FLOW MEASUREMENT

Chapter 7

7.1 INTRODUCTION

The accuracy of a fluid-flow measurement is directly related to profit.

Flow rate measurement devices require accurate pressure and temperature measurement in order to calculate the output of the instrument.

Flow rate is expressed in

Volume units, e.g. cm3/s

Mass units , e.g. gram/sec

7.2 POSITIVE-DISPLACEMENT METHODS

A mechanically displacement components in the meter in order for any fluid flow to occur

For high-accuracy under steady-flow conditions

They are in certain forms,

1) Nutating disk meter

2) Rotary-vane flowmeter

3)Lobed-impeller flowmeter

Nutating-disk meter

Work on the nutating-disk principle Water enters the left side of the meter and strikes the disk, which

is eccentrically mounted. In order for the fluid o move through the meter the disk must wooble or nutate about the vertical axis.

Both the top and bottom of the disk remain contact with the mounting chamber.

A readout mechanism, count the number of rotation to indicate the volumetric flow rate

Rotary Vane Flowmeters

As fluid enters the meter, vanes are moved causing the rotor to turn. The vanes are spring loaded and able to slide freely in the rotor body as it turns, When the fluid enters the inlet port, the vanes extend against the housing wall toenclose the measuring chamber, they retract at the outlet to discharge the fluid into the system. Each complete revolution of the rotor moves several fixed volumes of fluid through the meter from inlet to outlet.

Lobed Impeller and Oval Gear Flowmeters

Two lobed impellers (rotors) are mounted on parallel shafts and are geared-synchronized to keep them correctly positioned in relation to each other. These lobes rotate in opposite directions, so as fluid enters the meter and causes the impellers to rotate, a measuring chamber is formed.

The oval gear flowmeter is a variation of the lobed impeller flowmeter. The lobed impellers are replaced by a pair of meshed oval gears.

Example 7.1

7.3 Flow Obstruction Methods

Apply the head loss or pressure drop measurement as an indication of the flow rate

The one-dimensional flow system, the continuity equation is

Employ the Bernoulli equation that describes the

relationship between pressure and velocity of a flow.

where,

Sloving both equation, give the pressure drop

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cc g

up

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up

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Volumetric flow rate,

Discharge coefficient ,

Discharge coefficient is not constant, depend on Reynolds number and the channel geometry

Finally, volume flow rate for incompressible flow

ideal

actuald

Q

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212

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Obstruction flow meters

Three typical obstruction meters

1. Orifice low cost but high permanent pressure drop

2. Flow nozzle- high permanent pressure drop

3. Venturi - High accuracy and small pressure drop

7.6 Flow Measurement by Drag Effects

The flow enters the bottom of the tapered vertical tube and causes the bob or float to move upward. The bob will rise to a point in the tube such that the drag forces are just balanced by the weight and buoyancy forces.

Turbine Meter

The turbine wheel rotates as fluid passes a permanent magnet attached to the wheel which also rotates with the wheel

A reluctance pick up/motion sensor is attached to the top meter to detect pulse for each revolution.

Total pulse is an indication of flow.

The flow coefficient K for turbine meter is Q= f/K where f is pulse frequency. Flow coefficient is dependent of flow rate and kinematic viscosity n of fluid

Turbine flow meter

The turbine flow meter (better described as an axial turbine) translates the mechanical action of the turbine rotating in the liquid flow around an axis into a user-readable rate of flow (gpm, lpm, etc.). In the turbine-wheel body a permanent magnet is enclosed so that it rotates with the wheel. A reluctance pickup attached to the top of the meter detects a pulse for each revolution of the turbine wheel.

Turbine flow meter

The volumetric flow is proportional to the number of wheel revolutions, the total pulse output may be taken as an indication of total flow

Q= f / K

K: flow coefficient (dependent on flow rate and kinematic viscosity of the fluid)

f : pulse frequency

Turbine flow meter

Turbine flow meters are used for the measurement of natural gas and liquid flow.The flow accurately within 0.5 % over a rather wide range of flow rates.

VORTEX-SHEDDING FLOWMETER

When a bluff body is placed in a flow stream, vortices are shed alternately from the back side. The frequency of vortex shedding is directly proportional to the liquid velocity.

The piezoelectric sensor mounted inside the vortex shedder detects the vortices.

The fluid parameter which governs the operation of the vortex-shedding meter is the Strouhal number S,

S=fs d /ufs : shedding frequency u: velocityd: diameter of characteristicdimension of the bluff body

Ultrasonic Flowmeter.

The Doppler effect is used to measure flow in a pipe, one transducer transmits an ultrasonic beam of ~0.5 MHz into the flow stream.

Liquid flowing through the pipe must contain sonically reflective materials such as solid particles or entrained air bubbles.

Ultrasonic Flowmeter.

The movement of these materials alters the frequency of the beam reflected onto a second, receiving transducer.

The frequency shift is linearly proportional to the rate of flow of materials in the pipe and therefore can be used to develop an analog or digital signal proportional to flow rate

LAMINAR FLOWMETER

Channel or tube where Reynolds number is less than about 2000

Volumetric flow rate,

When Red =(um d)/

LAMINAR FLOWMETER

7.7 Hot-Wire and Hot Film Anemometer

To study rapidly varying flow conditions.

Also known as thermal anemometer

Measures a fluid velocity by noting the heat convectedaway by the fluid. The core of the anemometer is an exposed hot wire either heated up by a constant current or maintained at a constant temperature (refer to the schematic below). In either case, the heat lost to fluid convection is a function of the fluid velocity.

Hot-Wire and Hot Film Anemometer

Thermal Mass Flowmeters

A precision tube is constructed with upstream and downstream externally wound resistance temperature detectors.

Between the sensors is an electric heater.

The temperature difference T1 T2 is directly proportional to the mass flow of the gas

May be detected with

an appropriate bridge

circuit

Thermal Mass Flowmeters

The rate of heat absorbed by a flow stream is directly proportional to its mass flow. As molecules of a moving gas come into contact with a heat source, they absorb heat and thereby cool the source. At increased flow rates, more molecules come into contact with the heat source, absorbing even more heat. The amount of heat dissipated from the heat source in this manner is proportional to the number of molecules of a particular gas (its mass), the thermal characteristics of the gas, and its flow characteristics

Thermal Mass Flowmeters

7.8 Magnetic flowmeters

The fluid represents a conductor moving in the field

Also known as electromagnetic flow meter or induction flow meter, obtain the flow velocity by measuring the changes of induced voltage of the conductive fluid passing across a controlled magnetic field.

E: magnetic flux density

U: velocity of the conductor,cm/s

L:length of the conductor,cm

VoltBLuE 810

A typical magnetic flow meter places electric coils around (inline model) / near (insertion model) the pipe of the flow to be measured and sets up a pair of electrodes across the pipe wall (inline model) or at the tip of the flowmeter (insertion model). If the targeted fluid is electricallyconductive,

i.e., a conductor, its passing through the pipe is equivalent to a conductor cutting across the magnetic field. This induces changes in voltage reading between the electrodes. The higher the flow speed, the higher the voltage.

Magnetic flowmeters

7.9 Flow-Visualization Methods

Basic optical effect - angular deflection of the light ray is proportional to the density in the flow. The deflection of the ray is a measure of the average density gradient integrated over the x coordinate. Useful for indicating density variations in two dimensions.

Liquid-flow visualization technique add a dye to the liquidhydrogen-bubble method - electrolyze the water to produce very small hydrogen bubbles.

Flow-Visualization Methods

7.10 The Shadowgraph

Direct viewing the flow phenomena. Useful for viewing turbulent flow region but no to evaluate local densities.

7.11 The Schlieren

A resultant variation in illumination on the screen, is known as schlieren effect.

Schlieren flow visualization is based on the deflection of light by a refractive index gradient. The index gradient is directly related to flow density gradient. The deflected light is compared to undeflected light at a viewing screen

Schlieren photography is similar to the shadowgraph technique and relies on the the fact that light rays are bent whenever they encounter changes in density of a fluid. Schlieren systems are used to visualize the flow away from the surface of an object

The refractive index or index of refraction of a substance is a measure of the speedof light in that substance. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium

Schematic of schlieren flow visualization

The contrast on the screen is directly proportional to the density gradient in the flow

7.12 The Interferometer

To obtain a direct measurement of density variation in test section. The appearance of fringes on the screen may be directly related to changes in the density in the flow field within the test section.

7.13 The Laser Doppler Anemometer (LDA)

To measure precisely mean fluid flow velocity in steady laminar flow and high frequency turbulence intensity in turbulent flow. It use a Doppler shift in frequency that is directly proportional to the flow velocity.

7.15 Pressure Probes

To measure the local static and stagnation pressures.

Pressure different

Therefore,

2

02

1 upp

)(2 0

ppu

Example 7.9

1 inH2O is approximately equal to 249 Pa at 0 C