HEADLOSS ESTIMATION. Mekanika Fluida 1 HST

Transcription

1 HEADLOSS ESTIMATION Mekanika Fluida HST

2 Friction Factor : Major losses Laminar low Hagen-Poiseuille Turbulent (Smoot, Transition, Roug) Colebrook Formula Moody diagram Swamee-Jain

3 3 Laminar Flow Friction Factor l D 3 L 3L gd Hagen-Poiseuille 8LQ gd 4 L D g Darcy-Weisbac 3L L gd D g D Re Slope o - on log-log plot

4 4 Turbulent Pipe Flow Head Loss Proportional to te lengt o te pipe Proportional to te o te velocity (almost) wit surace rougness Is a unction o density and viscosity Increases Is o pressure square independent L D g

5 5 Smoot, Transition, Roug Turbulent Flow L D g Hydraulically smoot pipe law (von Karman, 930) Roug pipe law (von Karman, 930) Transition unction or bot smoot and roug pipe laws (Colebrook) Re log.5 3.7D log D.5 log 3.7 Re (used to draw te Moody diagram

6 riction actor 6 Moody Diagram 0. C p D l laminar D E+03 E+04 E+05 E+06 E+07 E+08 Re smoot

7 Swamee-Jain 976 limitations /D < x 0 - Re >3 x 0 3 less tan 3% deviation rom results obtained wit Moody diagram easy to program or computer or calculator use Q D g.78 L D g D L 5/.D log log 3.7D 5.74 Re / LQ 9.4 L Q g g no 0.04

8 8 Swamee-Jain gets an Te callenge tat S-J solved was deriving explicit equations tat are independent o te unknown parameter. 3 potential unknowns (low, ead loss, or diameter): 3 equations or tat can ten be combined wit te Darcy Weisbac equation L D g 8 LQ g D log 3.7D 5.74 Re 0.9

9 9 Colebrook Solution or Q 8 LQ g D 5 D.5 log 3.7 Re 8 LQ 5 g D D.5 4 log 3.7 Re Re 4Q D Re Re 4Q D g D L 5 g D 8 LQ 3 8 D g LQ 5

10 Colebrook Solution or Q log 3.7 LQ g D D g D L 5/ 3.5 log 3.7 L Q g D D g D L 5/ 3 log g L Q D L D g D

11 Swamee D? D / 4 5 /5 Q Q Q Q g g Q g g LQ g D 5 D D Q g 64 Q 8g Q 64 D 8g / Q D Q Q g g Q g / 4 /5 Q 5/ 4 Q Q D 8g g Q g / 4 /5 /5 64 5/ 4 Q Q g Q g /5 / 4 /5 5/ 4 /5 / 4 /5 5/ 4 Q Q 4 4 g Q g /5 / 5 /5

12 Pipe Rougness pipe material pipe rougness (mm) glass, drawn brass, copper commercial steel or wrougt iron aspalted cast iron 0. galvanized iron 0.5 cast iron 0.6 concrete rivet steel corrugated metal 45 PC 0.

13 3 Solution Tecniques ind ead loss given (D, type o pipe, Q) 0.5 Re 4Q D 5.74 log 3.7D Re 0.9 ind low rate given (ead, D, L, type o pipe) 8 LQ 5 g D Q D 5/ g L log.5 L 3.7D g D 3 ind pipe size given (ead, type o pipe,l, Q) D LQ 9.4 L Q g g 0.04

14 4 Exponential Friction Formulas Commonly used in commercial and industrial settings Only applicable over collected Hazen-Williams exponential riction ormula range o data = RLQ m D n C = Hazen-Williams coeicient

15 Head loss: Hazen-Williams Coeicient 5 C Condition 50 PC 40 Extremely smoot, straigt pipes; asbestos cement 30 ery smoot pipes; concrete; new cast iron 0 Wood stave; new welded steel 0 itriied clay; new riveted steel 00 Cast iron ater years o use 95 Riveted steel ater years o use Old pipes in bad condition

16 Hazen-Williams vs Darcy-Weisbac Bot equations are empirical 0.675LQ D C Darcy-Weisbac is dimensionally correct, and. Hazen-Williams can be considered valid only over te range preerred o gatered data. Hazen-Williams can t be extended to oter luids witout urter experimentation. 8 LQ g D 5 SI units

17 7 Minor Losses Most minor losses can not be obtained analytically, so tey must be measured Minor losses are oten expressed as a loss coeicient, K, times te velocity ead. Cp = Hig Re ( geometry, Re) C p g l l C p g l = K g

18 Head Loss due to Sudden Expansion: Conservation o Energy 8 l t p H g z p H g z p l g p p g p p l z = z Wat is p - p?

19 Head Loss due to Sudden Expansion: Conservation o Momentum 9 M M W Fp F p x M x Fp Fp M x x M x F A M x A A A A p A pa x A p p A g ss A Apply in direction o low Neglect surace sear Pressure is applied over all o section. Momentum is transerred over area corresponding to upstream pipe diameter. is velocity upstream. Divide by (A )

20 Energy Head Loss due to Sudden Expansion 0 g p p l g A A p p A A g g l g l g l A A g l A A K Momentum Mass

21 Contraction EGL HGL c K c g Expansion!!! vena contracta losses are reduced wit a gradual contraction

22 Entrance Losses Losses can be reduced by accelerating te low gradually and eliminating te vena contracta K e.0 K e 0.5 reentrant e K e g K e 0.04

23 3 Head Loss in alves Function o valve type and valve position Te complex low pat troug valves oten results in ig ead loss v K v g Wat is te maximum value tat K v can ave? How can K be greater tan?

24 p z H p z g Example cs p g H t 4 l valve 00 m D=40 cm L=000 m Find te discarge, Q. D=0 cm L=500 m cs 00m= + g Use S-J on small pipe l

25 Non-Circular Conduits: Hydraulic Radius Concept A is cross sectional area P is wetted perimeter R is te Hydraulic Radius (Area/Perimeter) Don t conuse wit radius! = 5 L Dg R p D For a pipe = A 4 D P = p D = D= 4 4 R L = 4 R g We can use Moody diagram or Swamee-Jain wit D = 4R!

26 6 GENERAL CONSIDERATION HGL-EGL DRAWING

27 EGL & HGL or a Pipe System Energy equation g p z All terms are in dimension o lengt (ead, or energy per unit weigt) HGL Hydraulic Grade Line L g p z p HGL z EGL Energy Grade Line p EGL z HGL g g EGL=HGL wen =0 (reservoir surace, etc.) EGL slopes in te direction o low 7

28 EGL & HGL or a Pipe System A pump causes an abrupt rise in EGL (and HGL) since energy is introduced ere 8

29 EGL & HGL or a Pipe System A turbine causes an abrupt drop in EGL (and HGL) as energy is taken out Gradual expansion increases turbine eiciency 9

30 EGL & HGL or a Pipe System Wen te low passage canges diameter, te velocity canges so tat te distance between te EGL and HGL canges Wen te pressure becomes 0, te HGL coincides wit te system 30

31 EGL & HGL or a Pipe System Abrupt expansion into reservoir causes a complete loss o kinetic energy tere 3

32 EGL & HGL or a Pipe System Wen HGL alls below te pipe te pressure is below atmosperic pressure 3

33 Example () 33

34 Example () 34

35 Example (3) 35