Chapter 15 Flow Measpurements

7/28/2019 Chapter 15 Flow Measpurements

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Chapter 15 Flow Measurements

Measuring flow rate is extremely important for many industrial

processes, and often is necessary in the lab also. The term flow rate is

ambiguous, we should specify whether we mean mass flow rate or

volume flow rate.


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Conservation of Mass

dmsys

dt m

inlet

mexit

(From Thermo)

tdV U

CS

CV

ndA 0 (From Fluids)

m UA

ndA U

A


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Volume Flow

If the density is constant, then this tells us that the volume flow is

fixed, orQin = Qout where

Q UA

ndA U A

m UA

ndA U A

So if we want to measure volume flow rate, we need somethingsensitive to average velocity.

If we want to measure mass flow rate, we need something to average

mass flux


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15.2 Flow Characteristics

Laminar/Turbulent determined by Reynolds number


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Volume Flow Rate Measurement

Brute Force Method. Measure the velocity, do the integral.


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Bernoullis Equation

P1 P2

V2

2 V12

2gc


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Obstruction Meters

P1

P2

V2

2 V1

2

2gc


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15.3.1 Obstruction Meters

for = const

p1

V1

2

2

p2

V2

2

2

Qideal V2A2 A2

1 A2 /A1 2

1/ 22gc P1 P2

V1 A2A1

V2

P1 P2 V2

2

2gc1 A2 /A1

2


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Velocity Approach Factor

E1

1 A2 /A1 2

1/ 2

For round pipes, make b= d/D where d is the smaller diameter whileD

is the larger,

E1

1b4

CQactual

Qideal

K CEC

1b4

discharge coefficient

flow coefficient

Qactual KA22gc P1 P2


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Venturi Meters

0.95 < C< 0.98


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Flow Nozzles


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Bore diameters from 0.375 to 24


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Orifice Flow Meters


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Losses in Orifice Flow Meters


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Relative performance


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Application

h k d l d i l


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Choked Flow and Sonic Nozzles

If the flow inside of one of these devices becomes sonic, the mass

flow rate becomes fixed with changes in the downstream pressure.This can be used to limit the mass flow, and can also be something to

be avoided, because when it occurs, our calibrations we have been

talking about are no longer valid. Choked flow exists if

po

p1

2

k1

k/ k1

We can use this fact to fix the mass

flow at a value equal to

m 1A 2RT1k

k12

k1

2

k1

i l l


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Laminar Flow Elements

The obstruction meters are something you are most likely to see in an

industrial setting, since they are cheap and rugged. If more accuracy isdesired, and you have more money and you arent flowing something

really nasty, a laminar flow element may be more appropriate.

Remember that flow is laminar at small Reynolds number:Re = UD/n.

This tells us that we can make flow laminar if we put it through a

sufficiently smallD.

L i Fl El


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Laminar Flow Elements

We do this because the pressure drop/flow rate relationship for

laminar flow is very nicely behaved:

Q d1

4

128

p1 p2L

Re 2000

The important part is the fact that Q varies linearly with DP. Once again,the manufacturer of this meter will provide the sensitivity.

M i L i Fl El


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Meriam Laminar Flow Elements

R


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Rotameters

Q AwC2gf f w

Afw

1/ 2

Aw 4

D by 2 d2

2% full scale

T bi Fl M


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Turbine Flow Meters

1/2%

V Sh ddi M


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Vortex Shedding Meters

StfD

V

V t Sh ddi M t


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St fDV

V t Sh ddi M t


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Q K1

K1

d3

4St

M Fl M t


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Mass Flow Meters

Thermal Flow Meter 1st law, ideal gas:

E m cpDT

Ch M Fl M t


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Cheaper Mass Flow Meters

Old S h l


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Old School


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St ti P


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Static Pressure

A very fortunate result of boundary layer theory tells is that the

pressure gradient normal to a wall is negligible. This means that if we

measure the pressure at the wall, it is the same as in the bulk fluid. So,

we can put a small hole in the wall of whatever we are looking at and

measure the pressure there.

V l it Pit t St ti P b


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Velocity--Pitot-Static Probe

ps

Us2

2

pT

UT2

2

Us 2pT ps

Us2 DP

2 U

dDP

2

DP2 1

DP

2

Pitot probe errors


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Pitot probe errors

Kiel Probes


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Kiel Probes

Static Pressure Probes


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Static Pressure Probes

Transmission Effects


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Transmission Effects

Many times, the pressure is transmitted to a sensor via some sort of

flexible tube. This tube will effect the response of the system, andwe need to be careful that it does not affect our results.

Thermal Anemometry


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Thermal Anemometry

Particle Image Velocimetry


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Particle Image Velocimetry

PIV


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PIV

PIV data


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PIV data

Flow meter calibration


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Flow meter calibration

Chapter 15 Flow Measpurements

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