L7 Densitiy Flow

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DENSITY MEASUREMENTBolton-Ch-12

Density is defined as mass per unit volume.

Relative density is the ratio of mass of a volume to the mass of anequal volume of water.

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Weight methods

Can be used forcontinuous monitoringof the density of fluidsin motion.

The fluid passesthrough a U-shapedtube which has aflexible connectors sothat it can pivot aboutthem.

The weight of the fluidin the U results in aforce on the tubesupport.

Force-balance systems


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With a pneumatic force-balance system, the force causesthe pressure to change in a flapper-nozzle system.

The changing pressure then results in a changing forceapplied to the tube support by means of a bellowsarrangement.

At balance when the U is horizontal, the pressure in thesystem is measure of the weight of the fluid in the U tube.

Since the volume of the U is constant then the pressure isa measure of the density of the fluid.

Used for densities up to 1600 kg/m3 and with slurries andfluid containing solid matter, provided the flow rate is highenough to avoid deposition of entrained solids.

Load Cell If the level of a liquid in a container is kept constant then any

change in its weight will be due to a change in density. Load cells in the supports of the container can be used to

give continuous responses related to this change in weight.

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Buoyancy methodsHydrometer

The upthrust acting on a bodyimmersed or partially immersed in afluid is equal to the weight of thefluid it has displaced (Archimedesprinciple).

Hydrometer is essentially aweighted tube which floats in aliquid to a depth which depends onthe density of the liquid.

The weight of hydrometer is thenequal to the weight of the fluiddisplaced by the hydrometer.

A scale on the stem of theinstrument enables the density tobe read off as the value at the liquidsurface.

The instrument is simple and

cheap.


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Torque tube

A float is completely immersed and so because the

volume of liquid displaced does not change, theupthrust force on the float only changes if thedensity of the liquid changes.

This upthrust force is used to twist a tube. This can

be monitored by means of a pneumatic system.

Such method can be used for high temp liquids andboth open and closed tanks.

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Pressure methods

The difference in pressure between any twolevels in a liquid or gas is equal to hg,

where h is the vertical distance between the levels, isthe density and g the acceleration due to gravity.

Differential pressure methodsThe level of liquid in the container is maintained at aconstant level. The pressure at some level below thesurface depends only on the density.


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Bubbler method Based on the principle that the

pressure in an open tube in aliquid when fed with gas, islimited by the gas escaping asbubbles.

Two tubes are used with thesame gas supply connected toboth. The open ends of thetubes are at different depths inthe liquid and so there is thus adifference in pressureproduced between the twotubes.

For a constant heightdifference between the tubes,the pressure difference isrelated to the liquid density.

Not suitable for closed vesselsor liquids containing particleswhich might block the tubes.

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Vibrating tubes The tube is fixed at each end

Tube oscillated by magnetic forces using AC in the drive coilthe coilbeing located at the mid point.

The amplitude is monitored by pickup coil

The tube is maintained in oscillation at its natural frequencythefrequency depends on the total mass of the tube and its contents.

Since the tube has a constant volume the frequency is affected bychanges in the density of the fluid inside.

Can be used with liquids and liquid-solid mixtures.


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FLOW MEASUREMENT

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FLOW MEASUREMENT

Fluid: A substance that flows. Reynolds number =

If

the velocity = v

Time = t

Cross sectional area of tube = A

The volume of fluid that has movedthrough this distance in time t = Avt

Volume rate of flow Q = Avt/t = Av

A fluid in motion has: potential energy,

kinetic energy,

pressure energy and

heat energy;

its total energy is equal to sum of all energies

Flow measurements can includemeasurements of three different quantities,the actual velocity of the fluid at some pointin the fluid, the volume rate of flow, and themass rate of flow.

viscosityfluid

densityfluid

velocityfluid

diameterpipe

v

D

vD


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The volume flow rate Q through a pipe or duct is just theintegral of the velocity distribution, V(x,y), over the cross-sectional area A.

For Engg purposes, an average velocity Vis often used:

Flowmeters measure Q and/or V, while velocity probesmeasure V(x,y). However, the output of a velocity probe canbe integrated to obtain Q or V.

Bernoullis equation for the flow of incompressible fluidsbetween points 1 and 2 may be written in terms of local oraverage velocity as

A

dAyxVAA

QV ),(

1

A

dAyxVQ ),(


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gravitytodueonaccelerati

elevation

velocitylinear

density

pressureabsolute

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2

1

2

221

2

cg

g

Z

V

P

c g

ZZ

g

VVPP

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ObstructionMeters


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With velocity change there willbe pressure change.

At points of maximum

restriction, hence max velocity,min pressures are found.

A certain portion of thispressure drop becomesirrecoverable owing todissipation of kinetic energy;therefore, the output pressurewill always be less than theinput pressure.

Venturi with its guided re-expansion, be the mostefficient.

Losses of about 3040% ofdifferential pressure occurthrough the orifice meter.

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Electromagnetic flowmeters

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L7 Densitiy Flow