[email protected] 6.2 gross volume flow rate flow, flow volume, & flow rate there are...

23/4/21 [email protected] 1

6.2 Gross Volume Flow Rate

Flow, Flow Volume, & Flow RateFlow, Flow Volume, & Flow Rate

There are different flow measurement sensors. Many flow sensors actually measure flow rate.

o Mass flow rateo volumetric flow rate

Some flow sensors measure flow velocity. Some sensors measure pressure differences

Total flow (or flow volume) can be, therefore, derived from flow rate by integration.


Volume FlowIf the density is constant, then this tells us that the volume flow is fixed, or Qin = Qout where

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


Volumetric Flow (all fluids)

Q = A V

= m

=

m sec*

*

²m sec³

where:

Q = volumetric flow

A = cross sectional area ( m )

V = average fluid velocity ( )m sec

m3 sec

²

³


Mass Flow

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


Mass Flow

where:

m = mass flow ( )

= density ( )

Q = average fluid velocity ( )

A = cross sectional area ( m )

V = average fluid velocity ( )

kg sec

²

m sec

m sec

m = Q = A V

= m

=

* **

² m sec* *kg m ³

kg sec

kg m ³


Principles of Flow MeasurementPrinciples of Flow Measurement

Flow meters are used to measure liquid and gas (i.e. fluids) flow rate.

When fluid under a action of external force, it results a deformation, leads to a dynamic viscositydynamic viscosity caused by shear stress:

y

x

F

F

dy

dv


Flow Profiles & Reynolds Number

Re =

Re =

Re =

inertial forcesfrictional forces

density velocity diameterviscosity

V Dµ


Reynolds number( 雷诺数 )雷诺数是流体流动的惯性力与粘滞力之比，表示为：

— 雷诺数（无量纲数）；

— 流动横截面的平均流速，（ m/s ）；— 动力粘度，（ N·S/m2 ）；

— 运动粘度，（ m2/S ）；

— 流体的密度， (kg/m3) ； — 特征长度，（ m ）。


Viscosity

Dynamic viscosity

cP (centipoise)

Kinematic Viscosity

cst (centistoke)

A measure of how freely a fluid flows:

where:V = kinematic viscosity

V = dynamic viscosity

SG = specific gravity

cP

cstV = Vcst SGcP *


Viscosity

Viscosity can be highly temperature dependent in liquids.

Steam/gas – 0.01 cP

Water – 1.0 cP

Honey – 300 cP


Liquid and gas have very similar properties, except for their compressibility.

Adiabatic Gas:The amount of heat required to raise the temperature of a gas is equal to the amount of energy to expand the gas to do work.

Ideal Gas State Equation


Two types of flows: laminar flow turbulent flowdistinguished by Reynolds numberLaminar flow Re<2103

Transition flow Re in betweenTurbulent flow Re>1104

Accurate measurement of turbulent flow is difficult.

Laminar Flow

Turbulent Flow


Element volume flow rate:

r

rR

Volume flow rate:

Mean velocity:


Based on the continuity property of fluid:

Conversation of v.f.r.

Conversation of m.f.r.


Based on energy conversation property of fluid:

Conversation of energy(incompressible fluid)

1v

2v

z1

z2


Types of FlowmetersTypes of Flowmeters

Orificesflow m eter

Venturi T ubeflow m eter

Flow T ubeflow m eter

Flow Nozzlesflow m eter

Pilot T ubesflow m eter

Others

PressureT ypes

T urbineflow m eter

RecipocateingPiston flow m eter

Oval-Gearflow m eter

Others

Mecha nica lT ypes

Hot-w ireflow m eter

Resistive-bridgeflow m eter

Others

T herm a lT ypes

Vortexflow m eter

Electrom agneticflow m eter

UltrasonicFlow m eter

Others

O therT ypes

Flow m eters


TechnologiesTechnology Operating

PrincipleAdvantages Disadvantages Fluids

Measured

DP(Differential Pressure)Orifice platePitot tubeVariable areaVenturiV-ConeAccelabar

An obstruction in the flow, measure pressure differential before and after the obstruction

Low initial cost No moving parts Handle dirty media Easy to use Well understood technology Supported by AGA and API

Not highly accurate, particularly in gas flow Orifice plate and pitot tube can become clogged High maintenance to maintain accuracy Typically low turndown Pressure drop

LiquidsGases Steam

VortexInlineInsertion

Bluff body creates alternating vortices, vortex shedding frequency equal to fluid velocity

High accuracy No moving parts No maintenance Measures dirty fluids

Can be affected by pipe vibration Cannot measure low flows

Liquids GasesSteam

TurbineInlineInsertionDual turbine

Turbine rotates as fluid passes by, fluid velocity equal to blade rotational frequency

High accuracy Low flow rates Good for steam Wide turndown

Moving parts require higher maintenance Clean fluids only

LiquidsGasesSteam

MagneticMagElectromagnetic

Measures voltage generated by electrically conductive liquid as it moves through a magnetic field, induced voltage is equal to fluid velocity

High Accuracy Wide turndown Bi-directional No moving parts No pressure loss to system

Conductive fluids only Expensive to use on large pipes

Conductive liquids (condensate)


Technologies Cont’dTechnology Operating

PrincipleAdvantages Disadvantages Fluids

Measured

Transit-timeUltrasonic

Fluid velocity measured by time arrival difference of sound waves from upstream and downstream transducers

Low cost clamp-on installation Non-intrusive No maintenance Bi-directional Best for larger pipes

Typically not used on pipes < 2” Less accurate than inline or insertion meters Used primarily for liquids Susceptible to changes in fluid sonic properties

Most liquids (condensate)Gas (when spool-piece)

DopplerUltrasonic

Fluid velocity measured by sensing signals from reflective materials within the liquid and measuring the frequency shift due to the motion of these

reflective materials

Low-cost, clamp-on installation Non-intrusive Measures liquids containing particulates or bubbles Low maintenance Best for larger pipes

Can’t be used in clean liquids Less accurate than in-line or transit-time ultrasonic

Most liquids containing reflective materials

Thermal Mass

Measure heat loss of heated wire thermistor in fluid flow

Measure flow at low pressure Relative low cost Measure fluids not dense enough for mechanical technologies Easier to maintain than DP meter

Susceptible to sensor wear and failure Not very accurate Limited to fluids with known heat capacities

Gases


Bernoulli’s Equation


Obstruction Meters


Obstruction Metersfor = const


Velocity Approach Factor

For round pipes, make = d/D where d is the smaller diameter while D is the larger,

discharge coefficient

flow coefficient


1. Compressibility Effects In compressible gas flows,compressibility effects change the value of the discharge coefficient. ★The compressible adiabatic expansion factor,Y

② To gas:

① To fluid(incompressible):


And

(10.4)


Orifice Meter

The orifice meter consists of an accurately machined and drilled plate concentrically mounted between two flanges. The position of the pressure taps is somewhat arbitrary.


Orifice Type FlowmeterOrifice Type Flowmeter

Orifice type is the most popular liquid flowmeters in use today.

In practice, orifice type flowmeter is installed in the pipeline.

Usually, it’s suitable for low Reynolds NumberReynolds Number

flow of Re<5,000.

D d

Pa Pb


Orifice Plate Flowmeter


Orifice Meter

The orifice meter has several practical advantages when compared to venturi meters.

• Lower cost• Smaller physical size• Flexibility to change throat to pipe diameter

ratio to measure a larger range of flow rates

Disadvantage:• Large power consumption in the form of

irrecoverable pressure loss


Advantages: Low cost, especially on large sizes No need for recalibration Widely accepted

Disadvantages: Poor turndown (4:1 typical) Long installations (20D to 30D) Accuracy dependant on

geometry.

Complete Customer Data Sheet:

Customer details

Fluid

Operating pressure

Operating temperature

Estimate flow rate

Line size, Pipe Schedule, Material

Flange Specification

Required package option

Orifice Plates


Variable orifice flow meter Line sizes 2-8” Temp up to 842°F (450°C) Accuracy ±1.0% of rate Gas and Steam

applications Compact installation - 6

up and 3 down Up to 100:1 turndown


Digital variable orifice flow meter

Line sizes 2-4” Saturated Steam ONLY 347°F (175°C) Accuracy ±2.0% of flow Internal RTD for

Integrated mass flow measurement

Compact installation - 6 up and 3 down

Up to 50:1 turndown


Orifice Meter

where: = ratio of orifice diameter to pipe diameter ≈ 0.5 usuallyS0 = cross sectional area of orificeV = bulk velocity through the orificeC0 = orifice coefficient ≈ 0.61 for Re > 30,000

–


There is a large pressure drop much of which is not recoverable. This can be a severe limitation when considering use of an orifice meter.


Pressure Loss inOrifice Meters


Flow Nozzles


Orifice Flow Meters


Losses in Orifice Flow Meters


Relative performance


Venturi Meters

0.95 < C < 0.98


Permanent Pressure Loss


Coefficient of Discharge

Actual flow rate:

21

421

22

1

2

4

d

ppDcm d

whereD2 = orifice, venturi or nozzle inside diameterD1 = upstream and downstream pipe diameterd = D2 / D1 diameter ratio

Discharge Coefficient - cd

Diameter Ratio d = D2 /

D1

Reynolds Number - Re

104 105 106 107

0.2 0.60 0.595 0.594 0.594

0.4 0.61 0.603 0.598 0.598

0.5 0.62 0.608 0.603 0.603

0.6 0.63 0.61 0.608 0.608

0.7 0.64 0.614 0.609 0.609

Performance of Orifice Flow Meter

Performance of Orifice Meter

The pressure recovery is limited for an orifice plate and the permanent pressure loss depends primarily on the area ratio. For an area ratio of 0.5, the head loss is about 70 - 75% of the orifice differential.The orifice meter is recommended for clean and dirty liquids and some slurry services.The rangeability is 4 to 1The pressure loss is mediumTypical accuracy is 2 to 4% of full scaleThe required upstream diameter is 10 to 30The viscosity effect is highThe relative cost is low

Performance of Venturi MeterHigh pressure and energy recovery makes the venturi meter suitable where only small pressure heads are available.A discharge coefficient cd = 0.975 can be indicated as standard, but the value varies noticeably at low values of the Reynolds number.The pressure recovery is much better for the venturi meter than for the orifice plate.The venturi tube is suitable for clean, dirty and viscous liquid and some slurry services.The rangeability is 4 to 1Pressure loss is lowTypical accuracy is 1% of full rangeRequired upstream pipe length 5 to 20 diametersViscosity effect is highRelative cost is medium

Performance of Nozzle Flow Meter

Discharge Coefficient - cd

Diameter Ratio d = D2 /

D1

Reynolds Number - Re

104 105 106 107

0.2 0.968 0.988 0.994 0.995

0.4 0.957 0.984 0.993 0.995

0.6 0.95 0.981 0.992 0.995

0.8 0.94 0.978 0.991 0.995The flow nozzle is recommended for both clean and dirty liquidsThe rangeability is 4 to 1The relative pressure loss is mediumTypical accuracy is 1-2% of full rangeRequired upstream pipe length is 10 to 30 diametersThe viscosity effect highThe relative is medium


＃ The unrecoverable overall pressure loss , , associated with a flow meter depends on ratio and flow rate. ＃ The power, ,required to overcome any loss in a system is given by:

Where is the prime mover overall efficiency.


Obstruction Meter Selection

Selection between obstruction meter types depends on a number of factors that requires some engineering compromises. Primary considerations include:

1.Meter placement 2.Overall pressure loss 3.Accuracy 4.Overall costs


Orifice Meter ExampleA 5.25cm(2.067 in.) Schedule 40 pipe carries 35º API distillate at 50° F (SG=0.85). The flow rate is measured by an orifice meter which has a diameter of 3.81cm(1.5 in.) The pressure drop across the orifice plate is measured by a water manometer connected to the flange taps. If the manometer reading is 50.8cm(20 in.) of H2O, what is the flow rate of the oil in m3/h(GPM) ?


So Q=17.2GPM


Example A 10cm diameter square edge orifice plate is

used to meter the steady flow of 16 water ℃through a 20cm pipe. Flange taps are used and the pressure drop measured is 50cm Hg. Determine the pipe flow rate. The specific gravity of mercury is 13.6

( μ = 1.08 ×10-3 Pa.s, ρ= 999kg/m3)


Solution from (10.14)

Without information concerning either or , cannot be determined explicitly

and a trial and error approach must be undertaken.Guess a value for and iterate. So we make a simple program as follows:

Q U C

C


d0,d1(D),p1,p2,T=273.15+t,ρ,κ,μ,R,liquid,gas

liquid

gas


Standards Values for the flow coefficientsnd

expansion factors of the orifice a plate, venturi and flow nozzle, have been tabulated and are available in standard flow handbooks along with standardized construction, installation, and operation techniques.

ISO5167-87 GB2624-93


Sensor Installation Sensor Installation QuestionQuestion

When we select a velocity-based sensor to measure the flow rate (assume a laminar flow), where should we install the sensor to get an accurate reading on the flow rate?

Laminar Flow

x

INSERTIONS NEED STRAIGHT RUN (Min 10 up, 5 down)*

*If insufficient straight run, consider Sage inexpensive Captive Flow Conditioners

EEEE

CAPTIVE FLOW CONDITIONERS OPTIONALLY INSTALLED BY USERS UPSTREAM OF INSERTION METERSIF INSUFFICIENT STRAIGHT RUN


Turbine FlowmetersTurbine Flowmeters

Turbine flowmeter is one type of velocity meters, and found widespread use for accurate liquid measures.

The unit consists of a multiple-bladed rotor mounted within a pipe, perpendicular to flow

The rotational speed is a direct function of volume flow rate.

The meter factor K is found by direct calibration.

(1) End fitting — flange shown;

(2) flowmeter body; (3) rotation pickup —

magnetic, reluctancetype shown;

(4) permanent magnet; (5) pickup cold wound on

pole piece; (6) rotor blade; (7) rotor hub; (8) Rotor shaft bearing —

journal type shown; (9) rotor shaft; (10) diffuser support and flow

straightener; (11) diffuser;(12) flow conditioning plate

(dotted) — optional with some meters.


Turbine Flowmeter SystemTurbine Flowmeter System

Sensor Specifications Accuracy: ½ % of reading Repeatability: 0.1 % of reading Max Temperature Range:

-450 to 450 ºF Material of construction:

stainless steel Installation Kits:

340 SS, 0.065” Max Pressure Drop:

5 PSI

Conditioner Specifications Accuracy: 0.1% of f.s. Repeatability: 0.025% Max Input: 20 mv pp min Output: 4-20 mA

or 1-5 V dc Response t: 2 sec fixed Freq input: 65-7600 Hz Power: 10-32 V dc

or 15-32 V dc Operating T: -20 to 60 ºC


Area Meters The pressure causing the flow through an area meter is

relatively constant such that the rate of flow is directly proportional to the metering area

The variation in area is produced by the rise and fall of a floating element

This type of flow meter must be mounted so that the floating element moves vertically and friction is minimal


RotametersRotameters fall into the category of flow measurement devices called variable area meters. These devices have nearly constant pressure and depend on changing cross sectional area to indicate flow rate. Rotameters are extremely simple, robust devices that can measure flow rates of both liquids and gasses.

Fluid flows up through the tapered tube and suspends a ‘float’ in the column of fluid. The position of the float indicates the flow rate on a marked scale.

Some Facts About Variable Area Flowmeters

Called “ float type”, “rotameter’’, or “variable area” flowmeters.

By far the most common specified, purchased, and installed flowmeter in the world


RotametersThree types of forces must be accounted for when analyzing rotameter performance:

• Flow• Gravity• Buoyancy

Flow

Buoyancy

Gravity

For our analysis neglect drag effect

Variable Area Flowmeters

Fluid flow moves the float upward against gravity.

Float will find equilibrium when area around float generates enough drag equal to weight - buoyancy.

Some types have a guide rod to keep float stable.

Low Cost (pricing usually starts < $50)

Simple Reliable Design Can Measure Liquid or Gas

Flows Tolerates Dirty Liquids or Solids

in Liquid

Measuring Principles of Variable Area Flowmeters Flow Rate Analysis. The forces acting on the bob lead to equilibrium between: the weight of the bob fgVf acting downwards the buoyancy force 0gVf and the drag force F acting upwards.

• Where Vf is the volume and f is the density of the bob, γffg 0 is the density of the fluid, γ00g and • g is the gravitational acceleration:

FgVgV fff 0


After Mechanical Energy Balance analyses and simplification , Cd is a empirical coefficient:


00

0

2 2 2 20

02 2

0

0

0

1/ ,

2 ( )

( ) (2 tan tan )

2 ( )(2 tan tan )

2 ( )(2 tan )

d

f f

f

f fv

f

f fv

f

c

V gA

A

A R r hr h

V gq hr h

A

gVq r h

A

ff 0v 0 0

f 0

设＝称为流量系数，则

2V( - )q =Av= A

AR= r +h tanφ


刻度修正

转子流量计指示值修正

仪表出厂前标度： 20℃ ， 0.10133MP 液体 ------水气体 ------ 空气

液体流量的修正

气体流量的修正

0101

0101 Q

TP

TPQ

修改量程

z

zz

A

gVkhQ

)(2

用一个用水标定的转子流量计来测量苯的流量，流量计的读数为 28 m3/h ，已知转子密度为 7920 kg/m3 的不锈钢，苯的密度为 0.831 kg/L ，求苯的实际流量是多少？

例

已知： ρs=1 kg/L ， ρy=0.831

kg/L ， ρz=7.92 kg/L ，

QN =28 m3/h ，代入修正公式式可得：

解

所以苯的实际流量是 31.08m3/h 。


VARIABLE AREA (ROTAMETER)

CHARACTERISTICS

Recommended Service: Clean, Dirty & Viscous Liquids

Rangeability: 10 to 1 Pressure Loss: Medium Accuracy: 1 to 10% Straight Run Required: None Viscosity Effect: Medium Relative Cost: Low Sizes: <= 4” Connections: Threaded or Flanged Type of Output: Linear


Questions to Ask at Sensor Questions to Ask at Sensor SelectionSelection

What range do you intend to cover?0 to 100% ___, 25 to 100% ___, 50 to 100% ___, Other ____

What accuracy do you need? % ____, 15% ____, 10% ____, other ____

What do you intend to do with meter output?indicator ____, recorder ____, computer ____, other ____

What type of enclosure do you want?application specified ____, not-specified ____, other ____

Who will provide service on the sensor?vendor ____, user ____, other ____

What type of sensor service life do you want?one time ____, on_board ____, long life ____, other ____


Vortex Shedding Meters


Vortex Flowmeter Liquid, Gas, and Steam 1-12” (25 to 300mm) Temperature up to 750°F(400°C) EZ-Logic menu-driven user interface In-process removable sensor (below

750psig) Fully welded design with no leak path Optional remote mount electronic Accuracy

Liquid ±0.7% of rate Gas and Steam ±1.0% of rate

Turndown up to 20:1

Vortex


Vortex-shedders

Circle shedder

Triangle shedder


Insertion Vortex Meter Liquid, Gas, and Steam Model 60/60S Hot Tap, retractable Model 700 Insertion low temp, low pressure Model 910/960 Hot tap, retractable

960-high temp up to 500°F (260°C), high pressure

Optional Temperature and/or Pressure Transmitter

Line sizes 3-80” (76 to 2032mm) No moving parts EZ-Logic menu driven user interface Accuracy

Liquid ±1.0% of rate Gas and Steam ±1.5% of flow rate test

conditions Turndown up to 20:1

VBar


Turbo-Bar Insertion Turbine Flow Meter

Liquid, Gas, and Steam Liquid flow velocity down to 1 ft/sec Model 60/60S Hot Tap, retractable Model 700 Insertion low temp, low pressure Model 910/960 Hot tap, retractable

960-high temp up to 750°F (400°C), high pressure

Optional Pressure and/or Temperature Transmitter

Line sizes 3-80” (76 to 2032mm) EZ-Logic menu driven user interface Nominal Accuracy

Liquids ±1.0% of rate Gas and Steam ±1.5% of rate

Turndown up to 25:1TMP


Low-cost Water Vortex Meter

1200

2200

3100

2300

No Moving Parts Flow Range 1 to 15 ft/s (0.3 to 4.5 m/sec) Accuracy ±1.0% of Full Scale 1/2 to 20” Line Size Microprocessor-based electronics with

optional local display Maximum Fluid temperature 160°F (70°C) Model 2300 for acids, solvents, De-ionized,

and ultra pure water (1/2 to 8”) Model 2200 Fixed Insertion for (2 to 20”) Model 1200 for water, water/glycol (1-3”) Model 3100 retractable insertion (3-20”) Models 1200 and 2200 have Aluminum

Enclosure option for wet environments or heavy industrial installations


涡街流量计的特点优点 :

涡街流量计测量精度较高；量程比宽 , 可达 30:1 ；使用寿命长，压力损失小，安装与维护比较方便；测量几乎不受流体参数变化的影响，用水或空气标定后的流量计无须校正即可用于其它介质的测量；易与数字仪表或计算机接口 , 对气体、液体和蒸汽介质均适用。

缺点 :流体流速分布情况和脉动情况将影响测量

准确度，因此适用于紊流流速分布变化小的情况，并要求流量计前后有足够长的直管段。


Ultrasonic FlowmetersUltrasonic Flowmeters

Ultrasonic flowmeters can be divided into Doppler meters and time-of-travel meters.

Doppler meters measure frequency shift caused by liquid flow. 2 transducers are mounted in a case. The frequency shift is proportional to the liquid velocity.

Time-of-travel meters have 2 transducers mounted on each side of the pipe. A time difference proportional to the flow can be detected.

Ultrasonic Flowmeters There are various types of ultrasonic flowmeters in use for

discharge measurement: (1) Transit time: This is today’s state-of-the-art technology

and most widely used type. This type of ultrasonic flowmeter makes use of the

difference in the time for a sonic pulse to travel a fixed distance.

First against the flow and then in the direction of flow. Transmit time flowmeters are sensitive to suspended solids

or air bubbles in the fluid. (2) Doppler: This type is more popular and less expensive,

but is not considered as accurate as the transit time flowmeter.

It makes use of the Doppler frequency shift caused by sound reflected or scattered from suspensions in the flow path and is therefore more complementary than competitive to transit time flowmeters.

Principle of transit time flowmeters.

Transit Time Flowmeter

Principle of Operation The acoustic method of discharge measurement is based on

the fact that the propagation velocity of an acoustic wave and the flow velocity are summed vectorially.

This type of flowmeter measures the difference in transit times between two ultrasonic pulses transmitted upstream t21 and downstream t12 across the flow.

If there are no transverse flow components in the conduit, these two transmit times of acoustic pulses are given by:

Since the transducers are generally used both as transmitters and receivers, the difference in travel time can be determined with the same pair of transducers. Thus, the mean axial velocity along the path is given by:

Example

The following example shows the demands on the time measurement technique:

Assume a closed conduit with diameter D = 150 mm, angle = 60°, flow velocity = 1 m/s, and water temperature =20°C.

This results in transmit times of about 116 s and a time difference

t =t12 – t21 on the order of 78 ns. To achieve an accuracy of 1% of the corresponding full-scale

range, t has to be measured with a resolution of at least 100 ps (1X10–10s).

Standard time measurement techniques are not able to meet such requirements so that special techniques must be applied.

Digital timers with the state-of-the –art Micro computers will make it possible to measure these time difference.


Transit Time Ultrasonic Flowmeter

Liquid applications-Clean 2-100” (50 to 2540mm) Accuracy typically ±2.0% of

rate Non-Intrusive No wetted parts Multiple outputs available EZ-Logic menu driven user

interface Bi-Directional Transducer cable length up to

300’


Electromagnetic Flowmeter Field Serviceable Design

Field replaceable sensors and coils

No Liner Required No liner failure

Solid State Sensor Design Encapsulated coil and electrode assembly

insensitive to shock and Vibration

Plurality of Sensors Uniquely powerful magnetic field

Non-standard Flow Tube Lengths Easy replacement of existing meters

Measures Low Conductivity Media Conductivity down to 0.8 µS/cm


6.2 Gross Mass Flow Rate

Volume flowmeter plus Density Measurement


Density - Liquids

Liquids

The density of a liquid is inversely proportional to temperature:

1T

8.2877100

8.303790

8.317680

8.32970

8.337860

8.34350

8.345140

8.343632

Weight Density

Lbs/gal

Temperature

°F

WATER


Density - Gases

where: = Density ( )

= absolute pressure (psia) = 14.7 + Pgage

SG =Specific Gravity

= absolute temperature = F° + 460 = ° Rankin

lbs ft3

Ta

a =

2.7 SG

Ta

Density of Gas:

a

Gases

= 1T

The density of a gas varies proportionally with pressure and inversely with temperature:

a


Density - Steam

3.7406001541.00

3.1005801324.30

2.5805601131.80

2.150540361.50

1.780520811.40

1.480500680.00

.820440381.20

0.536400247.10

0.338360152.92

0.20332089.6

Densitylbs/ft³

Temperature°F

Pressurepsia

Saturated Steam Table

0.14350080

0.15344080

0.16140080

0.17036080

0.18132080

0.03550020

0.03844020

0.03940020

0.04136020

0.04432020

Densitylbs/ft³

Temperature°F

Pressurepsia

Superheated Steam Table

Superheated steam:Saturated steam:


Actual vs. Standard Flow - Gas

Standard Volume Flow:

Gas flow in standard units relates the volume flow of gas to the same amount of mass flow of gas at standard conditions:

where:

Q = Q standard actual

operating

standard conditions

= specific gravity ( , at standard conditions )

= density of gas at operating pressure and temperature

= density of gas at standard conditions (at 14.7 psia, 60°F)

= standard time or

standard time

³ft unitQstandard

Qactual

operating

standard

= actual volumetric flow (ACFM, ACFH, etc…)

gas air

³m unit

SG

Actual Volume Flow:Q = V A (actual , , etc)

(actual ,hr, , etc)

* ³ft sec

³m sec

³ft min

³m sec


Energy Flow

Chilled/hot water energy (Btu) calculations require (1) flow and (2) temperature inputs.

Btu is defined as the amount of energy required to raise the temperature of 1lb water at 39°F by 1°F.

where:

E = energy flow ( )

m = mass flow ( )

A = cross sectional area (ft²)

V = average fluid velocity ( ) = density ( )

h = Btu’s (heat content) of water at supply temperature ( )

h = Btu’s (heat content) of water at return temperature ( )

Btu sec

lbs sec

ft sec

Btu lbs

lbs ³ft

Btu lbs

s

r

lbsft³

ftsec

E = m (h – h )

E = A V (h - h )

E = ft²

E =

s r

rs

Btulbs

Btusec


Thermal Mass Flowmeter

Thermal Flow Meter 1st law, ideal gas:


WHAT IS A THERMAL MASS FLOW METER?

It is a Meter that directly measures the Gas Mass Flow based on the principle of conductive and convective heat transfer – more detail later…


DIGITAL THERMAL MASS FLOW METERS


INPUT/ OUTPUTS

24 VDC Power (draws less than 100 ma) 115 VAC/ 230VAC or 12 VDC Optional Outputs 4 – 20 ma of Flow Rate Outputs 12 VDC Pulses of Totalized Flow (Solid State,

sourcing, transistor drive – 500ms Pulse)

Modbus® compliant RS485 Communications


Coriolis Meters ( 科里奥利质量流量计 )

When fluid is passed through a U-bend, it imposes a force on the tube wall perpendicular to the flow direction (Coriolis force). The deformation of the U-tube is proportional to the flow rate. Coriolis meters are expensive but highly accurate.


Coriolis Mass Flowmeter ( 科里奥利质量流量计 ) 科里奥利质量流量计 ( 简称科氏力流量计 ) 是一种利用流体在振动管中流动而产生与质量流量成正比的科里奥利力的原理来直接测量质量流量的仪表。科氏力流量计结构有多种形式，一般由振动管与转换器组成。

科氏力流量计测量原理


U 形管受到一个力矩的作用，其管端绕 R-R轴扭转而产生扭转变形，该变形量的大小与通过流量计的质量流量具有确定的关系。

ω 为转动角速度

转弹性模量


Calibration and standards

1 液体流量标准装置

2 气体流量标准装置


1 液体流量标准装置

1. 标准容积法容积法液体流量标准装置由水源、流量稳压装置、试验管道、切换机构和标准计量容器等几个部分组成。其中流量稳压装置有高位水槽和气液容器稳压法两种。标准计量容器是经过精确标定的，其容积精度可达万分之几，其上装有读数装置，有各种不同的容积可根据流量范围需要选用


1— 水池； 2— 水泵； 3— 高位水槽； 4— 溢流管； 5— 稳压容器； 6— 夹表器； 7— 切换机构； 8— 切换挡板； 9— 标准容积计量槽；10— 液位标尺； 11— 游标； 12— 被校流量计

标准容积法流量标准装置


2. 标准质量法这种方式是以秤代替标准容器作为标准器，用秤量一定时间内流入容器内的流体总量的方法来求出被测液体的流量。秤的精度较高，这种方法可以达到 ±0.1 ％的精度

3. 标准流量计法这种方式是采用高精度流量计作为标准仪表对其他工作用流量计进行校正。用作高精度流量计的有容积式、涡轮式、电磁式和差压式等型式，可以达到 ±0.1 ％左右的测量精确度。


4. 标准体积管图为单球式标准体积管的原理示意图。合成橡胶球经交换器进入体积管，在流过被校验仪表的液流推动下，按箭头所示方向前进。橡胶球经过入口探头时发出信号启动计数器，橡胶球经过出口探头时停止计数器工作。橡胶球受导向杆阻挡，落入交换器，再为下一次实验作准备。被校表的体积流量总量与标准体积段的容积相等，脉冲计数器的累计数相应于被校表给出的体积流量总量。这样，根据检测球走完标准体积段的时间求出的体积流量作为标准，把它与被校表显示值进行对比，即可得知被校表的精度。


1— 被校验流量计； 2—交换器； 3— 球； 4—终止检测器；5—起始检测器； 6— 体积管； 7— 校验容积； 8— 计数器

单球式标准体积管原理示意图


2 气体流量标准装置对于气体流量计，常用的校正方法有：用

标准气体流量计的校正法，用标准气体容积的校正法，使用液体标准流量计的置换法等。标准气体容积校正的方法采用钟罩式气体流量校正装置，其系统示意图如图所示。

1— 钟罩； 2— 导轨和支架；3— 平衡锤； 4— 补偿锤；5 、 6— 挡板； 7— 发讯器

钟罩式气体流量校正装置

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