形状阻力公式大全

1、Flow in valves and fittingsResista nee coefficie nt K, valves and fitt ings head loss and flowvelocity | Pipe equivale nt len gth L/DPressure drop or head loss is proportional to the velocity in valves or fittings. For the most engineering practices it can be assumed that pressure drop or head loss

2、due to flow of fluids in turbule nt range through valves and fittings is proportional to square of velocity.To avoid expensive testing of every valves and every fittings that are in stalled on pipeli ne, the experime ntal data are used. For that purpose resista nee coefficie nt K, equivale nt le ngt

3、h L/D and flow coefficient Cv, Kv are used. These values are available from differe nt sources like tablesand diagrams from differe nt authorsand from valves manu facturers as well.Kinetic energy, which is represented as head due to velocity is gen erated from static head and in crease or decrease i

4、n velocity directly is proportional with static head loss or gain. Velocity head is:where is: hL - head loss; v - velocity;gn - accelerationof gravity;The nu mber of velocity heads lost due to resista nee of valves and fittings is:where is: hL - head loss; K - resista neecoefficie nt; v - velocity;g

5、n - accelerati on of gravity;The head loss due to resistance in valves and fittings are always associated with the diameter on which velocity occurs.The resista nce coefficie nt K is con sidered to be con sta nt for anydefined valves or fittings in all flow conditions,as the head lossdue to friction

6、 is minor compared to the head loss due to change in directi on of flow, obstructi ons and sudde n or gradual cha nges in cross secti on and shape of flow.in straight pipe is expressed by the DarcyHeadloss due to frictionequati on:where is: hL - head loss; f - friction factor; L - length; D- interna

7、ldiameter; v - velocity;gn - acceleratio n of gravity;It follows that:where is: K- resistance coefficient; f - friction factor; L- lengt; D - in ternal diameter;The ratio L/D is equivale nt len gth in pipe diameters of straight pipe that will cause the same pressure drop or head loss as the valves o

8、r fittingsunder the sameflow conditions.As the resistancecoefficie nt is K is con sta nt the equivale nt le ngth L/D will vary inv ersely with the cha nge in frictio n factor for differe nt flow con diti ons.For geometrically similar valves and fitt in gs, the resista nee coefficie nt would be con s

9、ta nt. Actually there are always smaller or bigger geometrical non similarity in valves and fittings of differe ntnominal size, so the resista neecoefficie ntis notcon sta nt. The resista nee coefficie nt K for a give n type of valves or fittings, tends to vary with size as does friction factor for

10、straight clean commercial steel pipe at the same flow conditions.Someresista nces in pip ing like sudde n or gradual con tract ionsandenlargements, as well as pipe entrances or exists are geometrically similar. Therefore the resista nee coefficie nt or equivale nt len gth L/D is for these items inde

11、pendent of size.The values for resista nee coefficie ntor equivale nt len gth L/D arealways associated with in ternalpipe diameter where the resista neeis occurri ng.If the resista nee coefficie nt or equivale nt len gth L/D should be used for differe nt internal pipe diameter tha n the diameter for

12、 which existi ng values can be found follow ing relatio nship can be used:where is: K - resista nee coefficie nt;D -in ternal diameter;where subscript a defines K and d with the referenee to internal pipe diameter, and subscript b defines K and d with the referenee to the internal diameter for which

13、 values of K can be found in tables or diagrams.This equation can also be used if the piping system has more thanone size of valves and fitt ings to express the resista nee coefficie nt or equivale nt len gth L/D in terms of one size.Resistance coefficientK calculator for valves and fittingscan beus

14、ed.Resista nee coefficie nt K for in ternaldiameter sudde n and gradual con tracti on and enl argeme ntUsing momentum, continuity and Bernoulli equation the resistance due to sudde n enl argeme nts may be expressed as:and the resista nce factor due to sudde n con tract ion as:where is:K1 - resistanc

15、e coefficient;d1 - internal diameter(smaller);d? - in ternal diameter (larger);Using B as diameter ratio, both equation can be expressed as:B - diameter ratio di/d 2；where is: K - resista nce coefficie nt;In order to express the resistance coefficient in terms of larger pipe diameter, following rela

16、tion should be used:where is:Ki - resista nce coefficie nt based on smaller internaldiameter;K2 - resista nce coefficie nt based on larger internalIf the enlargement is not sudden but gradual, or if angle of gradual enl argeme nt is differe nt from 180, Gibs on coefficie nt Ce ca n be used for diffe

17、re nt an gle of diverge nee as follows:In other words, if an gle of diverge nee is bigger tha n 45, theresista nee coefficie nt is equal to one for sudde n enl argeme nt.Cc can beFor gradual con tract ion the resista nee coefficie nt on the samebasis based on Crane test data, con tracti on coefficie

18、 ntused for differe nt an gles of conv erge nee, as follows:q = l,6sin for0j45for 455 180Using above expressi onsfor enl argeme ntandeon tracti oncoefficie nt, resista nee coefficie nt can be calculated as:For gradual enl argeme nt: = C7jl-,)1=236sin|l-卉;for45=pf9r45130，s，|where is: Ce - coefficie n

19、tof enl argeme nt; Ki - resista neecoefficient based on smaller internal diameter; B - diameter ratio di/d 2；0 - enlargement angle;For gradual eon tract ion:where is:CC - coefficie nt of con tracti on;Ki - resista nee coefficie nt basedon smaller internal diameter;B - diameter ratio di/d 2；0 -enl ar

20、geme nt an gle;For resista neecoefficie ntbased on the large pipe diameterexpressi on:should be used, with above equati ons.where is:Ki - resista nee coefficie nt based on smaller in ternaldiameter;K2 - resista nee coefficie nt based on larger internaldiameter; B - diameter ratiodi/d 2；Equati ons fo

21、r gradual enl argeme nt and con tract ion can be used for resista nee coefficie nt calculatio n for reducedborestraight-through valves like ball valves and gate valves. The total resista nee coefficie nt for this type of ball and gate valves is the summati on of resista nee coefficie nt for gradual

22、eon tract ion and gradual enl argeme nt.You can calculateresista neecoefficie nt using resista neecoefficient K and equivale nt len gth l/d calculator.Flow coefficie nt Cv, pressure drop, eon trol valve flow rateSelect ing the correct valve size for a give n applicati on requires kno wledge of proce

23、ss eon diti ons that the valve will actually see in service. In the industry of eontrol valves it is practice to use flow coefficie nt and flow characteristics.In the UK and in the USA coefficient Cv is used and it is defined as flow rate of water in gpm at 60OF that creates pressure drop of1 psi ac

24、ross the valve. Basic equation for valve sizing for liquid service is:where is: G - flow coefficie nt gpm;q - flow rate gpm; p-pressure drop bar; S- specific gravity (relative density)-;To aid in establishinguniform measurement of liquid flowcoefficients Cv, standardized testing facility by Fluid Co

25、ntrolInstitute (FCI) are used by manufacturers.The effect of viscosityof fluids other than water should be considered when selectingthevalve, as in creased viscosity of fluid is reduc ingthe valvecapacity.Ano ther coefficie ntK/ is used in some coun tries, particularly inEurope and is defi ned as fl

26、ow rate of water in m3/h that creates2 2pressure drop of 1kg/cm across the valve (1 kg/cm is equal to bar).Control valve sizing is based on the calculationof flow coefficientfor given pressure drop and flow rate. Liquid flow capacity of a valve in metric un its can be conv erted toCv as:where is: G

27、- flow coefficient gpm;qm- flow rate l/m;p -3den sity kg/m; p - pressure drop bar;Also, liquid flow capacity of a valve can be con verted toK/ as:where is:KV - flow characteristic m3/h;qh - flow rate m3/h;S-specific gravity (relative den sity) - ; p - pressure dropbar;Above equations are used in flo

28、w coefficientCv, pressure drop andcon trol valve flow rate calculator.Flash ing and cavitati on, vapor pressure at valve vena con tractaFlash ing or cavitatio nin side a valve can have a sig nifica ntin flue nee on valve capacity. Flash ing and cavitati oncan reduce theflow through valve in manyliqu

29、id services. Also, damagecan be made to the valve as well as to the piping system. The effect is represented by the change from liquid to vapor state of fluid, result ing in the velocity in crease dow nstream from the valve.As liquid passes through the restrictio n area in side the valve flow stream

30、 is contracted.The smallest cross section area of stream isjust downstream of the actual physical restriction at a point called ven a con tracta. At that point the velocity is at its maximum and pressure at the minimum.As the fluid exits the valve, away from vena con tracta, velocity decrease and pr

31、essure in crease, so the critical point for flash ing and cavitation is at the point where the pressure is smallest which is in vena con tracta. If pressure at vena con tracta drops bellows the vapor pressure of the fluid, due to in creased velocity at this point, bubbles will form in the flow strea

32、m.If pressure dow nstream of the vena con tracta in crease above the vapor pressure, bubbles will collapse or implode produci ng cavitati on. Cavitati on releases en ergy and produces a no ise. If cavitati on occurs close to solid surfaces, the en ergy released gradually wears the material leaving t

33、he rough surface. Cavitation can also damage the dow nstream pipeli ne, if at that place the pressure rises above the vapor pressure and bubbles collapse.Chocked flow valve pressure drop and cavitatio n in high pressure recovery valveFormation of bubbles in the valve resultingof flashing andcavitati

34、 on effect reduces the flow rate through valve and limits the capacity. This is called chocked flow. Limiting pressure drop in valve is determ ined by experime nt for each valve. Limit ing pressure drop for chocked flow in valve can also be calculatedusing:where is: p allow - maximum allowable press

35、ure drop for chockedflowpsi;Km - valve recovery coefficient from manufacturerliterature - ;p1 - valve inlet absolute pressure psia;pv -vapor absolute pressure of the liquid at inlet temperature psia; rc - critical pressure ratio 0,70 - 0,95;In high recovery valve, cavitationcan occur on pressure dro

36、p belowthat produces chocked flow. Therefore cavitati on in dex is used to determine the chocked flow pressure drop at which cavitation damage will beg in in high recovery valve:where is: Kc - cavitationindex from manufacturer literature -;P1 - valve inlet absolute pressure psia;pv - vapor absolutep

37、ressure of the liquid at inlet temperature psia;pc - pressuredrop that creates cavitati on in high recovery valves psi;This equati on can be used any time outlet pressure is greater tha n the vapor pressure of the liquid.Flow and discharge through Venturi, nozzle and orifice | Dischargecoefficie nt,

38、 pressure and diameter ratioThe rate of flow of any fluid through an orifice or no zzle, may be calculated using follow ing equati on:where is: q - flow rate;Cd - coefficie nt of discharge;A - crosssection area; B - diameter ratio dd 2； gn - acceleration of gravity; hL - head loss;In stead of coeffi

39、cie nt ofdischarge Cd, more convenient is the useof flow coefficie ntC which is represe nted by:where is: C- flow coefficie nt; -diameter ratiod/d 2;Cd - coefficie nt of discharge;BFlow rate through no zzles and orifices are tha n calculated as:where is: q - flow rate; C - flow coefficie nt;A - cros

40、s sect ionarea; p - pressure drop; p - density; gn- acceleration of gravity; hL - head loss;The values of hL and p are measured differential static head or pressure before and after the nozzle or orifice. Values for coefficient of discharge or flow coefficient (C or Cd) can be calculated based on ap

41、plicable sta ndards like ISO 5167 or similar ASME sta ndards.Coefficie nt of discharge for orifice flow can be calculated usingReader-Harris/Gallagher (1998) equation (ISO 5167):G = 0.5961+0.02614 - 0216/十 0.000521+ 0.0188 + 0.0063,W+ro 043+O.0g?-Ifl2i-0.123B n l-o.11-4-0.011(0.75-0.0254 Jwhere is:

42、B - diameter ratiodi/d 2； Rgd - Reyno Ids nu mber based onbigger diameter;d1 - internal diameter (smaller);d? - internaldiameter (larger);Li and L2 are functions on tap type and it is:Li=L2=0 - for corner tapsLi=1； L2= - for D and D/2 tapsLi=L?=di - fordim for 1 tapsCoefficie nt of discharge for Ven

43、 turi tubes can be obta ined based on the type of Venturi tube. There are three types of Venturi tubes and each type has differe nt range of diameters and Reyno Ids nu mber for which coefficie nt of discharge is defi ned as follows:Venturi tubes with as cast convergent section Cd=; Rangefor which co

44、efficie nt of discharge is defi ned:100 mm D 800 mm B 2x10e5 ReD 2x10e 6Cd=; Range forVen turi tubes with a machi ned con verge nt secti on which coefficie nt of discharge is defi ned:50 mm D 250 mm52x10e ReD 2x10eVen turi tubes with a rough-welded sheet-ir on conv erge nt sect ion Cd=;Range for whi

45、ch coefficie nt of discharge is defi ned: 200 mm D 1200 mm52x10e ReD .For compressible flow through orifices expa nsion factor is (ISO5167):where is: 丫 - expansion factor; x - specific heat ratio;B -diameter ratio di/d 2； pi - inlet pressure;P2 - pressure in Venturithroat or after the orifice or no

46、zzle;Above equations are used in Venturi tube flow rate meter and Venturi effect calculator and in orifice plate sizing and flow rate calculator.This equation can be used for gas flow though the orifice and discharging to the atmosphere. For that purpose the pressure differenee equals to the upstrea

47、m gauge pressure. This applies only if absolute atmospheric pressure divided by absolute upstream pressure is bigger than critical pressure ratio for sonic flow con diti ons.Whenthe smoothly convergent nozzle is used compressible fluid can reach the speed of sound at minimum cross sect ion or throat

48、, if upstream pressure is high eno ugh.Whenthe velocity of compressible fluid reaches the speed of sound, maximum flow has bee n reached, and in crease of upstream pressure or decrease of dow nstream pressure will not in crease the flow any more.For short tubes where relationL/D is not bigger than t

49、he flow ofdischarge to the atmosphere can be calculated using above equations, with flow coefficie ntC somewhere betwee n the values for orificeand no zzle.If the entrance to the short tube is well roun ded the n the flow coefficie ntC for no zzles can be used and if the pipe entrance issquare shape

50、d and sharp then flow coefficientCfor orifice is moreappropriate.Flow discharge through valves, fittings and pipe, resistancecoefficie nt KFor discharge of liquids through valves, fitt in gs a nd pipes Darcy formula can be expressed as:= 0 20871where is:q - discharge flow rate l/m in;d - internal pi

51、pe diameter mm;hL - head loss m;K - resistance coefficient -;This equati on can be used for discharge calculati on from pipes, fitt ings and valves whe n resista nce coefficie ntK, static headdifferencehL and internal pipe diameter d is known. The resistancecoefficient is the sum of all resistances

52、in the piping system.For discharge of compressible flow of fluid from a pipe to a larger area or larger cross secti on like in the case of discharge to the atmosphere, a modified Darcy formula can be used:where is:w - discharge mass flow rate kg/s;丫 - expa nsion factor -;d - internal pipe diameter m

53、m; p - pressure drop Pa; p -3density kg/m; K - resistance coefficient -;Gas pressure regulator capacity - flow coefficie nt Cg, Kg |Critical flow rateFor gas pressure regulators that are operating in the range of inlet pressure up to 100 bar following equations for sub-critical and critical flow behavior are used (EN 334):Sub-critical flow:Critical flow:1*：幻亡 A + AJS-仏+ 273)1 2where is:3Q- gas flow rate