flow measurement- 2 abril 2011

Prof. Dr. Nabil Abel Aziz MAHMOUD 4/3/2011 1

Ain Shams University Faculty of Engineering

Mechanical Power Engineering Department

Second Year

Course Title: MEP 281 Measurements

Flow Measurements

Prepared by :

Prof. Dr. Nabil Abdel Aziz MAHMOUD


Table of Contents Conversion Factors Flow Rate Measurement 1. Constant Area, Variable Pressure Drop Meters. [ obstruction Meters ] 1.1. The Sharp Edge Orifice. 1.1.1. Orifice Disadvantages. 1.2. The Nozzle Flow Meter and The Venturi Flow meter. 1.2.1. Effect of Compressibility. 1.2.2. Expansion Factor for Compressible Flow. 1.3. The Sonic Nozzle. 1.4. The Laminar Flow Element ( LFE). 1.5. Obstruction Meter Selection. 2. Constant Pressure Drop, Variable area Meters. 2.2. The Rotameters. 3. Turbine Flow Meters. 4. Electromagnetic Flow Meters. 5. Ultra Sonic Flow Meters. 6. Positive Displacement Meters. 6.1. The Rotary Vane Flow Meter. 6.2. The Lobed Impeller Flow Meter. 6.3. Domestic Flow Meter 7. Other Types of Flow Meters 7.1 Piston water flow meter 7.1.1 Oscillating Piston Flow Meter 7.1.2 Rotary Piston Flow Meter 7.2 Vortex Flow Meter 7.3 Ultrasonic Flow Meter 7.3.1 Time of Flight Flow Meter 7.3.2 Doppler Flow Meter 7.4 Elbow Flow Meter 7.5 Target Flow Meter 7.6 Mass Coriolis Flow Meter 7.7 Thermal Mass Flow Meter 8. Selecting a Flow Meter 9. Working with Flow Meters 10. Flow Meter Calibration. 10.1 Sources of Errors in Flow Meter Calibration. 11. Flow meter Selection Guide References. Appendix


MASS 1.0 lbm = 453.59237 g 1.0 slug = 32.174 lbm 1.0 kg = 2.2046 lbm LENGTH 1.0 inch = 2.54 cm 1.0 m = 3.208 ft = 39.37 inches 1.0 cm = 0.01 m = 0.3937 in = 0.0323 ft 1.0 mm = 0.001 m = 1*10-3 m 1.0 µm = 0.000001 m = 1*10-6 m 1.0 nm = 0.000000001 m = 1*10-9 m 1.0 km = 1000 m = 0.612 miles 1.0 miles = 5280 ft TIME 1.0 min = 60 s 1.0 h = 60 min 1.0 day = 8.64*104 s FORCE 1.0 N = 1 kg.m/s2 = 1*105 dynes 1.0 lb = 4.44822 N PRESSURE 1.0 Pa = 1 N/m2 = 1.4504*10-4 lb/in2 1.0 lb/in2 = 6894.76 N/m2 1.0 atm = 14.696 lb/in2 = 760 Torr 1.0 bar = 14.505 lb/in2 = 1*105 N/m2 = 1*108 dynes/cm2 1.0 inch Hg = 3376.8 N/m2 1.0 inch H2O = 248.8 N/m2 = 0.0362 lb/in2 AREA 1.0 m2 = 10.76 ft2 1.0 cm2 = 1*10-4 m2 = 0.155 in2 VOLUME 1.0 cm3*103 = 1 Liter = 1*10-3 m3 = 0.2642 galons 1.0 gallon = 231.0 in3 1.0 ft3 = 0.0283 m3 POWER 1.0 w = 1 .0 J/s = 860.42 cal/hr 1.0 hp = 745.7 W = 550.0 ft.lb/s

1.0 kW = 1*103 W = 3412 BTU/hr 1.0 BTU/hr = 778.16 ft.lb/hr ENERGY 1.0 J = 1.0 N.m = 1*107 ergs 1.0 erg = I dyne.cm 1.0 cal = 4.1855 J 1.0 BTU = 778.16 ft.lb = 252.16 cal = 1055.06 J VISCOSITY 1.0 N.s/m2 = 0.672 lbm /ft.s SPECIFIC HEAT 1.0 kJ/kg.°C = 0.23884 BTU/lbm.°F THERMAL CONDUCTIVITY 1.0 W/m.°C = 0.5778 BTU/hr.ft.°F HEAT TRANSFER COEFFICIENT 1.0 W/m2.°C = 0.1761 BTU/hr.ft2.°F PHYSICAL CONSTANTS

• Standard Acceleration of Gravity g = 9.80665 m/s2 = 32.1742 ft/s2

• Speed of Light c = 2.998*108 m/s

• Plank's Constant hp = 6.626*10-38 J.S

• Stefan-Boltzmann Constant σ = 5.673*10-8 W/m2.K4 = 0. 1712*10-8 BTU/lbm.mole.°R

• Universal Gas Constant R = 8.3143 J/gmole.K = 1.9859 BTU/lb.mole.°R

Conversion Factors


FLOW RATE MEASUREMENT 1. Constant - Area, Variable Pressure Drop Meters : [ Obstruction meters ] This method is involving placing a fixed area flow restriction of some type in the pipe carrying the fluid. This flow restriction causes a pressure drop which varies with the flow rate; thus measurement of the pressure drop by means of a suitable differential pressure pick - up allows the flow rate measurement. The most common practical devices that utilize this principle: - The sharp edge orifice flow meter. - The nozzle flow meter. - The venturi flow meter. - The sonic nozzle. - The laminar flow element. 1.1 The Sharp - Edge Orifice: This is the most widely used flow metering element because of its simplicity, low cost and the great volume of research data available for predicting its behavior, figure (1). There are different types of this meter such as: - Flanged taps - Corner taps - Vena contraction taps (D & D/2 taps) - Pipe taps (2 1/2 D & 8D taps) If we assumed one - dimensional flow, incompressible (Constant ρ ), frictionless fluid and no heat transfer or elevation change, the theory gives the volume flow rate as ; See the Appendix :

( )( )

thQ fA

fAfA

P P=

−

−2

12

21

2 1 2ρ

[m3/sec] (1)

Where: Qth : Theoretical mass flow rate A1f , A2f : Cross-section flow areas where pressure 1 2P P, are measured, [ m2 ] ρ : Flow density, [kg / m3]

1 2P P, : Static pressures, [N / m2]


Actually, the real situation deviates from the assumption of the theoretical model, and this requires experimental correction factors, for example:

• 1 2fA fA, : Are areas of the actual flow cross-section which are not the same as those of the pipe and orifice. • Usually there is a friction effect which affects the measured pressure

drop.


Therefore, a discharge coefficient may be defined as:

dC aQ

thQ= (2)

Where dC : Discharge coefficient of the orifice meter aQ : Actual flow rate [m3

/ sec]

And thus :

( )

( )ρ

PP

AA

ACdQa212

122

1

2 −

−= [m3/sec] (3)

Or

( )aQ dC

A P P

aQ dC A FPd

ma dC A F P

d

=−

−

=

=

2

1 4

2 1 2

22

2 2

β ρ

ρ

ρ

∆

∆

Where:

Dd=β : Diameters ratio < 1.0

D : Pipe diameter, [m] d : Orifice diameter , [m]

F : Velocity appreach factor = −1 1 4/ β 1A : Pipe cross - section area [m2 ] 2A : Orifice cross - section area [m2 ] ρ : Fluid density usually measured upstream the orifice, i.e. ρ1 ∆P

d : Differential pressure drop across the orifice, [N/m2]

To determine the discharge coefficient, cd, an experimental calibration is necessary. The discharge coefficient varies mainly with the Reynolds number, RN, based on orifice diameter, figure (2). This calibration can be carried with a single fluid, such water, and the results can be used for any other fluids as long as Reynolds numbers are the same.


1.1.1 Orifice disadvantages The orifice has the largest permanent pressure loss of any of the obstruction meters (other than the laminar flow element). This is one of its main disadvantages since it represents a power loss that must be replaced by whatever pumping machinery is causing the flow. This permanent pressure loss is given approximately by:

Pressure loss, (∆P)Loss ( )2d 1)P( β−∆≅ (4)

Where: ∆P

d : is the differential pressure drop used for flow measurement.

It should be noted that, the standard calibration data assume no significant flow disturbances such as elbows, bends, tees, valves, etc. for a certain minimum distance upstream of the orifice. The presence of such disturbances can invalidate the standard data. Standard data available requires: - Pipe diameter 2 inches or greater - β (Diameters ratio) (0.2 - 0.7) - RN Above 10000 - Upstream pipe length≈ 10 D - Downstream pipe length ≈ 5 D


Also, orifice discharge coefficients are quite sensitive to the condition of the upstream edge of the hole. The standard orifice design requires that this edge be very sharp, and also that the orifice plate be sufficiently thin relative to its diameter. 1.2 The Nozzle Flow Meter And The Venturi Flow Meter: Nozzle and venturi flow meters are shown in figures ( 3 and 4 ). The nozzle and venturi flow meters are all operate on exactly the same principle as the orifice.


The significant differences laying in numerical values of certain characteristics: - Discharge coefficients for nozzle and venturi are larger than those of the

orifice plate.

- For the same diameter ratio, β = 21

AA

, these devices give a lower

value for the pressure loss, (∆P)Loss, compared to that of the orifice plate as shown in figure (5) .

Due to the lower value of the pressure loss in the venturi meter, it gives a definitive improvement in power losses over an orifice and is often indicated for measuring very large flow rates. The initial higher cost of a venturi over an orifice may be offset by reducing operating costs. Note that for orifice, venturi and nozzle:

d

d

P)(Q

or

)P(2

41

2AdCQ

∆∝

ρ∆

β−=

Where (∆P)d is the differential pressure across the meter (∆P)d = P1 – P2


This indicates that the measured discharge is proportional to the square root of the differential pressure. In the previous analysis, we assumed that the flow is incompressible, (ρ constant). Actually this is not true in cases where the fluid has higher velocities. In these cases, pressure and therefore density are changed through the flow. Therefore, compressibility effect should be taken into consideration. 1.2.1 Effect of compressibility: For a steady, compressible, isentropic flow between two sections 1 and 2, one can prove that:

(((( )))) (((( )))) .....24

42

Mk2

4

M 221

2V222

P2P1 ++++−−−−++++++++====ρρρρ

−−−− (5)

Where: The conditions at section 1, assumed to be stagnation conditions at inlet, (V1 = 0), M2 is the Mach number at section 2 and k is the specific heat

ratio Cp/Cv .

The term ( )1 2

2 22 2

P P

V

−=

ρφ called the compressibility factor

For 1.04 0.4=M

1.02 3.0

2

2

≅≅=

φφM

Equation (5) shows that for M ≤ 03. , the compressibility factor φ ≅ 1 Or

( )1 2 2 22 2P P V− = ρ ( 6 )

Or

1 22 2

2

2P P

V= +

ρ (Eular’s equation for incompressible flows)

Thus for M ≤ 03. , the flow may be considered incompressible flow and equation (3) is valid for all the above mentioned three devices, orifice, nozzle and venturi meters. If M > 0.3, compressibility effects will appear and can be represented by a factor called expansion factor.


1.2.2 Expansion factor for compressible flow When the flow of an ideal compressible gas is considered, the following equations may be applied : - State equation. P = ρ RT (7) - Energy equation. h01 = h02

pC TV

pC TV

1 12

2 2 22

2+ = + (8)

- Assuming isentropic flow ctevkp = (9) If V1 ≠ 0, the mass flow rate, m, can be calculated from the following equation:

( )( ) ( )m

A

kPP

k

kP

kPP

k

kPP=

−−

−+

2

1 4 221

2

1 1 122

1

12

1β

ρ/

/ (10)

But for a venturi meter for incompressible flow equation (3) gives :

( )( )

QC

dA

A A

P P=

−

−2

12 1

2

2 1 2

1/ρ

Or

( )( )

m QC

dA

A A

P P= =

−

−ρ

ρ

ρ11 2

12

2 1

2 1 2

1/

So for compressible flow, the mass flow rate may be calculated from :

( )( )

m Cd

Y A

A A

P P=

−

−2 1

12

2 1

2 1 2

1

ρ

ρ/


Where: Y is the expansion factor and is equal to :

( )

Y

l

kP

P

k

k

kP

P

k

kP

P

P

P

=−

−

−−

−

−

1 2

1 4

1 42

2

1

1

22

11

1

2

1

1 2

1

β

β/

/

Thus, for all the three devices, orifice, venturi and nozzle, flow rate calculations are made on the basis of equation (3) with appropriate empirical constants:

( )

1

2P1P2YF2ACaQ d ρ

−=

Or )PP(2YF2ACam 211d −ρ=

Where F = velocity approach factor

( )F

AA

=

−

=−

1

12

21

1

1 4β (11)

( )

1A/

2AD

d = RATIO DIAMETER ==β (12)

Y : is the expansion factor So when flow measurements of a compressible fluid are made an additional parameter, the expansion factor Y, is used.


For venturi and nozzle flow meters, the expansion factor Ya could be calculated from the following equation :

( )

( ) ( )Y

a

kP

P

k

k

k kPP

PP

kPP

=−

−−

−

−

−

1 2

22

11

11

21

1 21

1 4

1 42

21

/

/( ) /

/β

β

(13)

While for orifices with flanged taps or vena-contracta taps, the following empirical expression of Yb is given by:

[ ]Yb

P P

P k= − +

−1 0 41 0 35 4 1 2

1

1. . β (14)

For orifice with pipe taps, the following relation applies : ( )[ ]Y

P P

P k11 0 3 3 3 1 1 4 5 2 0 7 5 1 2 1 3 1 2

1

1= − + + +

−. . .β β β (15)

Figure (6) and figure (7) give the variation of Ya and Y1 , for air (k=1.4) and for different values of β . Thus, we have the following semi-empirical equation which is conventionally applied to venturi, nozzle and orifice flow meters:

( )ma

Cd

A Y F P P= −2

2 1 1 2ρ [kg /sec] (16)


1.3 The Sonic Nozzle : All the obstruction meters discussed above may be used with gases or liquids. In gases flow, when the flow rate is sufficiently high, the pressure differential becomes quite large, and eventually sonic conditions may be achieved at the minimum flow area. Under these conditions, the flow is said to be “choked “and the flow rate takes its maximum value for the given inlet conditions. For an ideal gas with a constant specific heat, the pressure ratio for this choked conditions, assuming isentropic flow is :


( )* / ( )PP

k k

k1

12

1=

−

+ (17)

where P* : critical pressure at throat P1 : stagnation pressure at inlet This ratio is called the critical pressure ratio. By inserting this ratio in equation (10) gives the mass flow rate for choked nozzle :

( )( )

+

−

+=

1k

2 )1k/(2

1k

k2/1

1RT

21P2ACm d (18)

The above equation is frequently applied to a nozzle when the pressure ratio (P2 / P1) is less then the critical value. Under these conditions, the flow is dependent only on the inlet stagnation conditions P1 and T1 . The ideal sonic-nozzle flow rate given by equation (18) must be modified by an appropriate discharge coefficient, Cd, which is a function of the geometry of the nozzle and other factors. This coefficient is usually about 0.97. 1.4 The Laminar Flow Element : (LFE) Laminar flow element, LFE, is an obstruction meter where the primary element is a cylindrical matrix composed of a large number of parallel channels of a very small equivalent diameter. These channels maintain the velocity the same as in the pipe (theoretically) but reduce the Reynolds number so the flow becomes laminar. This results in a linear relationship between the differential pressure and flow rate. Figure (8) shows the construction details of a laminar flow element. These types of meters are differing from the metering devices discussed above in that they are generally designed to operate in the laminar flow regime. Pipe flows generally are considered laminar if RN < 2000. The relationship between flow rate and pressure drop across a length of pipe, L, of diameter d1 and containing a laminar flow follows a linear relationship. The energy equation for such case is :

P V

g

P V

gh

L1 1

2

22 2

2

2 1 2γ γ+ = + + −,

(19)


where hL,1-2 is the pressure loss from inlet, section 1, to exit, section 2.

The head loss term, hL,1-2 , can be estimated using the Darcy equation:

hL fL

d

V

g,1 21

12

2− = (20)

Where L is the distance between pressure taps, d1 is inside pipe diameter and f is the friction factor, which for a laminar flow is :

1dRe

64f = (21)

Where: Red1 is Reynolds number based on diameter d1.

And as Q Vd

Vd

= =1

12

4 212

4

π π

And this gives V1 = V2

Thus Qd

V=π 1

2

4 1


And from energy equation (19);

21

d

Q4

2

1

1d

L

1d

64Por

g2

21

V

1d

L

1d

1V

64

g

P

g2

21

V

1d

L

1dRe

64

g2

21

V

1d

Lf

21,Lh

P

π

µ=∆ρ

µ=ρ∆

==−=γ

∆

Therefore,

Qd P

L =

πµ14

128

∆ m3/sec (23)

or, Q = K ∆P or Q P∝ ∆ Where: Q : Volume flow rate, m3/sec d1 : tube inside diameter, m L : Tube length between pressure taps, m µ : Fluid viscosity, in [N sec/m2 ] ≡ kg/m.sec ∆P : Pressure drop = ( P1 – P2 ); N/m2 K : Meter Constant The above equation reveals that volume flow rate is linear with pressure drop in a laminar flow element. Q ∝ ∆P Note that for orifice, venturi and nozzle:

( )Q Cd

A P=−

∝

2

1 4

2

β ρ∆

∆

or

Q P

Thus for orifice, venturi and nozzle, the volume flow rate is linear to the square root of the differential pressure.


The simplest type of laminar flow element consists of two pressure taps separated by a length of piping. However the Reynolds number constraint for laminar flow restricts the size of pipe diameter that can be used. This limitation is overcome in commercial unit through the use of laminar flow elements which consist of a bundle of small diameter tubes, or some proprietary design of geometric passages (small spherical balls, honey comb, etc.) placed in parallel. The strategy of a laminar flow element is to divide up the flow by passing it through the tube bundle so as to reduce the flow rate per tube such that the individual Reynolds number in each tube remains below 2000. Pressure drop is measured between the entrance and the exit of the laminar flow element. Because of the additional entrance and exit losses associated with the laminar flow element, a flow coefficient is used to modify the above equation. This coefficient must be determined by calibration. So;

Q dCd P

L=

πµ

4

128

∆ or Q = Cd K (∆P/µ)

Where K is the meter constant. For any given meter there will exist a flow rate above which laminar flow will no longer exist in the laminar flow element. The main disadvantage of this meter is that the pressure loss is equal to the differential pressure because it is completely the result of viscous friction. Laminar flow elements offer some distinct advantages over other pressure differential meters. These include: 1- A high sensitivity even at extremely low flow rates. 2- The ability to measure pipe system flow in meter direction. 3- A wide usable flow range. 4- The ability to indicate an average flow rate in pulsating flows. Disadvantages of the meter:

1. Their use is restricted to clean fluids or the tubes will be clogged by dirty. 2. The entire pressure drop measured remains a system pressure loss.

1.5 Factors Affecting Obstruction Meter Selection : - Meter placement. - Overall pressure loss. - Accuracy and overall costs.


2. Constant - Pressure Drop, Variable Area Meters: 2.1 Rotameters: The rotameter remains a widely used insertion meter for flow rate indication. As depicted in figure (9), the meter consists of a float within a vertical tube, tapered to an increasing cross sectional area at its outlet. Flow entering through the bottom passes over the float, which is free to move. The basic principle of the device is based on the simple balance between the weight of the float Fw and both the buoyancy forces FB acting on the float in the moving fluid and drag force FD.

The force balance in the vertical direction gives: FD

FB

F

dC bA fmU

f bV b bV

+ =

+ =

W(24)

(25)

ρ γ γ2

2

Where: Cd : Drag coefficient Ab : Frontal area of the body (float) ρf ,γf : Density and specific weight of the passing fluid γb : Specific weight of the float Vb : Volume of the float Um : Mean flow velocity in the annular space

FB

FW

FD


Note that: γ = ρ g and from the above equation:

Um C

d

g Vb

Ab

b f

f=

−

1 21 2

/ρ ρ

ρ (26)

The drag coefficient, Cd , is dependent on the Reynolds number and hence on the viscosity. However special floats may be used that have an essentially constant drag coefficient and thus offer the advantage that the meter reading will be independent of the viscosity. It must be noted from the above equation, as (Vb , Ab , ρb , ρf and Cd are constants; Um = constant i.e. It is not function of the discharge Q . And

Q A Um

AC

d

g Vb

Ab

b f

f= =

−

1 21 2

/ρ ρ

ρ (27)

From the above equation, as Um is constant therefore; Q α A So, to get a variable measured value for Q, the area A must be vary with the variation of the discharge Q, so a taper tube must be used. Where: A is the annular area and is given by:

( )A D ay d= + −

π4

2 2

D : is the taper tube diameter at inlet d : is the maximum body (float) diameter y : is the vertical distance measured from the entrance of the tapered tube a : is a constant depending on the tube taper, a = 2 tan α 2α : is the total taper angle of the tube


[ ]d2y2a2yaD2D24

A −++π=

Since D d≅ and as a = 2 tan α is constant and very small, so; ∴ a2 y2 may be neglected ; Therefore ; A α D a y and as ( a and D ) are constants, ∴ A α y It may be noted that for many practical meters, the quadratic area relation given above becomes nearly linear for the actual dimension of the tube and the float. Assuming such a linear relation, the equation for mass flow rate becomes:

Q yC

d

g Vb

Ab

b f

f∝

−

1 21 2

/ρ ρ

ρ

or,

( )m f Q C y b f f= = −ρ ρ ρ ρ1 (28)

Where:

C1 : Is now an appropriate constant for the meter =

bAbVg2

dC

121

And if ρf and ρb are constants, Both (Q & m ) ≈ y Thus the float’s vertical position, y, gives a direct measure for the flow rate which can be read from a graduated scale. The tubes of the rotameters are made often of high strength glass to allow direct observation of the float position. Where greater strength is required, metal tubes can be used and the float position detected magnetically throughout the metal wall.


3. Turbine Meters : If a turbine wheel is placed in a pipe containing a flowing fluid, its rotary speed depends on the flow rate of the fluid. By reducing bearing friction and other losses to a minimum, one can design a turbine whose speed varies linearly with the flow rate. Thus a speed measurement allows flow rate measurement. In the turbine - wheel body a permanent magnet is enclosed so that it rotate with the wheel. The speed can be measured with great accuracy by counting the rate at which turbine blades pass a given point, using a magnetic pick up to produce voltage pulses. By feeding these pulses to an electronic - pulse rate meter, one can measure the flow rate, and by accumulating the total number of pulse during a timed interval, the total flow is obtained. These measurements can be made very accurately because of their digital nature, figure (10).


Dimensional analysis of the turbine flow meters, shows that ( if bearing friction and shaft power output are neglected) the following relation should hold :

=

νdn

fdn

Q 2

3 = f (Re ) (29)

Where: Q : volume flow rate, [m3/sec] n : rotor angular velocity, [rps] d : meter bore diameter, [m] ν : Kinematics viscosity, [m2/sec] For negligible viscosity effects, a simplified analysis gives that: Q = k n (30) Where: k : is a constant for a given meter and is independent of the fluid properties n : is rotor angular velocity or pulse rate Turbine meter can follow transient flow accurately since their fluid mechanical time constant is of the order of 2 - 10 msec.


4. Electromagnetic Flow Meters : A magnetic flow meter (mag flow meter) is a volumetric flow meter which does not have any moving parts and is ideal for wastewater applications or any dirty liquid which is conductive or water based. Magnetic flow meters will generally not work with hydrocarbons, distilled water and many non-aqueous solutions). Magnetic flow meters are also ideal for applications where low pressure drop and low maintenance are required. The operating principle of an electromagnetic flow meter, figure (11) is based on the fundamental principle that an electromotive force (emf) of electric potential, E, is induced in a conductor of length, L, when moves with a velocity, u, through a magnetic field of magnetic flux β. E = u β L x 10-8 [V] (31) Where: u : velocity of the conductor, [cm/s] β : Flux density, [gauss] L : length of conductor, [ cm]


In general, electrodes are embedded in the pipe wall in a diametrical plane that is normal to the known magnetic field, and the flow rate is found by :

Q u d E

Ld

K E= = =πβ

π2

4

2

4 1 (32)

The static sensitivity K1 is a meter constant found by calibration and supplied by the manufacturer. The relation between flow rate and measured potential is linear. The electromagnetic flow meter comes commercially as a package flow device, which is installed directly in line and connected to an external electronic output unit. Units are available as : - Dc units, using permanent magnets. - Ac units, using variable flux strength magnets. The magnetic flux strength of an Ac unit can be increased on site to produce a strong signal at low flow rates of low conductivity fluids, such as water. Special designs include a flow sensor unit which actually can clamp over (not in line with) a non magnetic pipe, a design favored to monitor blood flow rate through major arteries during surgery. The electromagnetic flow meter has a very low pressure loss associated with its use due to its open tube, no obstruction design. This absence of internal parts is very attractive for metering corrosive and dirty fluids. The operating principle is independent of fluid density and viscosity, responding only to average velocity. The use of any meter is limited to fluids having a reasonable value of electrical conductivity. The addition of salt to a fluid will increase its conductivity.


To apply this principle to flow measurement with a magnetic flow meter, it is necessary first to state that the fluid being measured must be electrically conductive for the Faraday principle to apply. As applied to the design of magnetic flow meters, Faraday's Law indicates that signal voltage (E) is dependent on the average liquid velocity (V) the magnetic field strength (B) and the length of the conductor (D) (which in this instance is the distance between the electrodes).In the case of wafer-style magnetic flow meters, a magnetic field is established throughout the entire cross-section of the flow tube. If this magnetic field is considered as the measuring element of the magnetic flow meter, it can be seen that the measuring element is exposed to the hydraulic conditions throughout the entire cross-section of the flow meter. With insertion-style flow meters, the magnetic field radiates outward from the inserted probe.

Advantages Disadvantages No moving parts. Can be used with dirty fluids. Low pressure drop (No obstruction). No maintenance. No contact between fluid and the meter. Not function of µ or ρ .

Limited for fluids with reasonably value for electric conductivity.


6. Positive Displacement Meters (Volume flow meters): Positive displacement meters contain mechanical elements that define a known volume. The free moving elements are displaced by the action of the moving fluid. A counting mechanism counts the number of elements displacement to provide a direct reading of volume of fluid passed through the meter. These meters usually used as volume meters. Volume per unit time can be discerned in conjunction with a timer. This metering method is common to water, gasoline and natural gas meters, where steady flow is exist. Obviously it is not suited for transient flow measurements. Several types of these flow meters can be used. 6.1 The Rotary - Vane Flow Meter : One type of the positive displacement flow meter is the rotary - vane type flow meter shown in figure (12). The vanes are spring loaded so that they continuously maintain contact with the casing of the meter. A fixed quantity of fluid is trapped in each section as the eccentric drum rotates, and this fluid finds its way out from the exit port. An appropriate register connected to the shaft of the eccentric drum to record the volume of the fluid displaced. The uncertainty of the rotary vane meter is of the order of 0.5%, and the meters are insensitive to viscosity since the vanes always maintain good contact with the inside of the casing.

Fixed Casing


6.2 The Lobed - Impeller Flow meter : This meter, shown in figure (13) may be used for either gas or liquid flow measurements. The impeller and case are carefully machined so that accurate fit is maintained. In this way, the incoming fluid is always trapped between the two rotors and is conveyed to the outlet as a result of their rotation. The number of revolutions of the rotors is an indication of the volumetric flow rate.

6.3 Domestic Water Flow meters:

• Nutating disk • Single jet – Dry water flow meter • Multi-jet – Dry water flow meter • Single jet – Super Dry water flow meter • Multi-jet – Super Dry water flow meter

This type of flow meters is usually used for domestic water flow measurement. The following are some examples of these meters

Prof. Dr. Nabil Abel Aziz MAHMOUD

Nutating Disc:

A typical nutating disk is shown in moveable disk mounted on a concentric sphere located in a spherical sidechamber. The pressure of the liquid passing through the measuring chamber causes the disk to rock in a circulating path without rotationly moving part in the measuring chamber.

A pin extending perpendicularly from the disk is connected to a mechanical counter that monitors the disk's rocking motions. Each cycle is proportional to a specific quantity of flow. As is true with all positivevariations below a given threshold will affect measuring accuracies. Many sizes and capacities are available. The units can be made from a wide selection of construction materials.

This type of flow meter is normally used for water service, such as raw water supply and evaporator feed. The fluid enters an opening in the spherical wall on one side of the partition and leaves through the other side. As the fluid flows through the chamber, the disk wobbles, or executes a nutating motion. Since the volume of fluid required to make the disc complete one revolution is known, the total flow through a nutating disc can be calculated by multiplying the number of disc rotations by the known volume

The top of the shaft operates a revolution counter, through a crank and set of gears, which is calibrated to indicate total system flow.

Abel Aziz MAHMOUD 4/3/201130

A typical nutating disk is shown in the figures below. Nutating-disk metersmoveable disk mounted on a concentric sphere located in a spherical sidechamber. The pressure of the liquid passing through the measuring chamber causes the disk to rock in a circulating path without rotating about its own axis. It is the only moving part in the measuring chamber.

A pin extending perpendicularly from the disk is connected to a mechanical counter that monitors the disk's rocking motions. Each cycle is proportional to a

ow. As is true with all positive-displacement meters, viscosity variations below a given threshold will affect measuring accuracies. Many sizes and capacities are available. The units can be made from a wide selection of

type of flow meter is normally used for water service, such as raw water supply and evaporator feed. The fluid enters an opening in the spherical wall on one side of the partition and leaves through the other side. As the fluid flows

the disk wobbles, or executes a nutating motion. Since the volume of fluid required to make the disc complete one revolution is known, the total flow through a nutating disc can be calculated by multiplying the number of disc rotations by the known volume of fluid.

The top of the shaft operates a revolution counter, through a crank and set of gears, which is calibrated to indicate total system flow.

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disk meters have a moveable disk mounted on a concentric sphere located in a spherical side-walled chamber. The pressure of the liquid passing through the measuring chamber causes

ng about its own axis. It is the

A pin extending perpendicularly from the disk is connected to a mechanical counter that monitors the disk's rocking motions. Each cycle is proportional to a

meters, viscosity variations below a given threshold will affect measuring accuracies. Many sizes and capacities are available. The units can be made from a wide selection of

type of flow meter is normally used for water service, such as raw water supply and evaporator feed. The fluid enters an opening in the spherical wall on one side of the partition and leaves through the other side. As the fluid flows

the disk wobbles, or executes a nutating motion. Since the volume of fluid required to make the disc complete one revolution is known, the total flow through a nutating disc can be calculated by multiplying the number of

The top of the shaft operates a revolution counter, through a crank and set of gears,


Single jet dry water flow meter Operation

• A tapered inlet creating a single jet of water that is projected into the measuring chamber where it strikes the blades of the impeller.

• The impeller rotation speed is in relation to the velocity of water flow • A magnet and gear train converts the number of rotations into a volume

which is displayed on the indicating device (register dial face) • Body has only single water entry and exit

• While water flows only one wing of the impeller is being touched


Single jet dry water flow meter

1- Cover

2- Totalizer

3- Ring nut

4- Pressure plate

5- Impeller wheel

6- Housing


Multi jet dry water flow meter Operation

• Multi jet meters use multiple ports surrounding the internal measuring chamber, to create a jet of water against the impeller

• The impeller rotation speed is in relation to the velocity of water flow • A magnet and gear train converts the number of rotations into a volume

which is displayed on the indicating device (register dial face) • Water flows via tangential entries and push the impeller

• All impeller wings are in touch with water simultaneously while water flows.

• Some models equipped with an adjusting port to allow for recalibration, compensate for inaccuracy in older meters.


Multi jet dry water flow meter

1- Cover

2- Totalizer

3- Pressure plate

4- Impeller wheel

5- Housing


Comparaison: Multi-jet vs. Single-jet

Multi-jet

• High resistance to flow

• Longer life expectancy

• Many parts

• More expensive

• Less sensitive to installation conditions

• Most utilized meter worldwide

Single-jet

• Limited resistance to flow

• Shorter life expectancy

• Economic solution

• Sensitivity to installation conditions

• Popular for sub-metering applications

Prof. Dr. Nabil Abel Aziz MAHMOUD 4/3/2011

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Single jet super dry water flow meter Used for water with higher rates of dust and impurities may be flow in the water and have the same concept of the single jet dry meter but with more filters to decrease impurities effect on the meter readings.


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Multi jet super dry meter Used for water with higher rates of dust and impurities may be flow in the water and have the same concept of the single jet dry meter but with more filters to decrease impurities effect on the meter readings.


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7. Other Types of flow meters 7.1 Piston Water flow meter

7.1.1 Oscillating Piston flow meter Application: Provide a cost effective and reliable solution for a wide range of industrial flow measurement applications.

Oscillating piston flow meters typically are used in viscous fluid services such as oil metering on engine test stands where turndown is not critical. These meters also can be used on residential water service and can pass limited quantities of dirt, such as pipe scale and fine (viz,-200 mesh or -74 micron) sand, but not large particle size or abrasive solids.

Construction: An oscillating piston flow meter, comprising: A measuring chamber having a bottom, a cylindrical jacket, a central journal a guide ring, a separating wall, an inlet and outlet openings; and a piston located in the measuring chamber and having a bottom, a cylindrical skirt, a pilot journal engage-able with and rotatable about the central journal of the measuring chamber, and a guiding slot extending in the skirt and the bottom and up to separating wall of the measuring chamber, where in at least one of the central journal of the measuring chamber and the pilot journal of the piston is formed as a resiliently pliable thin-wall cylinder.

The figure shows: the parts of an Oscillating Piston Flow meter.


Working principle: Liquid enters a precision-machined piston. The position of the piston divides the chamber into compartments containing an exact volume. Liquid pressure drives the piston to oscillate and rotate on its center hub. The movements of the hub are senswall by a follower magnet. Each revolution of the piston hub is equivalent to a fixed volume of fluid, which is indicated as flow by an indicator/totalizer. Close clearances between the piston and the chamber ensure minimum liquid sliphighly accurate and repeatable measurement of each volume cycle. Maximum viscosity allowed: 4,000 centi

The figure shows: the working principle of the oscillating flow meter.

Dr. Nabil Abel Aziz MAHMOUD 39

machined chamber containing an oscillating (rotating) piston. The position of the piston divides the chamber into compartments containing an exact volume. Liquid pressure drives the piston to oscillate and rotate on its center hub. The movements of the hub are sensed through the meter wall by a follower magnet. Each revolution of the piston hub is equivalent to a fixed volume of fluid, which is indicated as flow by an indicator/totalizer. Close clearances between the piston and the chamber ensure minimum liquid sliphighly accurate and repeatable measurement of each volume cycle. Maximum viscosity allowed: 4,000 centi-poise.


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chamber containing an oscillating (rotating) piston. The position of the piston divides the chamber into compartments containing an exact volume. Liquid pressure drives the piston to oscillate and

ed through the meter wall by a follower magnet. Each revolution of the piston hub is equivalent to a fixed volume of fluid, which is indicated as flow by an indicator/totalizer. Close clearances between the piston and the chamber ensure minimum liquid slip for highly accurate and repeatable measurement of each volume cycle. Maximum



7.1.2 Rotary Piston flow meter Application: Measuring the volume of cold potable water passing through the pipeline. Working conditions: Water temperature ≤ 50 oC Water pressure ≤ 0.6 MPa

Working principle: The working principle is based on a calibrated chamber of a known capacity and a Rotaryactivated by the energy of the flow passing through. The water flowing through the meter drives the circular piston (not perfectly circular) in an eccentric path around the measuring chamber, the piston rotates while the chamber fills up and empties with a constant volume of water. Each revolution represents the transfer of a known quantity of water. The rotary action of the piston is transferred to a drive coupling from which it is transmitted to the combined gear and dial unit.The combined gear and dial unit which has a simple straight reading display counts these revolutions, indicating the total volume of water.

Solid particles are gathered by a strainer preventing damage. Partial obstruction of the strainer will have no adverse effect on tregistration.

A body ‘O’ ring seal between the measuring chamber and the meter body ensures that internal leaks which could byeliminated.


Rotary Piston flow meter

Measuring the volume of cold potable water passing through the

The working principle is based on a calibrated chamber of a known capacity and a Rotary Piston activated by the energy of the flow

The water flowing through the meter drives the circular piston (not perfectly circular) in an eccentric path around the measuring chamber, the piston rotates while the chamber

s with a constant volume of water. Each revolution represents the transfer of a known quantity of water. The rotary action of the piston is transferred to a drive coupling from which it is transmitted to the combined gear and dial unit.

ar and dial unit which has a simple straight reading display counts these revolutions, indicating the total volume of water.

Solid particles are gathered by a strainer preventing damage. Partial obstruction of the strainer will have no adverse effect on the accuracy of the meters

A body ‘O’ ring seal between the measuring chamber and the meter body ensures that internal leaks which could by-pass the measuring chamber are

4/3/2011

ar and dial unit which has a simple straight reading display

Solid particles are gathered by a strainer preventing damage. Partial obstruction he accuracy of the meters

A body ‘O’ ring seal between the measuring chamber and the meter body pass the measuring chamber are


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7.2 Vortex flow meter Application: Vortex flow meters are flow sensors that detect the frequency of vortices shed by a bluff body placed in a flow stream. The frequency of the vortices is proportional to the flow velocity. Vortex flow meters are used to measure the flow of liquids and/or gases.

Vortex-shedding flow meters are best used in turbulent flow with a Reynolds number greater than 10,000. One advantage of using this type of flow meter is its insensitivity from temperature, pressure, and viscosity. The major disadvantage to using this method is the pressure drop caused by the flow obstruction. Construction: All vortex shedding meter designs consist of two main components, the bluff body and the sensing device. There are many different of bluff body configurations. In some instances multiple struts are incorporated into the design. Bluff Bodies: Though the shape differs, actual dimensions of the bluff body are determined by the relationship between the diameters of the pipe, the viscosity of the fluid and the flow rate. The strut must have non-streamlined edges so that the vortex formation will occur. Sensors: There are four types of sensors commonly used to detect vortices developed by the bluff body and shed into the downstream flow. These sensors are strain gauge, magnetic pickup, ultrasonic detector and piezoelectric element. Working principal: An obstruction in a fluid flow creates vortices in a downstream flow. Every obstruction has a critical fluid flow speed at which vortex shedding occurs. Vortex shedding is the instance where alternating low pressure zones are generated in the downstream.


These alternating low pressure zones cause the obstruction to move towards the low pressure zone. With sensors gauging the vortices the strength of the flow can be measured.

The figure shows the working principal of the vortex shedding.

Vortex flow meters, also known as vortex shedding flow meters or oscillatory flow meters, measure the vibrations of the downstream vortexes caused by a barrier in the moving stream.


These alternating low pressure zones cause the obstruction to move towards the low pressure zone. With sensors gauging the vortices the strength of the flow


Vortex flow meters, also known as vortex shedding flow meters or oscillatory flow meters, measure the vibrations of the downstream vortexes caused by a barrier in the moving stream.

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These alternating low pressure zones cause the obstruction to move towards the low pressure zone. With sensors gauging the vortices the strength of the flow


Vortex flow meters, also known as vortex shedding flow meters or oscillatory flow meters, measure the vibrations of the downstream vortexes caused by a


The vibrating frequency of the vortex shedding is related to the velocity of the flow.

The number of vortices formed is directly proportional to the flow velocity and hence the flow rate. The vortices are detected downstream from the blunt body using an ultrasonic beam that is transmitted perpendicular to the direction of flow.

As the vortices cross the beam, they alter the carrier wave as the signal is processed electronically, using a frequencydiagram shows the basic principle of the vortex


The vibrating frequency of the vortex shedding is related to the velocity of the

The number of vortices formed is directly proportional to the flow velocity and hence the flow rate. The vortices are detected downstream from the blunt body

trasonic beam that is transmitted perpendicular to the direction of

As the vortices cross the beam, they alter the carrier wave as the signal is processed electronically, using a frequency-to-voltage circuit. The following

principle of the vortex-shedding flow meter:

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The vibrating frequency of the vortex shedding is related to the velocity of the

The number of vortices formed is directly proportional to the flow velocity and hence the flow rate. The vortices are detected downstream from the blunt body

trasonic beam that is transmitted perpendicular to the direction of

As the vortices cross the beam, they alter the carrier wave as the signal is voltage circuit. The following

shedding flow meter:


7.3 Ultrasonic flow meter Transient time and Doppler that have been extensively used in liquid applications of ultrasonic flow meters where they apply to liquid measurement and particularly transient time method yields much greater accuracies. 7.3.1 Time of flight flowThe electronics unit will measure internally the time it takes for signals to transmit from one transducer to another. At zero flow, we see no difference in time, but when flow is introduced, time for the transmission of signal from the downstream transducer to the upstream transducer will take longer than the upstream to downstream. Hence we will see a time differential which has a relationship with the velocity of the fluid being measured. Knowing the internal diameter of the pipe, we can now calc

Transient Time Ultra Sonic Flow Meter


Doppler flow meters are two types of ultrasonic flow meters

that have been extensively used in liquid applications around the world. meters where they apply to liquid measurement and time method yields much greater accuracies.

ime of flight flow meter The electronics unit will measure internally the time it takes for signals to transmit from one transducer to another. At zero flow, we see no difference in time, but when flow is introduced, time for the transmission of signal from the

er to the upstream transducer will take longer than the upstream to downstream. Hence we will see a time differential which has a relationship with the velocity of the fluid being measured. Knowing the internal

can now calculate the flow rate.

Transient Time Ultra Sonic Flow Meter

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flow meters are two types of ultrasonic flow meters around the world. The use

meters where they apply to liquid measurement and

The electronics unit will measure internally the time it takes for signals to transmit from one transducer to another. At zero flow, we see no difference in time, but when flow is introduced, time for the transmission of signal from the

er to the upstream transducer will take longer than the upstream to downstream. Hence we will see a time differential which has a relationship with the velocity of the fluid being measured. Knowing the internal


The transient time ultrasonic transducers can be mounted in one of two modes. The upstream and downstream ultrasonic transducers can be installed on opposite sides of the pipe (diagonal mode) or on

Diagonal and reflect m

It is important when installing an ultrasonic transit time flow meter to select a location where we would find the most fully formed flow profile; this that we should avoid bends and try to install our meters on straight runs of pipe. A rule of thumb in the industry is to give at least 10 diameter lengths upstream and 5 lengths downstream.


ultrasonic transducers can be mounted in one of two modes. The upstream and downstream ultrasonic transducers can be installed on opposite sides of the pipe (diagonal mode) or on the same side (reflect mode)

reflect modes for transient time ultrasonic flow m

It is important when installing an ultrasonic transit time flow meter to select a location where we would find the most fully formed flow profile; this that we should avoid bends and try to install our meters on straight runs of pipe. A rule of thumb in the industry is to give at least 10 diameter lengths upstream

4/3/2011

ultrasonic transducers can be mounted in one of two modes. The upstream and downstream ultrasonic transducers can be installed on

the same side (reflect mode).

time ultrasonic flow meter

It is important when installing an ultrasonic transit time flow meter to select a location where we would find the most fully formed flow profile; this means that we should avoid bends and try to install our meters on straight runs of pipe. A rule of thumb in the industry is to give at least 10 diameter lengths upstream


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7.3.2 Doppler flow meter The Doppler method relies on the existence of solid particles or bubbles in the liquid being measured. Doppler ultrasonic flow meters operate on the Doppler effect, whereby the transmitted frequency is altered linearly by being reflected from particles and bubbles in the fluid. The net result is a frequency shift between transmitter and receiver frequencies that can be directly related to the flow rate. One Doppler meter design mounts both the transmitting and the receiving transducers in the same case, attached to one side of the pipe. Reflectors in the flowing liquid return the transmitter signals to the receiver, with a frequency shift proportional to the flow velocity.

Doppler ultrasonic flow meter Now more updated signal processing is being used in many transient time flow meter designs, battery power up to 15 hours and flow readings obtained within seconds. This has considerably eased the job of the flow survey company and increased customer confidence in ultrasonic meters. Both transient time and Doppler ultrasonic flow meters may use clamp-on sensors with their associated assemblies and detect flow rate from the outside of the pipe without stopping the process or cutting through the pipe. The applications for this type of technology are manifold because now we are able to make sure our old or new pump is working to its capacity, gather data for flow balancing, and check if our permanently installed meters are measuring incorrectly or are in need of maintenances. Simply clamp on a flow meter where


47

there is no flow meter or where other flow meters make it impractical for installation. The ultrasonic meter can measure water, waste water, hydrocarbon liquids, organic or inorganic chemicals, milk, beer, lube oils and the list goes on. The basic requirement is that the fluid is ultrasonically conductive and has a reasonably well formed flow. Clamp-on ultrasonic flow meters measure flow through the pipe without any contact with the process media, ensuring that corrosion and other effects from the fluid will not affect the workings of the sensors or electronics.


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7.4 Elbow flow meter Elbow meters are based on the principle of "conservation of momentum." Momentum conservation requires that the momentum flux (momentum per unit time) remain unchanged as steady flow occurs through an isolated system of fluid. Since momentum is a vector quantity, a change in direction of the flow causes a reduction of momentum in the original direction which is offset by an increase in the new direction. In an elbow, such as the mitered elbow shown in the figure below, the momentum in the horizontal direction is changed by the pipe turning down. This change in direction causes the flow to exert a force on the pipe elbow.

A differential pressure exists when a flowing fluid changes direction due to a pipe turn or elbow, as shown in the figure below. This pressure difference results from the centrifugal force. Since pipe elbows exist in plants, the cost for these meters is very low. However, the accuracy is very poor; there are only applied when reproducibility is sufficient and other flow measurements would be very costly.


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The volume flow rate can be calculated from:

F = Q (V2-V1) [Momentum Equation]

Where,

F = Force = the fluid density

Q = the discharge (flow) V = the velocity vector


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7.5 Target Flow meter Construction for Target Flow Meter: A sharp-edged disk is set at right angles to the direction of flow. The drag force exerted on the disk is measured and is related to the flow rate of the fluid. The drag force in this case is analogous to the frictional force exerted by the fluid on wall of a conduit.

Theory of Operation and Calibration of Target flow meters: Target meters can be calibrated using the same principal as that of frictional force exerted on a wall of a conduit. Flow rate = Fluid density* (drag force) 2 The drag force in this case is equivalent to the frictional force exerted by the fluid on the wall while flowing through a conduit. The deflection of the target and the force bar is measured in the instrument, or by electronic sensors.


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The force on the target can be expressed as: F = cd ρ v

2 At / 2 Where: F = force on the target (N) cd = overall drag coefficient obtained from empirical data ρ = density of fluid (kg /m3) v = fluid velocity (m /s) A t = target area (m2) Advantages of Target Flow meter: They are kind of expensive and rugged, BUT it can be used with a wide variety of fluids, and useful for dirty or corrosive fluids. Target meters require no external connections, seals, or purge systems. Target flow meters are commonly used to for liquid flow measurement and less commonly applied to steam and gas flow. Target Meters offer turndowns up to 20:1 with accuracy around 1%.


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7.6 Mass Coriolis Flow Meter This meter uses the Coriolis effect to measure the amount of mass moving through the element. The substance to be measured runs through a U-shaped tube that is caused to vibrate in a perpendicular direction to the flow. Fluid forces running through the tube interact with the vibration, causing it to twist. The greater the angle of the twist, the greater the flow. Coriolis meter consists of sensor – two flow tubes that are vibrated in opposition to each other and a transmitter. The frequency of oscillation of the sensor tubes is detected by coil assemblies called pick-offs—one on the inlet side of the tubes and one on the outlet side of the tubes.

When the tubes are filled with fluid, but there is no flow, the inlet and outlet sides of the tubes are subject to the same force operating in the same direction. The inlet and outlet pick-offs register oscillations at the same time. However, when there is flow through the tubes, it is accelerating (changing direction) on the inlet side and decelerating on the outlet side. This produces a slight twist in the flow tubes, which causes the inlet pick-off to register before the outlet pick-off. The magnitude of the time delay between the inlet and outlet sides of the tubes is directly proportional to the mass flow of the fluid.


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The Coriolis meter can also be used to measure density, temperature, volume flow and concentration. Density Measurement: The density of the fluid can be directly determined by changes in the natural frequency of the tubes' oscillations. The natural frequency is based on the mass of the flow tubes themselves, plus the mass of the fluid. When the total mass increases, the natural frequency decreases. Because the volume of fluid contained within the flow tubes is constant, and because the mass of the flow tubes is constant, the only cause of a change in total mass (and by extension the natural frequency) is a change in fluid density. Temperature Measurement: Most Coriolis meters include an RTD for process temperature measurement. The temperature value can be used to compensate measurement for the effect of temperature on flow tube stiffness. This effect is typically measured at the factory and included in the factory calibration. Volume Flow Measurement: Coriolis meters can calculate a highly-accurate volume flow measurement based on the direct mass flow, density, and temperature measurements. Concentration Measurement: Coriolis meters can also calculate a highly-accurate concentration measurement when the concentration of one or two components has a dominant effect on the fluid density.


7.7 Theory of Operation: This device operate either by flowing stream and measuring an associated temperature change, or by maintaining a probe at a constant temperature and measuring the energy required to do so. The components of a basic thermal mass flow meter inupstream and downstream temperature sensor and a heat source as illustrated in figure. The heater can protrude into the fluid stream or can be external to the pipe.

The mass flow is calculated as follows:


7.7 Thermal Mass flow meter

This device operate either by introducing a known amount of heat into the flowing stream and measuring an associated temperature change, or by maintaining a probe at a constant temperature and measuring the energy

The components of a basic thermal mass flow meter include a flow tube, an upstream and downstream temperature sensor and a heat source as illustrated in

The heater can protrude into the fluid stream or can be external to the pipe.

The mass flow is calculated as follows:

m =

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introducing a known amount of heat into the flowing stream and measuring an associated temperature change, or by maintaining a probe at a constant temperature and measuring the energy

clude a flow tube, an upstream and downstream temperature sensor and a heat source as illustrated in

The heater can protrude into the fluid stream or can be external to the pipe.


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8. Selecting a Flow Meter:

Experts claim that over 75 percent of the flow meters installed in industry are not performing satisfactorily and improper selection accounts for 90 percent of these problems. Obviously, flow meter selection is no job for amateurs.

The most important requirement is knowing exactly what the instrument is supposed to do. Here are some questions to consider:

• Is the measurement for process control (where repeatability is the major concern), or for accounting or custody transfer (where high accuracy is important)?

• Is local indication or a remote signal required? If a remote output is required, is it to be a proportional signal, or a contact closure to start or stop another device?

• Is the liquid viscous, clean, or slurry? • Is it electrically conductive? • What is its specific gravity or density? • What flow rates are involved in the application? • What are the processes' operating temperatures and pressures?

Accuracy, range, linearity, repeatability, and piping requirements must also be considered.

It is just as important to know what a flow meter cannot do as well as what it can do before a final selection is made. Each instrument has advantages and disadvantages, and the degree of performance satisfaction is directly related to how well an instrument's capabilities and shortcomings are matched to the application's requirements. Often, users have expectations of a flow meter's performance that are not consistent with what the supplier has provided. Most suppliers are anxious to help customers pick the right flow meter for a particular job. Many provide questionnaires, checklists, and specification sheets designed to obtain the critical information necessary to match the correct flow meter to the job.

Technological improvements of flow meters must be considered also. For example, a common mistake is to select a design that was most popular for a given application some years ago and to assume that it is still the best instrument for the job. Many changes and innovations may have occurred in recent years in the development of flow meters for that particular application, making the choice much broader.


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9. Working with Flow Meter:

Although suppliers are always ready to provide flow meter installation service, estimates are that approximately 75 percent of the users install their own equipment. But installation mistakes are made. One of the most common is not allowing sufficient upstream and downstream straight-run piping for the flow meter.

Every design has a certain amount of tolerance to nonstable velocity conditions in the pipe, but all units require proper piping configurations to operate efficiently. Proper piping provides a normal flow pattern for the device. Without it, accuracy and performance are adversely affected. Flow meters are also installed backwards on occasion (especially true with orifice plates). Pressure-sensing lines may be reversed too.

With electrical components, intrinsic safety is an important consideration in hazardous areas. Most flow meter suppliers offer intrinsically safe designs for such uses.

Stray magnetic fields exist in most industrial plants. Power lines, relays, solenoids, transformers, motors, and generators all contribute their share of interference. Users must ensure themselves that the flow meter they have selected is immune to such interference. Problems occur primarily with the electronic components in secondary elements, which must be protected. Strict adherence to the manufacturer's recommended installation practices will usually prevent such problems.


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10. Flow Meter Calibration: Calibration is, in general, based on the establishment of steady flow through the flow meter to be calibrated and subsequent measurement of the volume or mass of flowing fluid that passes through in an accurately timed interval. As in any other calibration, significant deviations of the conditions of use from those at calibration will invalidate the calibration. A typical calibration setup is shown :

A constant head tank maintains a fixed inlet pressure to the flow meter under test, irrespective of the flow rate. The flow rate through the meter is adjusted to


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the various desired values with a flow - control valve. Until a constant flow rate is established, the liquid is diverted from the weigh or volume tank which must be emptied before flow into it is started. When a constant flow rate is established, the flow diverter is suddenly moved to the tank position and a switch starts the electronic timer as the diverter passes the mid position. Flow is continued until the tank is filled, at which the motion of the diverter through the mid - position to the return position stops the timer. The weight or volume of the accumulated liquid during the timed interval is then determined to calculate the volume or mass flow rate. The calibration of flow meters to be used with gases can often be carried out with liquids as long as the similarity relations ( Reynolds number) are maintained. 10.1 Sources Of Errors In Flow Meter Calibration : There are many sources of errors in flow meter calibration. Some of these sources of errors are: - Variation in fluid properties (density, viscosity and temperature). In this case, it is better to use dimensionless groups ( Re, Cd, ….. ext.). - Orientation of the meter (horizontal, vertical or inclined). - Pressure level. - Flow disturbance upstream & downstream of the meter.


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10. 2 Advantages And Disadvantages

Of Different Flow Measuring Techniques:

Type Advantage Disadvantage

Orifice Plate • Simple concept • Not expensive

• Non linear output • Creates head loss

Venturi Tube • Simple concept • Expensive

• Non linear output • Expensive • Creates head loss (less

than orifice) Variable area (Rotameter)

• Visual output • Linear scale

• Creates head loss

Laminar Flow Element (LFE)

• A high sensitivity even at extremely low flow rates.

• The ability to measure pipe system flow in meter direction.

• A wide usable flow range.

• The ability to indicate an average flow rate in pulsating flows.

• Their use is restricted to clean fluids or the tubes will be clogged by dirty.

• The entire pressure drop measured remains a system pressure loss.

Ultra sonic Time of flight

• No moving parts • Non intrusive • No head loss

• Flow profile affects accuracy

• Unsuitable for fluids with more than 4% solids or gas bubbles

• Liquid density affects accuracy

Ultra sonic Doppler

• No moving parts • Non intrusive • No head loss • Suitable for fluids

contains solids or gas bubbles

Liquid density affects accuracy

• Poor accuracy Flow profile affects

accuracy


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Type Advantage Disadvantage Magnetic • Accurate

• No moving parts • No head loss • Linear output • Accommodate solids

in suspension

• Expensive

Turbine meter • Accurate • Expensive • Create head loss

Positive displacement meter

• Suitable for low flow usage

• Suitable for high viscosity usage

• Accurate

• Expensive


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11. Flow Meter Selection Guide:

Flow Meter

Element Recommended

Service Pressure

Loss Typical

Accuracy percent

Required Upstream

pipe, diameters

Viscosity

effect

Relative Cost

Orifice Clean, dirty liquids; some slurries

Medium ±2 to ±4 of full Scale.

10 to 30 High Low

Venturi meter

Clean, dirty and viscous liquids; some slurries

Low ±1 of full scale

5 to 20 High Medium

Flow nozzle Clean and dirty liquids

Medium ±1 to ±2 of full scale

10 to 30 High Medium

Pitot tube Clean liquids Very low ±3 to ±5 of full scale

20 to 30 Low Low

Elbow meter Clean, dirty liquids; some slurries

Very low ±5 to ±10 of full scale

30 Low Low

Target meter Clean, dirty Viscous liquids; some slurries


10 to 30 Medium Medium

Variable area (Rotameter)

Clean, dirty viscous liquids


None Medium Low

Positive Displacement

clean, viscous liquids

High ±0.5 of rate

None High Medium

Turbine Clean, viscous liquids

High ±0.25 of rate

5 to 10 High High

Vortex Clean, dirty liquids

Medium ± I of rate 10 to 20 Medium High

Electro-magnetic

Clean, dirty viscous conductive liquids and slurries

None ±0.5 of rate

5 None High


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Flow Meter

Element Recommended

Service Pressure

Loss Typical

Accuracy percent

Required Upstream

pipe, diameters

Viscosity

effect

Relative Cost

Ultrasonic (Doppler)

Dirty, viscous liquids and slurries

None ±5 of full scale

5 to 30 None High

Ultrasonic (Time-of-

travel)

Clean, viscous liquids

None ±1 to ±5 of full scale

5 to 30 None High

Mass (Coriolis)

Clean, dirty viscous liquids; some slurries

Low ±0.4 of rate

None None High

Mass (Thermal)

Clean, dirty Viscous liquids; some slurries

Low ±1 of full scale

None None High

Weir (V-notch)

Clean, dirty liquids

Very low ±2 to ±5 of full scale

None Very Low Medium

Source : Omega


63

REFERENCES:

1. Richard S. Figliola and Donald E. Beasley, “ Theory and Design for

Mechanical Measurements”, Jhon Wiley & Sons, 1991.

2. J. P. Holman and W. J. Gajda, “ Expeimental methods for Engineers “,

McGraw-Hill Book Company, 1978.

3. William C. Dunn, “Fundamental of Industrial Instrumentation and

Process Control”, McGraw-Hill, 2005

4. Roger C. Baker, “Flow Measurement Handbook”, Cambridge University

Press, 2000

5. E.L. Upp, Paul J. LaNass, ”Fluid Flow Measurement, A Practical Guide to

Accurate Flow Measuirement”, Second Edition, Gulf Professional

Publishing,2002

6. OMEGA, “Transactions in Measurement and Control, Flow and Level

Measurement” , Volume 4, WWW.Omega.Com


64

APPENDIX

Orifice Meter

For frictionless and incompressible flow,

( ) ( )

( )( )

( )( ) [ ]

( )

( )

( )

factorapproach velocity41

1F

P2P112FA2m

21IF

P2P1241

A2

Qm

P2P12

41

A2

sm3 P2P12

A1A2

21

A2

2uA2Q

AS

P2P12

A1A2

21

1u2

OR

A1

A22

12

u22p2p1

12 flow ibleincompressfor

flow)ess(frictionl 2

u22

2

P22

u21

1

P1

u2A22u1A11m

β−=

−ρ=

ρ=ρ=ρ

−ρβ−

=

ρ=

ρ−

β−=

ρ−

−

=

=

ρ−

−

=

−

ρ=−

ρ=ρ=ρ

+ρ

=+ρ

ρ=ρ=


65

EXAMS:

Flow Rate Measurement

1- a) Derive an equation to calculate the mass flow rate using a laminar flow element meter . For such meter, show that the mass flow rate is proportional to the differential pressure.

b) Explain the theory of operation of an ultra sonic flow meter. c) Show that the mass flow rate measured by a rotameter is function of the

height of the pop in the glass tube. Can we use a straight glass tube in a rotameter? Why?

2005

Flow Rate Measurement 1- a) Sketch an electromagnetic flow meter and derive its equation used to

calculate the mass flow rate. State the main types and advantages of such meter.

b) What is meant by positive displacement flow meters? Sketch a domestic water flow meter and explain how it works.

2006

Flow Rate Measurement 1- a) Describe a method for calibrating a venture meter for liquid

measurement. Could the calibration data be adapted to measure gas flow? If so, how?

b) Derive an equation to calculate the mass flow rate using a laminar flow element. What are the main advantages and disadvantages of this meter?

c) A rotameter is designed to measure a maximum flow rate of 40 it/min of water. The bob has 25 mm diameter, a total volume of 15 cm3 and a frontal area of 20 cm2 . The bob constructed so that its density is double that of water. The total length of the rotameter tube is 40 cm and the diameter of the tube at inlet is 25 mm. Determine the tube taper for a drag coefficient of 0.08. Assume a linear relation between the annular area of the rotameter, and the bob height, determine the meter constant.

d) What is meant by positive displacement flow meter? Sketch a domestic flow meter and explain how it works?

2009


66

Flow Rate Measurement 1- a) What are the advantages and disadvantages of an Electromagnetic Flow

Meter?

b) For a Laminar Flow Element (LFE) prove that Q = Cd K ∆p Where: Q is the discharge [m3/s] , ∆p is the differential pressure across the meter [Pa] , K is the meter constant and Cd is the discharge coefficient.

c) When a calibrated LFE is used to measure air discharge, it was found K = 11.6 x10-3 . If the LFE is used to measure the discharge of water, what will be the value of K given that: For air: Density ρ = 1.17 [kg/m3] and dynamic viscosity µ = 1.86x10-4 [Poise]

For water: Density ρ = 995.7 [kg/m3] and dynamic viscosity µ = 2.886 [kg/m hr] Note: 1 [Poise] = 1 [gm/cm s]

d) Discuss the construction and theory of operation of one of the following flow

meters: Vortex flow meter or Thermal Mass flow meter.

2010

flow measurement- 2 abril 2011

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