Flow measurement part II
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The document provides a comprehensive overview of various types of flow measurement devices, including variable head or differential meters such as orifice plates, venturi tubes, and pitot tubes. It discusses the principles of their operation, advantages, disadvantages, and specific applications, highlighting the relationships between flow and differential pressure. Key parameters like accuracy, installation requirements, and operational limits are also examined for different flow measurement methods.
Flow measurement part II
- 1. FLOW MEASUREMENT PART II ER. FARUK BIN POYEN, Asst. Professor DEPT. OF AEIE, UIT, BU, BURDWAN, WB, INDIA faruk.poyen@gmail.com
- 2. Contents: Variable Head or Differential Meter Orifice Plates Venturi Tubes Flow Nozzle Dall Tubes Pitot Tube Annubar Tube Elbow Tap Weir Flume 2
- 3. Variable Head or Differential Meter Working: A restriction in the line of a flowing fluid, introduced by the orifice plate or venturi tube or elbow, produces a differential pressure across the restriction element which is proportional to the flow rate. Head flow meters operate on the principle of placing a restriction in the line to cause a differential pressure head. The differential pressure, which is caused by the head, is measured and converted to a flow measurement. The devices in general, can therefore be termed as “obstruction type” flow meters. 3
- 4. Variable Head or Differential Meter The proportionality is not a linear one but has a square root of relationship in that flow rate is proportional to the square root of the differential pressure. This is derived from Bernoulli’s theorem. Velocity head is defined as the vertical distance through which a liquid would fall to attain a given velocity. Pressure head is the vertical distance through which a column of the flowing liquid would rise in an open-end tube as a result of the static pressure. 𝑉 = 𝐾 2𝑔ℎ 𝜌 𝑄 = 𝐾𝐴 2𝑔ℎ 𝜌 𝑊 = 𝐾𝐴 2𝑔ℎ 𝜌 where 𝐾 = 𝐴1 𝐴2 𝐴1 2−𝐴2 2 2𝑔 Coefficient of discharge: 𝐶 𝑑 = 𝑄 𝑎𝑐𝑡𝑢𝑎𝑙 𝑄 𝑖𝑑𝑒𝑎𝑙 4 V = velocity of flowing fluid Q = volume flow rate W = mass flow rate A = cross – sectional area of pipe through which fluid is flowing h = differential head (pressure) across the restriction element g = acceleration due to gravity ρ = density of the flowing fluid 𝐾 = 𝐶 1− 𝛽4 C = discharge coefficient β = diameter ratio = d (diameter of restriction element)/D (inside diameter of the pipe)
- 5. Variable Head Flow Meters Rate of Discharge: 𝑄 = 𝐴1 𝑉1 = 𝐴2 𝑉2 Applying Bernoulli’s equation (ideal flow assumption) 𝑝1 + 𝜌𝑉1 2 2 = 𝑝2 + 𝜌𝑉2 2 2 The differential pressure head ∆ℎ is given by: 𝑝1 − 𝑝2 𝜌𝑔 = ∆ℎ 𝑄 𝑎𝑐𝑡𝑢𝑎𝑙 is always less than 𝑄𝑖𝑑𝑒𝑎𝑙as there are losses due to friction and eddying motions. 5
- 6. Merits and Demerits – Differential Flow Meter Advantages of Differential Flow meter Relatively low cost for large lines Offers widest application coverage of any type of meter High accuracy (0.25 to 2 %) Easily removable without tripping of the process Highly adaptable Disadvantages & Limitations Relatively higher permanent pressure loss is involved Difficult to use for slurry services Exhibits square root relationship between head and flow rate, rather than linear characteristics, which limits the usable flow range ability to a 3:1 to 5:1 range. Low flow rates are not easily measured Faces difficulty to measure pulsating flow. The position of minimum pressure is located slightly downstream from the restriction at a point where the stream is the narrowest and is called the vena – contracta. Beyond this point, the pressure again rises but does not return to the upstream value resulting in a permanent pressure loss. 6
- 7. Parts of a Differential Flow meter It comprises two parts: Primary Element Secondary Element 7
- 8. Parts of a Differential Flow meter – Primary Elements Primary element causes restriction in the path of flow and produces differential pressure. It comprises i) Orifice plates ii) Venturi tubes iii) Flow nozzle iv) Dall tubes v) Pitot tubes vi) Annubar tubes vii) Elbow taps viii) Weir ix) Flume 8
- 9. Parts of a Differential Flow meter – Secondary Elements Secondary element measures the differential pressure. It comprises manometer bellow meter force balance ring balance. 9
- 10. Orifice The orifice meter when installed in small to moderate sized pipes is probably the cheapest and simplest flow measuring device at present available for metering liquids, gases and vapours. It is not suitable for high viscous liquids or fluids in a pulsating or extremely turbulent condition. When the fluid flows through the orifice, its velocity increases and the diameter of the jet decreases to minimum at a point v, known as the vena contracta. The jet expands until it again occupies the full bore of the pipe. The static pressure profile first shows a gradual decrease over the distance L to M due to friction losses in the pipe. 10
- 11. Orifice From M to P, as light rise occurs due to the resistance of the orifice plate. A sharp drop in the pressure occurs from P to R due to the fluid velocity through the orifice. Finally, there is a partial recovery of pressure from R to S. The net pressure loss due to friction and turbulence across the orifice is, typically, about 65% of the pressure difference measured by d/p diaphragm. The fluid flow is proportional to the square root of the pressure difference. 11
- 12. Orifice Advantages of Orifice - Simple construction. - Inexpensive. - Easily fitted between flanges. - No moving parts. - Large range of sizes and opening ratios. - Suitable for most gases and liquids. - Well understood and proven. - Price does not increase dramatically with size. 12
- 13. Orifice Disadvantages of Orifice - Inaccuracy, typically 1%. - Low rangeability, typically 4:1. - Accuracy is affected by density, pressure and viscosity fluctuations. - Erosion and physical damage to the restriction affects measurement accuracy. - Cause some unrecoverable pressure loss. - Viscosity limits measuring range. - Require straight pipe runs to ensure accuracy is maintained. - Pipeline must be full (typically for liquids). 13
- 14. Orifice Orifice Plate Designs: 1. Concentric – commonly used for general applications (gas, liquid & vapour). 2. Eccentric – recommended for fluids with extraneous matter to a degree that would clog up concentric type. 3. Segmental – recommended for fluids combine with vapour or vapour with fluids. Types of Orifice Plate Entrance 1. Square Edge – applicable for higher pipe Reynolds Number; typical Re 500 to 10,000 2. Quadrant – for lower pipe Reynolds Number; typically ranges from Re 250 to 3300. 3. Conical – for Reynolds Number typically range from Re 25 to 75. 14
- 15. Venturi Tubes Venturi meter is used instead of an orifice plate in process systems where it is important to minimize permanent pressure loss across the restriction device. In venturi, the restricting element is a tapered tube instead of sharp-edge orifice. The tube gives a smoother velocity change which results in a small permanent pressure loss of approximately 10% of the differential pressure measurement. 15
- 16. Venturi Tubes Advantages of Venturi - Less significant pressure drop across restriction. - Less unrecoverable pressure loss. - Requires less straight pipe up and downstream. Disadvantages of Venturi - More expensive. - Bulky - requires large section for installation. 16
- 17. Comparison Orifice and Venturi Meters 1. Orifice reducing element is sharp edged while venturi is tapered tube. 2. Permanent pressure loss of orifice is 65% of measured d/p while venturi is only 10%. 3. Venturi tube is less sensitive to Reynolds Number and gives more accurate measurement when the process flow varies over a wide range. 4. Venturi tube is less affected by dirty fluid which build up deposits at orifice plates and pressure tap connections. 5. Venturi tube meter is more costly compared to orifice plate costly compared to orifice plate and requires greater length of pipeline. 6. Orifice plate is relatively easy to change for new range. 17
- 18. Flow Nozzle Flow nozzle is a restriction consisting of an elliptical contoured inlet and a cylindrical throat section. Pressure taps used to measure the difference in static pressure created by flow nozzle are commonly located one pipe diameter (1D) upstream and ½ pipe diameter (1/2D) downstream from the inlet face of the nozzle. The Flow Nozzle is similar to the venturi but are in the shape of an ellipse. They have a higher flow capacity than orifice plates. Another main difference between the flow nozzle and the venturi is that although they have similar inlet nozzles, the flow nozzle has no exit section. These devices are more cost effective, but as such they provide less accuracy than venturis, and have a higher unrecoverable pressure loss. 18
- 19. Flow Nozzle Flow Nozzles can handle larger solids and be used for higher velocities, greater turbulence and high temperature applications. They are often used with fluid or steam applications containing some suspended solids, and in applications where the product is being discharged from service. 19
- 20. Flow Nozzle Advantages of Flow nozzle - High velocity applications. - Operate in higher turbulence. - Used with fluids containing suspended solids. - More cost effective than venturis. - Physically smaller than the venturi. Disadvantages of Flow nozzle - More expensive than orifice plates. - Higher unrecoverable pressure loss. 20
- 21. Dall Tube Dall tube consists of two conical reducers inserted into the fluid – carrying pipe. It has a shape very similar to venturi without throat. The construction of Dall is much simpler than that of venture which needs complex machinery. It is much shorter in length which makes its insertion into flow line easier. Its perimeter pressure loss is only 5 % of measured pressure differential and thus it is only half that due to a venturi. On the basis of maintenance and operational life, Dall and venturi are similar. 21
- 22. Dall Tube Advantages of Dall - Shorter lay length. - Lower unrecoverable pressure loss. Disadvantages of Dall - More complex to manufacture. - Sensitive to turbulence. - Accuracy based on flow data. 22
- 23. Pitot Tube The pitot tube is a tube with an open end facing the incoming fluid stream. The Pitot tube measures flow based on differential pressure and is primarily used with gas flows. The Pitot tube is a small tube that is directed into the flow stream. This measures the total pressure (dynamic and static combined). A second measurement is required, being of static pressure. The difference between the two measurements gives a value for dynamic pressure. The flow rate, like other devices, is calculated from the square root of the pressure. In calculating the flow rate from the pressure, the calculation is dependent on such factors as tube design and the location of the static tap. The Pitot-static probe incorporates the static holes in the tube system to eliminate this parameter. 23
- 24. Pitot Tube The Pitot tube is also used to determine the velocity profile in a pipe. This is done by measuring points at various distances from the pipe wall to construct a velocity profile. The Pitot tube is the primary device. It has the advantage over orifice meters of practically no pressure drop. Its usefulness is limited to clean gases and liquids as the sensing element is a small orifice. Foreign materials tend to plug the openings in the tube, and the classical Pitot tube senses impact pressure at one point only, thus decreasing accuracy. Assuming a steady, one – dimensional flow of an incompressible, frictionless fluid with no heat loss for free stream velocity and applying Bernoulli’s principle between a point in the free stream and another at the tip of the stagnation tube, we may write 𝑝𝑠𝑡𝑎𝑡 𝜌 + 𝑉2 2 = 𝑝𝑠𝑡𝑎𝑔 𝜌 24
- 25. Pitot Tube 𝑉 = 2(𝑝𝑠𝑡𝑎𝑔 − 𝑝𝑠𝑡𝑎𝑡) 𝜌 ∆𝑝 = 1 2 𝜌𝑉2 →→→→ 𝑉 ∝ ∆𝑝 𝑤ℎ𝑒𝑟𝑒 ∆𝑝 = 𝑝𝑠𝑡𝑎𝑔 − 𝑝𝑠𝑡𝑎𝑡 Pitot tubes develop a very low differential pressure, which can often be difficult to measure with the secondary element. Also the accuracy of the device is dependent on the velocity profile of the fluid. The velocity profile is also affected by turbulence in the flow stream. 25
- 26. Pitot Tube Advantages of Pitot tube - Low cost. - Low permanent pressure loss. - Ease of installation into existing systems. Disadvantages of Pitot tube - Low accuracy. - Low Rangeability. - Requires clean liquid, gas or vapour as holes are easily clogged. 26
- 27. Annubar Tube An annubar is very similar to a pitot tube. The difference is that there is more than one hole into the pressure measuring chambers. The pressure in the high pressure chamber represents an average of the velocity across the pipe. Annubars are more accurate than pitot tubes as they are not as position sensitive to the velocity to the velocity profile of the fluid. 27
- 28. Elbow Tap Elbow-Tap flow meter operates on the principle that when a fluid moves around a curved path, the acceleration of the fluid creates centrifugal force. In operation, the centrifugal force results in a higher pressure on the outside of the elbow than on the inside. Thus, a d/p is produced which is proportional to the square of the flow through the elbow. A pipe elbow can be used as a primary device. Elbow taps have an advantage in that most piping systems have elbows that can be used. In applications where cost is a factor and additional pressure loss from an orifice plate is not permitted, the elbow meter is a viable differential pressure device. If an existing elbow is used then no additional pressure drop occurs and the expense involved is minimal. They can also be produced in-situ from an existing bend, and are typically formed by two tapings drilled at an angle of 45o through the bend. These tapings provide the high and low pressure tapping points respectively. 28
- 29. Elbow Tap Tappings at 22.5° have shown to provide more stable and reliable readings and are less affected by upstream piping. However 45° tapings are more suited to bi-directional flow measurement. Velocity, pressure and elevation above the datum level for pressure taps on the inside and outside surfaces of a 90° elbow can be related like 𝐶 𝑘 𝑣2 2𝑔 = 𝑃0 𝜌𝑔 + 𝑍0 − 𝑃𝑖 𝜌𝑔 − 𝑍𝑖 𝑍𝑖 and 𝑍 𝑜are the lowest and highest points of tapping respectively. The volume flow rate is expressed as 𝑄 = 𝐴𝑣 = 𝐴 𝐶 𝑘 2𝑔( 𝑃𝑜 𝜌𝑔 + 𝑍0 − 𝑃𝑖 𝜌𝑔 − 𝑍𝑖) = 𝐶. 𝐴 2𝑔( 𝑃𝑜 𝜌𝑔 + 𝑍0 − 𝑃𝑖 𝜌𝑔 − 𝑍𝑖) The value of C ranges from 0.56 to 0.88 and A is the area of cross – section of the pipe 29
- 30. Elbow Tap Advantages of Elbow - Simplified installation. - Inexpensive. Disadvantages of Elbow - Low accuracy 30
- 31. Open Channel Meters – Fall under Differential Flow meters The "open channel" refers to any conduit in which liquid flows with a free surface. Included are tunnels, non-pressurized sewers, partially filled pipes, canals, streams, and rivers. Of the many techniques available for monitoring open-channel flows, depth-related methods are the most common. These techniques presume that the instantaneous flow rate may be determined from a measurement of the water depth, or head. Weirs and flumes are the oldest and most widely used primary devices for measuring open-channel flows. 31
- 32. Weir The flow rate over a weir is a function of the weir geometry and of the weir head (the weir head is defined as the vertical distance between the weir crest and the liquid surface in the undisturbed region of the upstream flow). Weirs are variable head, variable area flow meters employed for measuring large volumes of liquids in open channels. The device operates on the principle that if a restriction of specified shape and form is introduced in flow path, a rise in the upstream liquid occurs which is a function of the flow rate through the restriction. Weirs operate on the principle that an obstruction in a channel will cause water to back up, creating a high level (head) behind the barrier. The head is a function of flow velocity, and, therefore, the flow rate through the device. Weirs consist of vertical plates with sharp crests. The top of the plate can be straight or notched. Weirs are classified in accordance with the shape of the notch. The basic types are V-notch, rectangular, and trapezoidal. 32
- 33. Weir Applying Bernoulli’s equation at undisturbed region of upstream flow and at the crest of the weir, we get 𝐻 + 𝑉1 2 2𝑔 = 𝐻 − 𝑦 + 𝑉2 2 2𝑔 Where 𝑉1 and 𝑉2 are the upstream flow and flow at the crest respectively 𝑉2 = 2𝑔(ℎ + 𝑉1 2 2𝑔 ) If 𝑉1 is small compared to 𝑉2, then 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑙𝑎𝑦𝑒𝑟 𝑜𝑓 𝑓𝑙𝑢𝑖𝑑 = 2𝑔𝑦, 𝑦 = depth from the top surface of water level. 33
- 34. Weir 𝐸𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑙 𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 = 2𝑔𝑦𝐿 𝑊 𝑑𝑦 𝐸𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑙 𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 𝑜𝑓 𝑡ℎ𝑖𝑛 𝑙𝑎𝑦𝑒𝑟 = 𝐶 𝑑√2𝑔𝑦 𝐿_𝑊 𝑑𝑦, 𝐶 𝑑 is the coefficient of discharge valuing between 0.57 and 0.64 𝐿 𝑊 is the actual crest length 𝑄 𝑎𝑐𝑡𝑢𝑎𝑙 = 𝐶 𝑑 𝐿 𝑊 2𝑔𝑦 0 𝐻 𝑦𝑑𝑦 = 2 3 𝐶 𝑑 𝐿 𝑊 2𝑔(𝐻) 3 2 For rectangular weir, 𝑄 = 2 3 𝐶 𝑑(𝐿 𝑊−0.2𝐻) 2𝑔(𝐻) 3 2 For triangular weir, 𝑄 = 8 15 𝑡𝑎𝑛 𝜃 2 2𝑔(𝐻) 5 2 34
- 35. Flume Flumes are generally used when head loss must be kept to a minimum, or if the flowing liquid contains large amounts of suspended solids. Flumes are to open channels what venturi tubes are to closed pipes. Popular flumes are the Parshall and Palmer-Bowlus designs. The Parshall flume consists of a converging upstream section, a throat, and a diverging downstream section. Flume walls are vertical and the floor of the throat is inclined downward. Head loss through Parshall flumes is lower than for other types of open-channel flow measuring devices. High flow velocities help make the flume self-cleaning. Flow can be measured accurately under a wide range of conditions. 35
- 36. Flume Palmer-Bowlus flumes have a trapezoidal throat of uniform cross section and a length about equal to the diameter of the pipe in which it is installed. It is comparable to a Parshall flume in accuracy and in ability to pass debris without cleaning. A principal advantage is the comparative ease with which it can be installed in existing circular conduits, because a rectangular approach section is not required. Discharge through weirs and flumes is a function of level, so level measurement techniques must be used with the equipment to determine flow rates. Staff gages and float-operated units are the simplest devices used for this purpose. Various electronic sensing, totalizing, and recording systems are also available. 36
- 37. Flume 37
- 38. References: Chapter 11: Flow Measurement, “Industrial Instrumentation and Control” by S K Singh. Tata McGraw Hill, 3rd Edition. 2009, New Delhi. ISBN-13: 978-0-07-026222-5. Chapter 12: Flow Measurement, “Instrumentation, Measurement and Analysis”. 2nd Edition, B C Nakra, K K Chaudhry, Tata McGraw-Hill, New Delhi, 2005. ISBN: 0-07-048296-9. Chapter 7: Flowmeter, “Fundamentals of Industrial Instrumentation”, 1st Edition, Alok Barua, Wiley India Pvt. Ltd. New Delhi, 2011. ISBN: 978-81-265-2882-0. Chapter 5: Flow Measurement, “Principles of Industrial Instrumentation”, 2nd Edition. D. Patranabis, Tata McGaw-Hill, New Delhi, 2004. ISBN: 0-07-462334-6. 38