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在管路中的阻力計算(上) - hvac-net.org.tw

1 ( ) ! 1. (turbulent flow) Smooth turbulent ( laminar flow) Re < 2000 Transitional turbulent (transition flow) 2000< Re <4000 Rough turbulent ( turbulent flow ) Re > 4000 Re =64/f ( Reynold s Number) f friction factor ( ) Re = GDvD = / D m v m/s Kg/m3 Ns/m2 , Kg/ms G Kg / sm2 Re = GDvD =113= KgsmmmmKg 2 Re 2. (a) Darcy Weisbach Equation ( laminar flow) (full flow) 1Kg/cm2 (duct) (b) Colebrook White Equation (turbulent flow) (water flow pipeline).

6 j T = f 1] Re f 9.35 di 1.14 −2log10[+ ε 英制單位! = f 1] Re f 1.255 3.7di −4log10[+ e 公制單位! [ !f!值在下表中可以查知。

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Transcription of 在管路中的阻力計算(上) - hvac-net.org.tw

1 1 ( ) ! 1. (turbulent flow) Smooth turbulent ( laminar flow) Re < 2000 Transitional turbulent (transition flow) 2000< Re <4000 Rough turbulent ( turbulent flow ) Re > 4000 Re =64/f ( Reynold s Number) f friction factor ( ) Re = GDvD = / D m v m/s Kg/m3 Ns/m2 , Kg/ms G Kg / sm2 Re = GDvD =113= KgsmmmmKg 2 Re 2. (a) Darcy Weisbach Equation ( laminar flow) (full flow) 1Kg/cm2 (duct) (b) Colebrook White Equation (turbulent flow) (water flow pipeline).

2 ( compressed air or gas pipeline).. (c) Hazen Williams Equation ( transient flow) ( transitional turbulent flow) 4 C 25 C ( ) 3. Manning Equation Equation 3 (4 C 25 C) Hazen-Williams Equation Hazen-Williams Equation [ 1 ] f = [ C100 ] f / 100 Q gpm di in C [ 2 ] f = C -1085 di Q f mm / m Q m 3 / s di m C [ 3 ] Hazen-Williams Equation ё V = k C R S V m/s ,ft/s K C Hazen-Williams ( roughness coefficient ) R ( hydraulic radius ) m , ft S m/m, ft/ft [ 4 ] Hazen Williams Equation ё (elevation) P h h ( conservation of mass to fluid flow)

3 = M 1 A1V1 = 2A2V2 (conservation of energy to fluid flow) Bernoulli s Equation 4 Z1 + P1 / + V12 /2g = Z2 + P2 / + V22 /2g 1905 Hazen William ( ) V k C V k C Z1 + P1 / + V12 /2g Z2 + P2 / + V22 /2g f = [ C100 ] f = . C . f psi / ft Q gpm di in C [ 5 ] Hazen Williams Equation C т !Ib{fo! !Xjmmjbnt!Frvbujpo!! D !BCT!!!!!!!! !271! 21 BCT !271! 31 BCT !271! 41 BCT !271! 51 BCT !271!QWD!0!DQWD! !261! 21 QWD0 DQWD !241! 31 QWD0 DQWD !221!QF0QQ! !! !251! !251! ) *!251! ) *!241! )HJQ*!231! )DJQ*!231! 21 )HJQ*!221! 31 )HJQ*!:1! 41 )HJQ*!81! 21 )DJQ*!218! 31 )DJQ*!:6! 41 )DJQ*!91! 51 )DJQ*!76! !221! !91! !71! !}

4 51!*C Hazen-Williams ё Б ЪMoody diagram Darcy Weisbach ё 5 * ABS C AS ABS ABS A( ) B( ) ABS C Weisbach Equation [ 1 ] V = k C R S V ft / sec k R ft S ft / ft V = C R S S = h / L R= d / 4 h = Reynolds number h = f1 [dL] gV22 h f1 L d v g Darcy Weisbach Equation hf = f gVdiL22 .. hf = 4 f gVdiL22 .. White Equation (Reynolds number) Re Darcy Weisbach Equation f = 16 / Re ft e mm 6 =f1] [ + !=f1] [log410+ e ! !f! ! ! !! !! !! !!!! ! !!!!!f! !BCT!!!!!!!! !!1/6!!!! !1/1126! 21 BCT !!1/6!!!! !1/1126! 31 BCT !!1/6!!!! !1/1126! 41 BCT !!1/6!!!! !1/1126! 51 BCT !!1/6!!!

5 ! !1/1126!QWD!0!DQWD! !!1/7!!!! !1/1129! 21 QWD0 DQWD ! !1/9!!!! !1/1137! 31 QWD0 DQWD ! !2/1!!!! !1/1143!QF0QQ! !! !!1/7!!!! !1/1132! !!1/63!!! !1/1127! ) *!!6/1!!!! !1/126! ) *!!6/:!!!! !1/129! )HJQ*!!6/1!!!! !1/26! )DJQ*!!27!!!!! !1/6! 21 )HJQ*!!37!!!!! !1/9! 31 )HJQ*!!!6:!!!! !2/9! 41 )HJQ*!!!96!!!! !3/7! 21 )DJQ*!!!4:!!!! !2/3! 31 )DJQ*!!!6:!!!! !2/9! 41 )DJQ*!!!83!!!! !3/3! 51 )DJQ*!!!93!!!! !3/6! !!!3:!!!! !1/:! !!!4:!!!! !2/3! !!225!!!! !4/6! !!275!!!! !6/1! ft e mm ABS C=160 GIP C=120 Hazen Williams Equation f = C 7 f 160 = f120 C=160 C=120 C=160 C=120 40% 15% 30% Darcy Equation Colebrook Equation Colebrook Equation 1944 Moody Colebrook Equation f Moody Moody f f = [ 1 + ( 20000 Dk + Re106 ) 1/3] Re 4000< Re<10000000 Dk > Darcy Weisbach Equation (Darcy Weisbach Equation Darcy Equation) hf = 8 hf = !

6 F Colebrook Moody Darcy Weisbach Equation Darcy Equation Colebrook Moody f hf ( equivalent pipe length ) (Minor head loss) = KL V2 / 2g KL V L = KL Q di L L Darcy Equation hf = = KL2gv2 L = KL fD KL = f DL L KL f Hazen Williams Equation Moody Colebrook-White Equation DL !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!DL! ! 400 Y- 160 Б 10 75% 35 9 50% 150 25% 900 10 60 90 30 45 16 90 50 KL KL KL Б 10 90 Б

7 2 90 Б 90 1/4 90 1/2 45 3/4 17 45 ё Ш 2 ё Ш 180 ё ё ( ) V (continuity equation) Q = A V V=k 2DQ V m/s , ft/s Q l/min , gal/min D mm , in K.

8 (minor losses) = KL V2 / 2gKL 10 ( ) !V KL V k 2DQ g [ 1 ] Darcy Weisbach Equation hf = f gVdiL22 .. hf = 4 f gVdiL22 .. [ 2 ] Hazen William Equation f = [ C100 ] f = C -1085 . di . Q [ 3 ] Colebrook White Equation =f1] [ + .. =f1] [log410+ 11 [ 1 ] Manning s Equation V = 2/13/2 SRnk V m/s ,ft/s K , n R m , ft S m/m , ft/ft [ 2 ] Chezy s and Kutter s Equation V = C RS V m/s ,ft/s C R m , ft S m/m , ft/ft C Standard Units RnSnSC = Units RnSnSC = C n Manning R m , ft S m/m , ft/ft S = L H - H21 L H1 H2 H1 H1 !

9 H2 H2 12 flow direction Pipe L H1 H2 elevation elevation H1 H2 [ 1 ] R=PwA circularR44/2 DDD== !R m , ft A m2 , ft2 Pw (wetted perimeter) m , ft D m , ft [ 2 ] 13 ( Reynolds number ) vVR4Re= Re ( Reynolds number ) , V m/s , ft/s R m , ft m2 /s , ft2 /s [ 3 ] ё Hazen Williams ! , :Ra( ) Rymax( ) Rtm ( ) , : [ 1 ] Ra : L , L( : L ) , x , y , y = f(x) , 14 m , , LdxxfRa)( = hi , Ra : ( ) LhiRa = LxhhhhRan = )(321 Ra , , , , Ra , , Ra [ 2 ] Rymax : L , , , , Rymax m , s Rymax L , , Rt [ 3 ] Rtm : 15 Rtm.

10 L , Rz m z :4 Ra Rymax Rtm [ 4 ] (Ra) (Rymax) т (Ra) (Rymax) [ 5 ] 1 2Е д д Я !!!!!!!!!!!! ! ! -!nn! !! ! ! ! ! ! ! ! !1/12 1/16!1 !1/ 4!1/ 3 1/4!1/ 6 !1/96 ! !! ! ! ! ! ! !! ! !1 !1/1126 1/1132!1/ 12 1/14!1/ 36 2/36!1/ 56 7/1! 16 р ! !!1/ 44!1/14 1/9![ 6 ] /d т Т Т Т д 17 (Pipe-roughness chart after Moody) 18 Farshad (Farshad s new roughness chart for commonly used pipes) Farshad (conservation of mass ) (conservation of energy) (energy equation) (head and pressure) 3% %2 Hazen William Equation * ( transitional turbulent flow) * *4 C 25 C * 19 ( ).