1. Flow Measurement
M. Shahini

2. 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

3. 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).

4. 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

5. Important Principles of Fluid Flow in Pipes
Laminar versus Turbulent flow
Re<2000 :laminar
Re>4000 :Turbulent
2000<Re<4000 :transition

6. Bernoulli’s Equation
frictionless
incompressible

7. Flow Rate Measurement
Incompressible
Flat Velocity

8. The Orifice Plate

9. 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.

10. Venturi Tube
the oldest type of differential pressure flowmeter

11. 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

12. Nozzle

13. 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

14. Performance and Applications
Although 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.

15. Coriolis flowmeters

16. Coriolis flowmeters

17. 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  

18. Variable Area Flowmeters
meters in which the minimum cross-sectional area available to the flow through the meter varies with the flow rate.
rotameter and the movable vane meter: used in pipe flows
weir or flume used in open-channel flows.
movable vane is often used simply as a flow indicator rather than as a meter.

19. 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

20. 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.

21. 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

22. 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

23. 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

24. Movable Vane Meter

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

26. Weir
If the width of the weir is less than that of the upstream channel

27. Flume
method for flow metering with relatively low pressure loss.

28. 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.

29. 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

30. Measuring Principles of Variable Area Flowmeters
Rotameter

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

32. Flow Rate Analysis volume flow rate: Or m: open area ratio
D: tube diameter at the height of the bob

33. For laminar flow: For turbulent flow: Replacing Fd gives:
where the parameter  is defined in terms of a constant characteristic of the shape of the bob, K:
Conclusion: With either laminar or turbulent flow flow rate is proportional to m.

34. 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.

35. 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.

36. 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

37. Ru & Re Relationship
For turbulent flow
Turbulent:
Laminar:

38. Rotameter flow coefficient
The advantage of the Ruppel number is its independence of the flow rate
Laminar flow

39. Rotameter flow coefficient
Turbulent flow

40. Measuring Principles of Variable Area Flowmeters
Flow Rate Analysis for Weirs
Should be studied by the students

41. 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.

42. 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

43. Discretized Governing Equations

44. Boundary Conditions Along the walls: Along the axis of symmetry:
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.

45. Computed Results
Re=220