Volume Flow MeasurementsVolume Flow Measurements

Obstruction MetersObstruction Meters Orifice Meters

Venturi Meters

Flow Nozzles

Flow through a NozzleFlow through a Nozzle

2211

21

222111

21

vAvA

ibleincompress

vAvA

Avm

mm

1

1

1

1

v

A

m

2

2

2

2

v

A

m

Basic Equations:

a.) Continuity:

mass in = mass out

b.) Bernoulli’s Eqn.

Total pressure is constant throughout

pressuredynamicv

2

1

pressuretotalP

pressurestaticP

PPv2

1Pv

2

1

Pv2

1

.constessurePrTotalP

Bernoulli

2

0

02

2

221

2

11

2

0

Flow through a NozzleFlow through a Nozzle

P2

A

A1

1YCAQ

FlowalReFor

IdealP2

A

A1

1AvAQ

RateFlow

P2

A

A1

1v

2

1

2

2

2

1

2

222

2

1

2

2

Flow through a NozzleFlow through a Nozzle

P21

2

1

222

22

2

1

21

222

211

22221

12

1

2

1

2

1

2

1

2

1

when

A

Av

vA

Av

vvPPP

Flow through a NozzleFlow through a Nozzle

Y = Compressibility Factor

=1 for incompressible flow or when P<< Pabs

C= Discharge Coefficient

=f(Re) and

nature of specific flow meterP

Flow through a NozzleFlow through a Nozzle

P

Flow through a Venturi MeterFlow through a Venturi Meter

In a venturi, 0.95 < C < 0.98

Advantage:

Pressure recovery

Uses little power

Flow through a Venturi MeterFlow through a Venturi Meter

C

Re

2 x 105

11vde

R

0.98

Based upon the conditions in the pipe approaching the meter

Back to the NozzleBack to the NozzleP1 P2

P

P1

P2

Shorter and cheaper than venturi

But larger pressure drop.

Thus, more power lost in operating.

The Nozzle FlowmeterThe Nozzle Flowmeter

C

0.86

0.98

103105

Re

Flow Through an Orifice Flow Through an Orifice MeterMeter

Flow Through an Orifice Flow Through an Orifice MeterMeter

P1 P2

P

P1

d D

Flow Through an Orifice Flow Through an Orifice MeterMeter

-Cheapest and Simplest

-But biggest pressure drop and power lost (C~0.6 - 0.7)

-Side Note:

Pressure drop caused by friction and turbulence of shear layer downstream of vena contracta

CM

A

AC

2

1

21

1

0.6

0.85

=d/D0.1 0.8

Re

100k

5000

10k

Elbow Flowmeter

Laminar Flowmeter

Pitot-Static TubesPitot-Static Tubes

Rotameter, variable-area-Rotameter, variable-area-flowmeterflowmeter

Force balance Drag Force Gravity Buoyancy

(usually negligible)

cal

usecaluse mm

Derived on next slide

D

MgA

D

MgAm

D

MgV

MgV

DF

VAm

2

2

22

2

2

For a fixed x-position, A is fixed. Then

cal

usecaluse

caluse

mm

mm

Rotameter

Equations

Turbine Flow MetersTurbine Flow Meters

Vortex meters operate on the principle that when a non-streamlined object is placed in the middle of a flow stream, vortices are shed alternately downstream of the object. The frequency of the vortex shedding is directly proportional to the velocity of the liquid flowing in the pipeline.

Magnetic flowmeterMagnetic flowmeter

Based upon Faraday’s Law

The fluid is the conductor, must be electrically conductive.

E=BDVx10-8

E=voltage, volts

B=magnetic flux density, gauss

D= length of the conductor, cm

V=velocity of the conductor, cm/sec

Magnetic flowmeterMagnetic flowmeter

Magnetic Flow Meter

Coriolis Mass Flow MeterCoriolis Mass Flow Meter

Coriolis Mass Flow MeterCoriolis Mass Flow Meter

Vibrating Flow TubeFluid Force is Reacting to Vibration of Flow Tube

End View of Flow Tube Showing Twist

Twist Angle

Twist Angle

Flow Force

Flow Force

Flow

Flow

Coriolis Mass Flow MeterCoriolis Mass Flow Meter

Positive Displacement Meters