General Background:
The Virtual Moody Diagram is an on-line version of the traditional Moody diagram used for pipe flow analysis and design. In addition to eliminating the graphical interpolations neccessary when using the graphical method, the present calculator makes the process of computing the Reynolds number and roughness factor ratio transparent to the user. Furthermore, the estimates of the friction factor are formally more accurate than those obtained from the physical diagram. However, the experimental data on which the Moody diagram is based is fairly crude. A second source of error is that the roughness factors for various pipes are likely to be even less accurate than the original turbulence data. A more complete discussion of these errors can be found in White's Fluid Mechanics ( 4th edition).

The friction factor ( f ) is the usual nondimensional measure of the friction loss and is related to the pressure drop ( Dp ) over a distance L as follows:

Dp = - r( ¨öv2 )( L/D ) f,

where r is the fluid density, v is the fluid velocity, and D is the pipe diameter.

With the qualifier given below, the critical Reynolds number, i.e., the Reynolds number at which the flow switches from laminar to turbulent, is 2300. It should be noted that some texts on engineering fluid mechanics use a slightly different number. However, the value of 2300 appears to be the most popular number and is certainly the one I have used for many decades now.

Remarks on the Data:
All data for the physical properties of the fluids and the roughness estimates for different pipes were taken from White's Fluid Mechanics ( 4th edition ).

Numerical Issues:
The graphical version of the Moody diagram is based on Colebrook's formula which can be written as F( f, Re, e/D ) = 0, where e is the roughness factor. Colebrook's formula cannot be inverted analytically for f as a function of Re. When the graphical form of the Moody diagram is used, this implicit function is inverted graphically. In the present (on-line) form, we use a Newton solver to invert the implicit function numerically. The friction factor f is determined to within 0.0001. Because the typical values of f are of order 10-2, the results should be reasonably accurate. If smooth pipes ( e = 0 ) at large Reynolds numbers are considered, the tolerance may need to be decreased.

In the laminar regime ( Re < 2300 ), the (exact) analytical formula f = 64/Re was used. In the transition regime ( 2300 < Re < 4000 ), White ( Fluid Mechanics, 4th edition ) points out that the data is unreliable. To give a crude interpolation in the transition regime, we employ a simple linear interpolation between the laminar cutoff Re = 2300 and f = 64/2300 and

Re = 4000, f = fT ( 4000, e/D ),

where fT is the friction factor determined by Colebrook's formula.