Darcy friction factor formulae

In fluid dynamics, the Darcy friction factor formulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used in the Darcy–Weisbach equation, for the description of friction losses in pipe flow as well as open-channel flow. f = 0.0055 [ 1 + ( 2 × 10 4 ⋅ ε D + 10 6 R e ) 1 3 ] {displaystyle f=0.0055left} ε / D = 0 − 0.01 {displaystyle varepsilon /D=0-0.01} f = 0.094 ( ε D ) 0.225 + 0.53 ( ε D ) + 88 ( ε D ) 0.44 ⋅ R e − Ψ {displaystyle f=0.094left({frac {varepsilon }{D}} ight)^{0.225}+0.53left({frac {varepsilon }{D}} ight)+88left({frac {varepsilon }{D}} ight)^{0.44}cdot {mathrm {Re} }^{-{Psi }}} ε / D = 0.00001 − 0.04 {displaystyle varepsilon /D=0.00001-0.04} 1 f = − 2 log ⁡ ( ε / D 3.715 + 15 R e ) {displaystyle {frac {1}{sqrt {f}}}=-2log left({frac {varepsilon /D}{3.715}}+{frac {15}{mathrm {Re} }} ight)} f = 0.25 [ log ⁡ ( ε / D 3.7 + 5.74 R e 0.9 ) ] 2 {displaystyle f={frac {0.25}{left^{2}}}} ε / D = 0.000001 − 0.05 {displaystyle varepsilon /D=0.000001-0.05} 1 f = − 2 log ⁡ ( ε / D 3.71 + ( 7 R e ) 0.9 ) {displaystyle {frac {1}{sqrt {f}}}=-2log left({frac {varepsilon /D}{3.71}}+left({frac {7}{mathrm {Re} }} ight)^{0.9} ight)} 1 f = − 2 log ⁡ ( ε / D 3.715 + ( 6.943 R e ) 0.9 ) {displaystyle {frac {1}{sqrt {f}}}=-2log left({frac {varepsilon /D}{3.715}}+left({frac {6.943}{mathrm {Re} }} ight)^{0.9} ight)} f / 8 = [ ( 8 R e ) 12 + 1 ( Θ 1 + Θ 2 ) 1.5 ] 1 12 {displaystyle f/8=left^{frac {1}{12}}} 1 f = − 2 log ⁡ [ ε / D 3.7065 − 5.0452 R e log ⁡ ( 1 2.8257 ( ε D ) 1.1098 + 5.8506 R e 0.8981 ) ] {displaystyle {frac {1}{sqrt {f}}}=-2log left} 1 f = 1.8 log ⁡ [ R e 0.135 R e ( ε / D ) + 6.5 ] {displaystyle {frac {1}{sqrt {f}}}=1.8log left} 1 f = − 2 log ⁡ ( ε / D 3.7 + 4.518 log ⁡ ( R e 7 ) R e ( 1 + R e 0.52 29 ( ε / D ) 0.7 ) ) {displaystyle {frac {1}{sqrt {f}}}=-2log left({frac {varepsilon /D}{3.7}}+{frac {4.518log left({frac {mathrm {Re} }{7}} ight)}{mathrm {Re} left(1+{frac {mathrm {Re} ^{0.52}}{29}}(varepsilon /D)^{0.7} ight)}} ight)} 1 f = − 2 log ⁡ [ ε / D 3.7 − 5.02 R e log ⁡ ( ε / D 3.7 − 5.02 R e log ⁡ ( ε / D 3.7 + 13 R e ) ) ] {displaystyle {frac {1}{sqrt {f}}}=-2log left} 1 f = − 1.8 log ⁡ [ ( ε / D 3.7 ) 1.11 + 6.9 R e ] {displaystyle {frac {1}{sqrt {f}}}=-1.8log left} 1 f = Ψ 1 − ( Ψ 2 − Ψ 1 ) 2 Ψ 3 − 2 Ψ 2 + Ψ 1 {displaystyle {frac {1}{sqrt {f}}}=Psi _{1}-{frac {(Psi _{2}-Psi _{1})^{2}}{Psi _{3}-2Psi _{2}+Psi _{1}}}} if A ≥ 0.018 {displaystyle Ageq 0.018} then f = A {displaystyle f=A} and if A < 0.018 {displaystyle A<0.018} then f = 0.0028 + 0.85 A {displaystyle f=0.0028+0.85A} 1 f = − 2 log ⁡ ( ε / D 3.7 + 95 R e 0.983 − 96.82 R e ) {displaystyle {frac {1}{sqrt {f}}}=-2log left({frac {varepsilon /D}{3.7}}+{frac {95}{mathrm {Re} ^{0.983}}}-{frac {96.82}{mathrm {Re} }} ight)} ε / D = 0 − 0.05 {displaystyle varepsilon /D=0-0.05} 1 f = − 2 log ⁡ { ε / D 3.7065 − 5.0272 R e log ⁡ [ ε / D 3.827 − 4.657 R e log ⁡ ( ( ε / D 7.7918 ) 0.9924 + ( 5.3326 208.815 + R e ) 0.9345 ) ] } {displaystyle {frac {1}{sqrt {f}}}=-2log leftlbrace {frac {varepsilon /D}{3.7065}}-{frac {5.0272}{mathrm {Re} }}log left ight brace } 1 f = 0.8686 ln ⁡ [ 0.4587 R e ( S − 0.31 ) S ( S + 1 ) ] {displaystyle {frac {1}{sqrt {f}}}=0.8686ln left} 1 f = 0.8686 ln ⁡ [ 0.4587 R e ( S − 0.31 ) S ( S + 0.9633 ) ] {displaystyle {frac {1}{sqrt {f}}}=0.8686ln left} 1 f = α − α + 2 log ⁡ ( B R e ) 1 + 2.18 B {displaystyle {frac {1}{sqrt {f}}}=alpha -{frac {alpha +2log left({frac {mathrm {B} }{mathrm {Re} }} ight)}{1+{frac {2.18}{mathrm {B} }}}}} where f = 6.4 ( ln ⁡ ( R e ) − ln ⁡ ( 1 + .01 R e ε D ( 1 + 10 ε D ) ) ) 2.4 {displaystyle f={frac {6.4}{(ln(mathrm {Re} )-ln(1+.01mathrm {Re} {frac {varepsilon }{D}}(1+10{sqrt {frac {varepsilon }{D}}})))^{2.4}}}} f = 0.2479 − 0.0000947 ( 7 − log ⁡ R e ) 4 ( log ⁡ ( ε / D 3.615 + 7.366 R e 0.9142 ) ) 2 {displaystyle f={frac {0.2479-0.0000947(7-log mathrm {Re} )^{4}}{(log left({frac {varepsilon /D}{3.615}}+{frac {7.366}{mathrm {Re} ^{0.9142}}} ight))^{2}}}} f = 1.613 [ ln ⁡ ( 0.234 ε 1.1007 − 60.525 R e 1.1105 + 56.291 R e 1.0712 ) ] − 2 {displaystyle f=1.613left^{-2}} f = [ − 2 log ⁡ ( 2.18 β R e + ε / D 3.71 ) ] − 2 {displaystyle f=left^{-2}} , β = ln ⁡ R e 1.816 ln ⁡ ( 1.1 R e ln ⁡ ( 1 + 1.1 R e ) ) {displaystyle eta =ln {frac {Re}{1.816ln left({frac {1.1Re}{ln left(1+1.1Re ight)}} ight)}}} f = 1.325474505 log e ⁡ ( A − 0.8686068432 B log e ⁡ ( A − 0.8784893582 B log e ⁡ ( A + ( 1.665368035 B ) 0.8373492157 ) ) ) − 2 {displaystyle f=1.325474505log _{e}left(A-0.8686068432Blog _{e}left(A-0.8784893582Blog _{e}left(A+(1.665368035B)^{0.8373492157} ight) ight) ight)^{-2}} where In fluid dynamics, the Darcy friction factor formulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used in the Darcy–Weisbach equation, for the description of friction losses in pipe flow as well as open-channel flow. The Darcy friction factor is also known as the Darcy–Weisbach friction factor, resistance coefficient or simply friction factor; by definition it is four times larger than the Fanning friction factor.