Flow Measurement

M. Shahini

To Be Discussed Introduction Important Principles of Fluid Flow in Pipes Bernoulli’s Equation The Orifice Plate Venturi Tube Nozzle Variable Area Flowmeters Measuring Principles of Variable Area Flowmeters Internal Flow Analysis

Introduction Vast usage Both the accuracy and capability of many flowmeters are

poor in comparison to those instruments used for measurement of other common process variables such as pressure and temperature

Common types of differential pressure flowmeter are used; that is, the orifice plate, Venturi tube, and nozzle.

Bernoulli as the base of DPFs A differential pressure flowmeter consists of two basic

elements: an obstruction to cause a pressure drop in the flow (a differential producer) and a method of measuring the pressure drop across this obstruction (a differential pressure transducer).

Advantages & Disadvantages No need for calibration Simple, has no moving parts, and so, reliable.

Their limited range Permanent pressure drop Their sensitivity to installation effects (can be

minimized using straight lengths of pipe before and after the flowmeter)

Conclusion: when no accuracy is required or there is no applicable limitations, can be used for years come

Important Principles of Fluid Flow in Pipes Laminar versus Turbulent flow

Re<2000 :laminar Re>4000 :Turbulent 2000<Re<4000 :transition

Bernoulli’s Equation

•frictionless •incompressible

Flow Rate Measurement

•Incompressible

•Flat Velocity

The Orifice Plate

Correction Factors C :the discharge coefficient diameter ratio Reynolds number pipe roughness the sharpness of the leading edge of the orifice the points at which the differential pressure

across the plate are measured

:expansibility factor is used to account for the compressibility of the

fluid being monitored.

Venturi Tube

the oldest type of differential pressure flowmeter

Properties flow through a Venturi tube is closer to that

predicted in theory C is much nearer unity, being typically 0.95 permanent pressure loss caused by the Venturi

tube is lower less sensitive to erosion than the orifice plate suitable for use with dirty gases or liquids less sensitive to upstream disturbances

its size and cost

Nozzle

Properties because of its curved inlet, has a

discharge coefficient close to unity. cheaper than the Venturi tube. has no sharp edges to erode and cause

changes in calibration well suited for use with dirty and abrasive

fluids. commonly used for high-velocity, high-

temperature applications

Performance and ApplicationsAlthough the orifice plate is the cheapest, the cost of the fitting needed to mount it in the pipeline, particularly if on-line removal is required, can be significant.

Effective Factors:

the required performance, the properties of the fluid to be metered, the installation requirements, the environment in which the instrument is to be used, and, of course, cost.

Coriolis flowmeters

Coriolis flowmeters

Advantages & Disadvantages Higher accuracy than most flowmeters Can be used in a wide range of liquid flow

conditions   Capable of measuring hot and cold fluid

flow   Low pressure drop Suitable for bi-directional flow

•High initial set up cost

•Clogging may occur and difficult to clean

•Larger in over-all size compared to other flowmeters  

Variable Area Flowmeters meters in which the minimum cross-

sectional area available to the flow through the meter varies with the flow rate.

1. rotameter and the movable vane meter: used in pipe flows

2. weir or flume used in open-channel flows. movable vane is often used simply as a

flow indicator rather than as a meter.

Rotameter depending on the bob

shape and density, the tube shape and the fluid density and viscosity, the flow rate is linearly proportional to the height of the bob in the tube

Rotameter

the flow rate is determined by a conversion factor depending on the tube dimensions, the mass of the bob, the pressure and temperature, and the properties of the fluid.

Bob

In larger rotameters where the additional friction is acceptable, the bob can be allowed to slide up and down a rod on the tube axis to prevent any sideways motion

Characteristics Simple and strong construction High reliability Low pressure drop Applicable to a wide variety of gases and liquids Flow range typically 0.04 L h–1 to 150 m3 h–1 for water Flow range typically 0.5 L h–1 to 3000 m3 h–1 for air 10:1 flow range for given bob-tube combination Uncertainty 0.4% to 4% of maximum flow Insensitivity to nonuniformity in the inflow (no upstream

straight piping needed) Typical maximum temperature 400°C Typical maximum pressure 4 MPa (40 bar) Low investment cost Low installation cost

Movable Vane Meter The resistance

provided by the vane depends on the vane position and hence on the flow rate or Reynolds number

a recalibration is necessary when the fluid is changed

Movable Vane Meter

Weir measurement

of the difference in height h of the water surface over an obstruction across the channel and the surface sufficiently far upstream.

Weir If the width of the weir is less than that of

the upstream channel

Flume method for flow metering with relatively

low pressure loss.

Flume The flow velocity in the narrow portion of the

channel is increased and the water level sinks accordingly. Most of the head of water is recovered in the diffusing section of the weir. The water levels upstream and in the throat of the weir can be determined by simple floats and recorded on a chart by pens driven mechanically from the floats.

The flume must be used in streams with sediment transport to avoid the accumulation of deposits that would occur at the approach to a weir.

Characteristics of Weir & Flume Simple measurement of the water level Simple maintenance Reliable measurement of large flow rates

at low stream velocity Limited measurement accuracy (at best

about 2%) High installation costs, particularly for

flumes

Measuring Principles of Variable Area Flowmeters Rotameter

Flow Rate Analysis the buoyancy force drag force weight of the bob

Flow Rate Analysisvolume flow rate:

Or

m: open area ratio

D: tube diameter at the height of the bob

For laminar flow:Replacing Fd gives:

where the parameter is defined in terms of a constant characteristic of the shape of the bob, K:

For turbulent flow:Replacing Fd gives:

Conclusion: With either laminar or turbulent flow flow rate is proportional to m.

Flow rate correlation If the cross-sectional area of the tube is made to

increase linearly with length, i.e.,

since the cone angle of the tube is small

the flow rate is directly proportional to the height h of the bob.

Similarity Analysis Ruppel and Umpfenbach proposed the

introduction of characteristic dimensionless quantities, to permit the use of experimentally determined flow coefficients in flowmeter analysis. Lutz extended these ideas by showing that the transfer of flow coefficients from one flowmeter to another is possible if geometrical similarity exists.

Ruppel Number The basic scaling parameter for flow is the

Reynolds number, defined as:

where UIN is the velocity at the rotameter inlet

it has been found to be practical for rotameters to use an alternative characteristic number, the Ruppel number

Mass of the bob

Ru & Re Relationship

For turbulent flow

Turbulent:

Laminar:

Rotameter flow coefficient The advantage of the Ruppel number is its

independence of the flow rate

Laminar flow

Rotameter flow coefficient

Turbulent flow

Measuring Principles of Variable Area Flowmeters

Flow Rate Analysis for Weirs

Should be studied by the students

Rotameter: Internal Flow Analysis Computation of Internal Flow

Improvement of rotameter design could be assisted by detailed knowledge of the internal flow field, which is characterized by steep velocity gradients and regions of separated flow.

CFD Applications The application of computational fluid

dynamics to the flow in a rotameter involves the finite volume solution of the conservation equations for mass and momentum

Discretized Governing Equations

Boundary Conditions Along the walls:

At the input boundary, the initial profile for the u-velocity is taken from the experiment. At the outlet boundary, zero gradient is assumed for all dependent variables.

Along the axis of symmetry:

Computed Results

Re=220