9. fm 9 flow measurement co 4 adam

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9. fm 9 flow measurement co 4 adam

  1. 1. FLUID MECHANICS – 1 Semester 1 2011 - 2012 Week – 9 FLOW MEASUREMENT CO4 Compiled and modified by Sharma, Adam
  2. 2. Chapters to cover 1. Properties of Fluid 2. Fluid Statics 3. Fluid in Motion 4. Friction in Piping System 5. Flow Measurement 2
  3. 3. Chapters to cover 1. Properties of Fluid 2. Fluid Statics 3. Fluid in Motion 4. Friction in Piping System 5. Flow Measurement 3
  4. 4. Flow Measurement• Explain type of flow measuring equipments• Calculate fluid flow through – Pitot tube, – Orifice meter, – Venturi meter – Nozzle meter. 4
  5. 5. Types of Flowmeters F lo w m e t e r sP re ssu re M e c h a n ic a l T h e rm a l O th e r Types Types Types Types O r ific e s T u r b in e H o t-w ir e V o rte x flo w m e te r flo w m e te r flo w m e te r flo w m e te r V e n tu ri T u b e R e c ip o c a te in g R e s is tiv e -b r id g e E le c tr o m a g n e tic flo w m e te r P is to n flo w m e te r flo w m e te r flo w m e te r F lo w T u b e O v a l-G e a r O th e rs U ltr a s o n ic flo w m e te r flo w m e te r F lo w m e te r F lo w N o z z le s O th e rs O th e rs flo w m e te r P ilo t T u b e s flo w m e te r O th e r s 5
  6. 6. Pitot Tube 1 P2 2 P1,V1 Stagnation Point V2=0 P1 is a Static pressure: It is measured by a device (static tube) that causes no velocity change to the flow. This is usually accomplished by drilling a small hole normal to a wall along which the fluid is flowing. P2 is a Stagnation pressure: It is the pressure measured by an 6 open-ended tube facing the flow direction. Such a device is
  7. 7. Pitot TubeThe basic pitot tube simply consists of a tube pointing directly into thefluid flow. The fluid is at rest or stagnant inside the tube. A pressure iscreated in the stagnant tube that is greater than the pressure of thefluid stream. The magnitude of this increased pressure is related tothe velocity of the moving fluid. The pressure of the moving fluid iscalled the static pressure. (a) A Pitot probe measures stagnation pressure at the nose of the probe, while (b) a Pitot-static probe measures both stagnation pressure and static pressure, from which the flow 7 speed is calculated.
  8. 8. Pitot-Static TubeThe static and Pitot tube are often combined into the one-piece Pitot-statictube. Examples Used in aircraft nose 8
  9. 9. Pitot-Static TubeStagnationpressure tap Static pressure tap 2 V1 = 0 V 1 z1 = z2 9
  10. 10. Obstruction Flowmeters:Orifice, Venturi, andNozzle MetersFlowmeters based on this principleare called obstruction flowmetersand are widely used to measure flowrates of gases and liquids. Flow through a constriction in a pipe. 10
  11. 11. The losses can be accounted for by incorporating a correction factor called thedischarge coefficient Cd whose value (which is less than 1) is determinedexperimentally.The value of Cd depends on both b and the Reynolds number, andcharts and curve-fit correlations for Cd are available for various types ofobstruction meters.For flows with high Reynolds numbers (Re > 30,000), the value of 11Cd can be taken to be 0.96 for flow nozzles and 0.61 for orifices.
  12. 12. Common types of obstruction meters. 12
  13. 13. Pipe Flowrate Meters Example 1: Flow through an orifice meter The flow rate of water at 20°C (ρ = 998 kg/m3 and μ = 1.002x10-3 kg/m · s) through a 50-cm-diameter pipe is measured with an orifice meter with a 30-cm-diameter opening to be 250 L/s. Determine the pressure difference indicated by the orifice meter and the head loss. The discharge coefficient of the orifice meter is Cd = 0.61. 13
  14. 14. Pipe Flowrate Meters Assumptions 1 The flow is steady and incompressible. 2 The discharge coefficient of the orifice meter is Cd = 0.61. Properties The density and dynamic viscosity of water are given to be ρ = 998 kg/m3 and μ = 1.002x10-4 kg/ms, respectively. Analysis The diameter ratio and the throat area of the orifice are β = d D = 30 50 = 0.60 A0 = πd 2 4 = π (0.3) 2 4 = 0.07069 m 2 For a pressure drop of across the orifice plate, the flow rate is expressed as ∆P = P − P2 1 2( P − P2 ) Q = AoCd 1 ( ρ 1− β 4 ) 14
  15. 15. Pipe Flowrate Meters Substituting, 2∆P (0.25m /s = 0.07069 m 3 2 )( 0.61) ( )( 998 kg/m 3 1 − 0.60 4 )This gives a pressure dropof, ∆p = 14600 kg.m/s = 14.6 kPa 2 We know, ∆P = ρgh This is the head loss then, ∆P 14600 h= = = 1.49 m ρg (998)(9.81)
  16. 16. Pipe Flowrate Meters Venturi Meter This device consists of a conical contraction, a short cylindrical throat and a conical expansion. The fluid is accelerated by being passed through the converging cone. The velocity at the “throat” is assumed to be constant and an average velocity is used. The venturi tube is a reliable flow measuring device that causes little pressure drop. It is used widely particularly for large liquid and gas flows. P1 P2 16
  17. 17. Pipe Flowrate Meters Venturi Meter 17
  18. 18. Pipe Flowrate Meters Venturi Meter 2( p1 − p2 ) Qactual = CVQideal = C V A T ρ (1 − β 4 ) AT = π d 2 / 4 Area of the throat CV = CV (β = d / D, Re = ρ VD / µ ) 18
  19. 19. Pipe Flowrate MetersVenturi Meter A Venturi meter equipped with a differential pressure gage is used to measure the flow rate of water at 15°C (ρ = 999.1 kg/m3) through a 5-cm-diameter horizontal pipe. The diameter of the Venturi neck is 3 cm, and the measured pressure drop is 5 kPa. Taking the discharge coefficient to be 0.98, determine the volume flow rate of water and the average velocity through the pipe. 19
  20. 20. Pipe Flowrate Meters Assumptions 1 The flow is steady and incompressible. 2 The discharge coefficient of the venturi meter is Cd = 0.98. Properties The density and dynamic viscosity of water are given to be ρ = 999.1 kg/m3 and. Analysis The diameter ratio and the throat area of the orifice areβ = d D = 3 5 = 0.60A0 = πd 2 4 = π (0.03) 2 4 = 0.0007069 m 2 For a pressure drop of across the orifice plate, the flow rate is expressed as ∆P = 5 kPa 2( P − P2 ) Q = AoCd 1 ( ρ 1− β 4 ) 20
  21. 21. Pipe Flowrate Meters Substituting, (Q m /s = 7.069 ×10 m 3 -4 2 )( 0.98) ( 2(5000) )( 999.1 kg/m 3 1 − 0.60 4 )This gives a flow rate of,Q = 0.00235 m /s = 2.35 liters/s 3 Average velocity in pipe is, Q Q 0.00235 m 3 /s V= = = = 1.20 m/s A ρD / 4 π (0.05 m ) / 4 2 2 21
  22. 22. Pipe Flowrate Meters Nozzle Meter 2( p1 − p2 )Qactual = C n Qideal = C n A n ρ(1 − β4 ) A n = πd 2 / 4 Area of the hole C n = C n (β = d / D, Re = ρVD / µ ) Nozzle meter discharge coefficient 22
  23. 23. Pipe Flowrate MetersNozzle Meter A flow nozzle equipped with a differential pressure gage is used to measure the flow rate of water at 10°C (ρ= 999.7 kg/m3 and μ = 1.307 x 10-3 kg/m · s) through a 3-cm-diameter horizontal pipe. The nozzle exit diameter is 1.5 cm, and the measured pressure drop is 3 kPa. The nozzle has a discharge coefficient of Cd= 0.96.Determine the volume flow rate of water, the average velocity through the pipe, and the head loss. 23
  24. 24. It’s the same!!!!!!!!!!!All equations 2( p1 − p2 ) ORIFICE Qactual = CoQideal = Co A o ρ (1 − β 4 ) 2( p1 − p2 ) VENTURIQactual = C VQideal = CV A T ρ (1 − β 4 ) 2( p1 − p 2 ) Qactual = C n Qideal = C n A n NOZZLE ρ(1 − β4 ) 24
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  28. 28. Pitot-Static Tube An object is traveling at an elevation of 10,000 m in standard atmosphere. The pressure difference indicated by the Pitot-static probe attached to the roof is 2000 Pa. What is the velocity of the object? (The density of air at this altitude is 0.414 kg/m3) Pitot-static 28
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