Colebrook Equation Solution ComparisonsINPUT

Relative Roughness = 0.0000000 Reynolds Number = 1,000,000

Iterative Solution Check Value Check Value

Formula* using Goal Seek to given against Eq 1equation

1/f^.5 = -2log(e/3.7D + 2.51/(R*f^.5)) 0.0116451 1.000000 1.000000

1/f^.5 = 1.74-2log(2*e/D + 18.7/(R*f^.5)) 0.0116550 1.000000 1.000468

1/f^.5 = 1.14+2log(D/e)-2log[1+9.3/Re*(e/D)*f^.5] 0.0116396 1.000000 0.999743

Using the formula stated as Eq 1f 1/f^.5 -2log(e/3.7D + 2.51/(R*f^.5)) Diff x 1000

0.0116451 9.266784352 9.266784351 0.0000011

Using the formula stated as Eq 2f 1/f^.5 1.74-2log(2*e/D + 18.7/(R*f^.5)) Diff x 1000

0.0116550 9.262820283 9.26282028 0.0000009

Using the formula stated as Eq 3f 1/f^.5 1.14+2log(D/e)-2log[1+9.3/Re*(e/D)*f^.5] Diff x 1000

0.0116396 9.268961839 9.268961838 0.0000009

Colebrook Equation Solution ComparisonsINPUT

Relative Roughness = 0.0001500 Reynolds Number = 1,000,000

Iterative Solution Check User Defined UDF Solution Check

Formula* using Goal Seek Value Function Value1/f^.5 = -2log(e/3.7D + 2.51/(R*f^.5)) 0.0141058 1.000000 #VALUE! =fEq1() #VALUE! #VALUE!

1/f^.5 = 1.74-2log(2*e/D + 18.7/(R*f^.5)) 0.0141073 1.000000 =fEq2() #VALUE! #VALUE!

1/f^.5 = 1.14+2log(D/e)-2log[1+9.3/Re*(e/D)*f^.5] 0.0140955 1.000000 =fEq3() #VALUE! #VALUE!

Using the formula stated as Eq 1f 1/f^.5 -2log(e/3.7D + 2.51/(R*f^.5)) Diff x 1000

0.0141058 8.419792667 8.419792667 0.0000001

Using the formula stated as Eq 2f 1/f^.5 1.74-2log(2*e/D + 18.7/(R*f^.5)) Diff x 1000

0.0141073 8.419328968 8.41932897 0.0000001

Using the formula stated as Eq 3f 1/f^.5 1.14+2log(D/e)-2log[1+9.3/Re*(e/D)*f^.5] Diff x 1000

0.0140955 8.422864022 8.422864021 0.0000001

Colebrook Equation Solution ComparisonsINPUT

Relative Roughness = 0.0000000 Reynolds Number = 64,500

Iterative Solution Check Value % Deviation

Formula* using Goal Seek against Eq 1 to Eq1

1/f^.5 = -2log(e/3.7D + 2.51/(R*f^.5)) 0.0197517 1.000000 ###

1/f^.5 = 1.74-2log(2*e/D + 18.7/(R*f^.5)) 0.0197732 1.000610 0.108697% ###

1/f^.5 = 1.14+2log(D/e)-2log[1+9.3/Re*(e/D)*f^.5] 0.0197399 0.999665 -0.059633% ###

Explicit Equations: Max Error or Limits

Serghide's implementation of Steffenson 0.0197511 0.999983 -0.002978% Smooth Pipe w/ Reynolds# of ~170,000UDF "fSerg" #VALUE! #VALUE! #VALUE!

Zigrang and Sylvester 0.0197293 0.999363 -0.113527% Smooth Pipe w/ Reynolds# of ~64,500% Deviation to Eq 2 = -0.221983%

Swamee and Jain Eq 0.0196191 0.996228 -0.671401% 10^-6 <e/D <10^-2 and 5000 < Reynolds# < 10^8

Altshul-Tsal Eq 0.0198212 1.001973 0.351932% e/D = .05 independent of Reynolds#

Serghide's implementation of SteffensonA= 7.46 B= 7.07 C= 7.12 User Define Func "fSerg"f= 0.0197511 fSerg = #VALUE!

Colebrook Ratio: 1.000017 #VALUE!Error to Goal Seek: -0.002978% #VALUE!

Serghide's Max Error found is in Smooth Pipe at Rey of ~170,000

Zigrang and Sylvester maximum error is in Smooth Pipe at Reynolds of ~64,500

Swamee and Jain has stated limits of 10^-6 <e/D < .01 and 5000 < Reynolds# < 3x10^8

Altshul-Tsal Eqf ' = 0.11(12e/D + 68/Re)^.25 = 0.0198212

0.85*f ' + 0.0028 = 0.0196480Selected f based on 0.018: 0.0198212

Error to fCalc: 0.352%Note: Units for "D" are normally in inches but formula in C56 is modified for consistence with RelRoughness in C3I have not found any stated limits for Altshul-Tsal but large errors are found at high e/D's

Colebrook Equation Solution Comparisons Determine if Input Point is in the Laminar Flow, Critical Zone,

INPUT Transition Zone or Comp Turbulence, Rough Pipes Zone*Relative Roughness = 0.0000000 e/D * R * f^.5 = #VALUE! #VALUE!

Reynolds Number = 100,000 * Terminlogy is from the original Moody Diagram

Iterative Solution Check % Error User Defined UDF Solution Check

Formula* using Goal Seek Value to Eq1 Function Value

1/f^.5 = -2log(e/3.7D + 2.51/(R*f^.5)) 0.0179898 1.000000 =fEq1() #VALUE! #VALUE!

1/f^.5 = 1.74-2log(2*e/D + 18.7/(R*f^.5)) 0.0180085 1.000000 0.104250%

1/f^.5 = 1.14+2log(D/e)-2log[1+9.3/Re*(e/D)*f^.5] 0.0179795 1.000000 -0.057194%

% Error

Special Cases to UDF "fEq1"

Comp Turb Form of Eq1; 1/f^.5 = 2log(3.7/e/D) 0.0022384 0.309920 #VALUE!#VALUE!

Smooth Pipe Case 0.0176342 0.988916 #VALUE!for Reynolds Number < 10^5; f = 0.3164/Reynolds# ^ 0.25 0.0177925

for 10^5 < Reynolds Number < 3x10^6; f = 0.0032 + 0.221/Reynolds# ^ 0.237 0.0176342Deviation between the two Smooth Pipe Cases: 0.897656%