the flow appreciably. However, it is important that it must

be properly aligned with the flow to avoid significant errors that

may be caused by misalignment.


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Almost no calibrationrequired.

The difference between the static and stagnation pressures (which

is the dynamic pressure) is proportional to the density of the fluid

and the square of the flow velocity. It can be used to measurevelocity in both liquids and gases.

Disadvantageous of Pitot tube

Not suitable for measuring low velocities (< 5 m/s). Not suitable for the measurement of highly fluctuating velocities.

Pitot tube must be alignedwith the flow velocity to obtain good

results.

Hot-wire Anemometry

While Pitot tubes work well for high flow rates in gases, and avariety of flow rates in liquids, the technique fails for low air

velocities in gases. To solve this gap in velocity measurement

technology, the hot wire and hot film probes were developed. This

technique is fairly straight forward in concept, but much more

difficult in operation.


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Working of Hot-wire Anemometry

Working is that if you place a resistance wire in the flow ofair (or other gas) and heat the wire with a fixed current, the voltage

across the wire will indicate the resistance of the wire. If you know

the properties of the wire you can deduce what its temperature is.

Knowing this information, you can determine how much heat is

being carried away by the moving stream of gas flowing across the

wire or film.

Types of hot wire anemometer

1.Constant Current Anemometer


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Wheatstone bridge is fed by constant electric current. The series

resistivity of the

energy source is set

large w.r.t. to thetotal resistivity of

the bridge, in order

to keep current

constant at all times.

Temperature and

resistivity change of

the hot wire induces

an unbalance of the

voltage at the

vertical bridge diagonal, which is manifested as flow velocity.

2.Constant Temperature Anemometer

Maintaining constant resistance R ofthe probe implies that temperature is

also kept constant. The output

voltage provides measure of the heat

transfer from the probe. This heat

transfer is a measure of the fluid

parameter under consideration at

that time.

3.Thermal f low Anemometer


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An industrial version of the fine-wire anemometer is the thermal

flow meter, which follows the same concept but uses two pins or stings to

monitor the variation in temperature. The stings contain fine wires, but

encasing the wires makes them much more durable and capable of

accurately measuring air, gas, and emissions flow in pipes, ducts, and

stacks. Industrial applications often contain dirt that will damage the

classic hot-wire anemometer.

Advantageous

Advantageous of hot wire anemometer are given below:

Hot wire probes are extremely fast response devices.

With a wire size in the micrometers.

The probe can respond to temperature changes at rates faster than 1

millisecond. This makes this type of probe ideal for studies of

turbulent flows.

Scientific level meters are available from a number of companies

that will respond to these high rates of change.

Smaller hand held units that respond much slower are available for

a few hundred dollars and are a good solution to a low flow

application.


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The accuracy of these devices is typically around 1% or so and are

generally designed for use in air, although most can be calibrated

for other gasses as well.

High frequency response, >10 kHz (up to 400 kHz).

Limitations

The difficulty with this is that the density, temperature and actual

makeup of the gas flowing affect the heat absorption as well as the

flow.

o

Solutions

This has been handled in a number of ways:

1.The most straightforward is to use two wires. One in the flow and

one out of the flow, and make your measurement based on the

difference of these two values.

2.A second method is to make an assumption that the reading is being

made in standard air which has a known coefficient of absorption.

Using this method the only values that are needed are hot wire value

and the temperature of the air prior to the hot wire.

Needs to be recalibrated frequently due to dust accumulation.

It does not sense the flow direction

Fluid may decompose due to high temperature

These are very good measurements, however they may not be

appropriate for all applications.


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Laser Doppler anemometry (or velocimetry) (LDV)

Laser Doppler Anemometry is a technique for measuring the

direction and speed of fluids.

Why Laser Doppler Anemometry?

Most flow measuring instruments measure physical quantities which

are functions of the flow velocity. Measuring quantities by which flow

velocity is determined, often are functions of the properties of state of thefluid medium, which have to be known. They have to be taken into

account in the calibration of the measuring method. These difficulties led

to development of LDV.

Working of LDV

In its simplest form, LDV crosses two beams of collimated,

monochromatic, and coherent laser light in the flow of the fluid being

measured. The Laser Doppler Anemometer sends a monochromatic laser

beam toward the target and collects the reflected radiation. Change in

wavelength of the reflected radiation is a function of the targeted object's

relative velocity (Doppler Effect).Typically, a Helium-Neon or Argon ion

laser with a power of 10 mW to 20 W is used.


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Laser Doppler anemometers use a beam of light from alaser that is

divided into two beams, with one propagated out of the anemometer.

Particulates flowing along with air molecules near where the beam exits

reflect, or backscatter, the light back into a detector, where it is measured

relative to the original laser beam. When the particles are in great motion,

they produce aDoppler shift for measuring wind speed in the laser light,

which is used to calculate the speed of the particles, and therefore the air

around the anemometer.

Applications of laser Doppler anemometry

Investigation of boundary layers and shock wave interaction

phenomena for both laminar and turbulent flow

Determination of 3-D wing tip vortices near the tips of the

aircraft wings

Measurement of flow b/w the blades of turbines

In measurement of blood flows

Remote sensing of wind velocities

Advantages of laser Doppler anemometry

Non-Contact type of measurement
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Direct way of measuring local velocity in all three spatial

coordinates.

Very high frequency response of order of MHz is possible.

Very high accuracies of the order of 0.2 %.

Limitations of laser Doppler anemometry

Sufficient transparency is required between the laser source, the

target surface, and the photo detector.

Accuracy is highly dependent on alignment of emitted and reflected

beams.

Expensive prices have dropped as commercial lasers have matured

PARTICLE IMAGE VELOCIMETRY

Particle image velocimetry is anoptical method offlow visualization used

in education and research. It is used to obtain

instantaneousvelocity measurements and related properties influids.The

fluid isseeded with tracerparticles which, for sufficiently small particles,are assumed to faithfully follow theflow dynamics (the degree to which

the particles faithfully follow the flow is represented by the Stokes

number). The fluid with entrained particles is illuminated so that particles

are visible. The motion of the seeding particles is used to calculate speed

and direction (thevelocity field) of the flow being studied.

Other techniques used to measure flows are laser Doppler

velocimetry andhot-wire anemometry.The main difference between PIV

and those techniques is that PIV produces two-dimensional or even three-dimensionalvector fields,while the other techniques measure the velocity

at a point. During PIV, the particleconcentration is such that it is possible

to identify individual particles in an image, but not with certainty to track

it between images. When the particle concentration is so low that it is

possible to follow an individual particle it is called Particle tracking
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velocimetry,whileLaser speckle velocimetry is used for cases where the

particle concentration is so high that it is difficult to observe individual

particles in an image.

Particle image velocimetry Applications

Aerodynamics

Hydrodynamics

Internal Combustion Engines

Reactive Flows Mixing Flows

Spray Formation

Flows in Pumping and Rotating Machinery

Flows in Devices for Life Sciences and Biomedical Work

Quantifying the deformation and motion of solid materials or tissues

that have embedded markers or are in some other way visually

heterogeneous

Advantages Particle image velocimetry

Nonintrusive.

Capable of measuring an entire two-dimensional cross section

(geometry) of the flow field simultaneously.
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Allows the generation of large numbers of image pairs which,

are analyzed in real or later time. Thus near continuous

information may be gained.

High degree of accuracy, since each vector is the statisticalaverage for many particles within a particular tile.

Limitations of Particle image velocimetry

The particles will, due to their higher density, not exactly follow the

motion of the fluid (gas/liquid).

PIV in general will not be able to measure components along the z-axis.

The size of the recordable flow field is limited by the size of the

tracer particles.

The resulting velocity field is a spatially averaged representation of

the actual velocity field. Accuracy of spatial derivatives of the

velocity field, and spatial correlation functions (derived from PIV

velocity fields) are affected.

Rotameter

A rotameteris a device that measures theflow rate ofliquid orgas in a

closed tube.

It belongs to a class of meters calledvariable area meters,which measure

flow rate by allowing the cross-sectional area the fluid travels through, to

vary, causing a measurable effect.

Why Use a Rotameter (Variable Area Meter) to MeasureFlow

Their top six responses are clues as to why a rotameter continues tobe successful even after a hundred years.

1.No external power requiredRotameters are mechanical devices which

do not require power to provide flow measurement. This allows
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rotameters to be installed in hazardous areas and remote areas where it

would be expensive to supply power.

2.You can see the processCustomers not only get a flow measurement

reading but a look into their process. Is the process dirty or cloudy

looking which could mean filters need to be changed? Is the process thecorrect color, are their bubbles in the liquid.

3.Rotameters are cost effectiveRotameters can be installed with other

flow measurement technologies and be used to complement each other

at an economical price.

4.Simple to install and maintainRotameters are quickly installed by

connecting the process line to the inlet and the outlet of the rotameter.

Make sure the meter is vertical and you are now ready to measure flow.

5.

Low pressure dropMost small rotameters have only a few inches ofwater column pressure drop. This means rotameters can be installed in

many places in the process. Small pressure drops mean smaller pumps!

6.RepeatabilityGiven the same process conditions a rotameter will

accurately repeat the flow measurement day after day.

These six features assure rotameters will continue to be important

products to measure flow now and in the future.

Working of rotameter

When fluid or gas flows through a taper tube containing a float,

a pressure difference of P1 and P2 is created between upper and

lower side of the float. The float moves upwards by a force obtained

by multiplying the pressure differential by the maximum cross

sectional area of the float.

Due to taper tube, as the float moves upwards, the fluid passing area

increases as a result of which the differential pressure decreases.

Upward movement of float stops when the dead load is dynamically

balanced by the differential pressure. Tapering of metering tube is so


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designed that the vertical movement of the float becomes linearly

proportional to the rate of flow and the scale is provided to read the

position of the float, thus giving birth to flow rate indication.

Based on Bemoulli's theorem, the principle mentioned above can be

theoretically expressed as follows.

FLOW FORMULA

Where

Q = Volumetric flow rate

V = Volume of Float

C = Flow coefficient

Af = Maximum pressure receiving area of float.

A = Fluid passing Area

P = Float Density

g = gravimetric accelerationy = Fluid Density


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Advantageous

A rotameter requires no external power or fuel, it uses only the

inherent properties of the fluid, along with gravity, to measure flow

rate

A rotameter is also a relatively simple device that canbe mass

manufactured out of cheap materials, allowing for its widespread

use.

Since the area of the flow passage increases as the float moves up

the tube, the scale is approximately linear

Clear glass is used which is highly resistant to thermal shock and

chemical action.


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Disadvantageous

Due to its use of gravity, a rotameter must always be vertically

oriented and right way up, with the fluid flowing upward.

Due to its reliance on the ability of the fluid or gas to displace thefloat, graduations on a given rotameter will only be accurate for a

given substance at a given temperature. The main property of

importance is the density of the fluid; however, viscosity may also

be significant. Floats are ideally designed to be insensitive to

viscosity; however, this is seldom verifiable from manufacturers'

specifications. Either separate rotameters for different densities and

viscosities may be used, or multiple scales on the same rotameter

can be used. Due to the direct flow indication the resolution is relatively poor

compared to other measurement principles.

flow velocity

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