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2 Contents Introduction Bernoulli's Equation Pressure Differential Head Meters Venturi Flow meter

3 Introduction Why measure Flow?? Flow Types of Flow Velocity Profile

4 Why Measure Flow Billing Purposes To determine total quantity of fluid for billing purposes Monitor the Process Flow meters used to ensure process is operating satisfactorily

5 Why Measure Flow Improve the Process Heat & Material balance calculations Monitor a Safety Parameter Flow meters used to ensure process and equipment safety

6 Flow Liquid or Gas in Motion

7 Types of Flow Volumetric Flow Rate Volume of fluid which passes through a given surface per unit time Mass Flow Rate Mass of a substance which passes through a given surface per unit time

8 Velocity Profile Laminar Flow Regime Molecules move straight down pipe

9 Velocity Profile Turbulent Flow Regime Molecules migrate throughout pipe

10 Velocity Profile Transitional Flow Regime Molecules exhibit both turbulent and laminar behavior

11 Velocity Profile Many flow meters require a good velocity profile to operate accurately A distorted velocity profile can introduce significant errors into the measurement of most flow meters

12 Bernoulli s Equation Dynamic Pressure + Static Pressure + Weight 1/2ρV² + P + z = Constant

13 Examples

14 Pressure Differential Head Meters Orifice Primary Element Flow Nozzle PDH Venturi Secondary Element ΔP Transmitter

15 Venturi Tube To avoid pressure loss, venturi tube is used curved, stream lined section, long and gradually expanding down stream section 60% more flow than orifice Fluid can flow with much higher velocity without turbulence

16 Flow Pattern Flow through Venturi follows four paths Key 1 Conical divergent E 2 Cylindrical throat C 3 Conical convergent B 4 Entrance cylinder A 5 Connecting planes a 7 f 15 b Flow direction Figure - 1

17 Types of Venturi Tubes Basis of different types are different methods of manufacturing of internal surface of the entrance cone and the profile at intersection of cone and the throat. Three types of venturi tubes are 1. Cast 2. Machined 3. Rough welded sheet iron

18 Venturi- As Cast Convergent Section Fabricated by casting in a sand mould, or by other methods leave a finish on the convergent section surface similar to that produced by sand casting. The throat is machined and the junctions b/w cylinders & cones are rounded Use for pipe dia b/w 100 & 800 mm with beta ratio b/w 0.3 and 0.75 inclusive

19 Venturi - Machined Convergent Section Fabricated as previous type but with machined convergent section as the throat and the entrance cylinder. The junctions b/w the cylinders & cones may or may not be rounded Use for pipe dia b/w 50 & 250 mm with beta ratio b/w 0.4 and 0.75 inclusive

20 Venturi - Rough-Welded Sheet-Iron Convergent Section Fabricated by welding. For larger size it may not be machined but in smaller sizes the throat is machined Use for pipe dia b/w 200 & 1200 mm with beta ratio b/w 0.4 and 0.70 inclusive

21 Flow Measurement ε

22 Venturi Tube sizing Several standards are available for sizing of venturi Tubes like ISO, ASME, DIN and UNI This presentation shall cover ISO standard i.e. Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full Note: Figure 1 to be used as reference

23 Entrance Cylinder, A The minimum cylinder length, measured from the plane containing the intersection of the cone frustum B with the cylinder A, may vary for each type of venturi tube However, it is recommended to choose the length equal to dia D No diameter along the entrance cylinder shall differ by more than 0.4% from the value of the mean diameter

24 Conical Convergent, B The angle / overall length of convergent section B shall be 21 ±1 and 2.7(D-d) respectively Section B blended with section A by a curvature of radius R 1 which depends on venturi type

25 Cylindrical Throat, C The length of throat C shall be equal to d±0.03d whatever the type of venturi tube Throat C connected to section B and to the section E by radii of curvature R 2 and R 3 respectively and vary for each type of venturi No diameter along the throat shall differ by more than 0.1% from the value of the mean diameter

26 Conical Divergent, E Section E will be conical having angle, φ b/w 7 and 15. Recommended chosen angle is in b/w of 7 and 8. Its smallest diameter shall not be less than the throat diameter

27 General Venturi called truncated when outlet dia of section E is less than the D and not truncated when outlet dia is equal to D The portion E may be truncated by 35% of its length without significantly modifying pressure loss of device or its discharge co-efficient The roughness criterion, Ra shall always be less than 10-4 d

28 Characteristics of as cast The minimum section A length shall be equal to smaller of the following two values: D or 0.25D mm R 1 shall be 1.375D±0.275D R 2 shall be 3.625D ±0.125d Length of section C shall not be less than dl3. Furthermore, length of cylindrical part b/w end of R 2 & plane of pressure tapping, as well as length of cylindrical part b/w plane of throat pressure tapping & beginning of the joining curvature R 3, shall no be less than dl6 R 3 shall lie b/w 5d & 15d. However, value closer to 10d is recommended

29 Characteristics of machined The minimum section A length shall be equal to D R 1 / R 2 & R 3 shall be less than 0.25D / 0.25d and 0.25d respectively. Preferably equal to zero Length of cylindrical throat b/w end of R 2 & the plane of throat pressure tapping shall no be less than 0.25d Length of cylindrical throat b/w throat pressure tapping and beginning of R 3 shall no be less than 0.3d

30 Characteristics of Rough Welded Sheet- Iron The minimum section A length shall be equal to D Being the welded one there will be no joining curvatures b/w cylinder A and section B and so on Roughness criterion shall be 5x10-4 D

31 Pressure Tappings The u/s & throat tapping's shall be made under piezometer rings or a triple-t arrangements Tapping dia shall be in b/w of 4-10 mm if d 33.3 mm Tapping dia shall be in b/w of 0.1d-0.13d for throat and 0.1d-0.1D for upstream if d < 33.3 mm Tapping shall be cylindrical over a length at least 2.5 times the internal tapping dia, measured from inner pipeline wall

32 Pressure Tapings Spacing The spacing b/w upstream pressure tapping on entrance cylinder & plane of intersection b/w entrance cylinder A & convergent section B shall be, for: As cast 0.5D±0.25D for 100 mm < D < 150 mm Machined and rough welded sheet-iron: 0.5D±0.05D For all types of venturi, spacing b/w plane containing the axes of the points of break-through of throat pressure tapping & intersection of section B and C shall be 0.5d±0.02d

33 Discharge Co-efficients C Simultaneous use of extreme values for D, β, Re D shall be avoided which in turn increase the uncertainties as the effects of Re D, RalD and β on C are not yet sufficiently known

34 C of As cast As cast can only be used when 100 mm D 800 mm 0.3 β x10 5 Re D 2 x 10 6 Under these conditions value of C is 0.984

35 C of Machined Machined can only be used when 50 mm D 250 mm 0.4 β x10 5 Re D 1 x 10 6 Under these conditions value of C is 0.995

36 C of Rough Welded Sheet-Iron rough welded sheet iron Machined can only be used when 200 mm D 1200 mm 0.4 β x10 5 Re D 2 x 10 6 Under these conditions value of C is 0.985

37 Uncertainty of C The relative uncertainty of C is given below: For As cast is 0.7% For machined" is 1.0% For rough welded iron-sheet is 1.5%

38 Expansibility [Expansion] Factor, ε ε ε results are only known for air, steam and natural gas but formula could be used for which isentropic exponent is known Equation is applicable only for the values of D, β, Re D defined earlier and if p 2 /p

39 Table of Expansibility [Expansion] Factor

40 Pressure Loss Pressure loss caused by venturi tube is determined prior & subsequent installation of venturi in a pipe through which there is given flow Tapping locations with & without venturi in a pipe, Figure 2 to be followed Where Δp & Δp are difference in pressure prior to and a er venturi installation respectively

41 Pressure Loss

42 Straight lengths for Installations

43 Symbols & Subscripts

44 Symbols & Subscripts

45 For more details & information, please contact us. thepetrostreet Team

Head Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids

Head Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids Dr. J. M. Meyers Dr. D. G. Fletcher Dr. Y. Dubief 1. Introduction Last lab you investigated flow loss in a pipe due to the roughness