The Moody Diagram Calculator

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agraph
setGraphType(LogaritmicLogaritmic);
setViewport(750,550,70); 
setGraphArea(2,10,-3,-1);
setGridandTicks(1,1,1,1);
setLabelsandTitle(BottomLeft,"Reynolds number","Friction coefficient","The Moody Diagram");
initPicture();
drawGraphArea();
fill="none";
strokewidth="2";
stroke="blue";
plot("SwameeJain(pow(10,-8),1,x)",log(2320),10);
plot("SwameeJain(pow(10,-7),1,x)",log(2320),10);
plot("SwameeJain(pow(10,-6),1,x)",log(2320),10);
plot("SwameeJain(pow(10,-5),1,x)",log(2320),10);
plot("SwameeJain(pow(10,-4),1,x)",log(2320),10);
plot("SwameeJain(pow(10,-3),1,x)",log(2320),10);
plot("SwameeJain(5*pow(10,-3),1,x)",log(2320),10);
stroke="green";
plot("SwameeJain(pow(10,-2),1,x)",log(2320),10);
plot("SwameeJain(2*pow(10,-2),1,x)",log(2320),10);
plot("SwameeJain(3*pow(10,-2),1,x)",log(2320),10);
plot("SwameeJain(4*pow(10,-2),1,x)",log(2320),10);
plot("SwameeJain(5*pow(10,-2),1,x)",log(2320),10);
stroke="red";
plot("64/x",2,log(2320));
plot("SwameeJain(0.0,1,x)",log(2320),10);
text([10.05,log(SwameeJain(pow(10,-8),1,pow(10,10)))],"`epsilon=10^-8`","middleright","espsilon_-8");
text([10.05,log(SwameeJain(pow(10,-7),1,pow(10,10)))],"`epsilon=10^-7`","middleright","espsilon_-7");
text([10.05,log(SwameeJain(pow(10,-6),1,pow(10,10)))],"`epsilon=10^-6`","middleright","espsilon_-6");
text([10.05,log(SwameeJain(pow(10,-5),1,pow(10,10)))],"`epsilon=10^-5`","middleright","espsilon_-5");
text([10.05,log(SwameeJain(pow(10,-4),1,pow(10,10)))],"`epsilon=10^-4`","middleright","espsilon_-4");
text([10.05,log(SwameeJain(pow(10,-3),1,pow(10,10)))],"`epsilon=10^-3`","middleright","espsilon_-3");
text([10.05,log(SwameeJain(5*pow(10,-3),1,pow(10,10)))],"`5*10^-3`","middleright","espsilon_-53");
text([10.05,log(SwameeJain(pow(10,-2),1,pow(10,10)))],"`epsilon=10^-2`","middleright","espsilon_-2");
text([10.05,log(SwameeJain(5*pow(10,-2),1,pow(10,10)))],"`5*10^-2`","middleright","espsilon_-52");
text([10.05,log(SwameeJain(pow(10,-1),1,pow(10,10)))],"`epsilon=10^-1`","middleright","espsilon_-1");
text([2.1,-2.5],"Laminar","rightmiddle","laminar");
text([6,-2.5],"Turbulent","rightmiddle","turbulent");
createGradient("5%","#EEEEEE","95%","#AAAAAA","MyGradient");
setGradient("MyGradient",0.3);
axesBorder("2","black");
createGradient("5%","#DDDDDD","95%","#AAAAAA","MyGradient2");
setGradient("MyGradient2",0.3);
viewportBorder("3","black"); 
endagraph
Pointer coordinates: (x,y) Click coordinates: (x,y)
Input:  
Roughness d: m
Hydraulic diameter Dh: m
Velocity v: m/sec
Viscosity n: m2/sec
Output:  
Reynolds number: -
Friction coefficient l: -
   

Press the left mouse button and move over the Moody Diagram, see the transition between laminar and turbulent flow.
Digitised points:
 

Equations involved in the calculations

Hydraulic diameter `Dhr` and `Rhr` for river or channel flow or TSHD flow,

or `Dhp` and `Rhp` for pipe flow

Remark: In civil engineering the hydraulic radius `R_h` is `1/4` of the hydraulic diameter `D_h` because this way it matches the depth `H` of a river or channel, while in mechanical engineering it is `1/2` the hydraulic diameter `D_h`, matching the radius `R` of a pipe.

Relative roughness `epsilon=d/D_h`

Reynolds: `Reynolds` for calculating the horizontal axis

Swamee Jain: `SwameeJain` for calculating the friction coefficient `lambda`

T

[`dgr`C] 

 Viscosity

[m2/sec]
10 1.308 x 10−6
20 1.003 x 10−6
30 7.978 x 10−7
40 6.531 x 10−7
50 5.471 x 10−7
60 4.668 x 10−7
70 4.044 x 10−7
80 3.550 x 10−7
90 3.150 x 10−7
100 2.822 x 10−7
 
The original ASCIIMathML and ASCIIsvg scripts have been developed by by Peter Jipsen, Chapman University (jipsen@chapman.edu)
LaTeXMathML has been developed by Douglas Woodall (and exteded by Jeff Knisley), based on ASCIIMathML
The version of ASCIIMathML used here, is a modified and extended version, developed by Dr.ir. S.A. Miedema
Other sources: An ASCIIsvg manual by Robert Fant.  An ASCIIsvg manual by Peter Jipsen. An ASCIIMathML manual by James Gray.

Plugins and fonts required (depending on your browser): MIT MathML font packages, MathPlayer, Adobe SVGviewer
Look at: http://www.w3.org/TR/SVG11/ for detailed information about SVG.
Look at: http://www.w3.org/Math/ for detailed information about MathML

Copyright © Dr.ir. S.A. Miedema, Delft University of Technology, Faculty of Mechanical Engineering, Marine Technology & Materials Science
Department of Marine & Transport Technology, The Chair of Dredging Engineering