Friction Correlations
The friction in the Flow Simulator element can be calculated by the given equation, where:
If Re_{Dh} < Re_{Turb}, laminar friction calculations take place, otherwise, the turbulent friction calculation routine is used.
Nomenclature  Subscripts 

f: friction  F: fanning 
Re: Reynolds number  D: darcy 
FMULT: friction multiplier  turb: turbulent flow 
ε: sand grain roughness  lam: laminar flow 
A: Cross sectional area  Abuaf: Abuaf friction relation 
L_{+}: Inlet station + 1/9 of 2^{nd} station  Smooth: smooth surface 
XMU: dynamic viscosity  Rough: rough surface 
W: mass flow rate  SJ: SwameeJain approximation 
X: station length  Dh: hydraulic diameter 
L: equivalent diameter 
Laminar Friction
Calculates the friction coefficient for laminar flow in shaped ducts based on the references Yunus A. Cengel, 2006 and Bruce Munson, 2005.
For a Tube Element, Laminar Friction Inlets effects can be accounted. Friction coefficient for hydrodynamically developing flow with “Muzychka Yovanovich Laminar Inlet Effects” can be calculated as:
The friction coefficient for combining developing flow and fully developed flow can be calculated as:
Darcy type friction is calculated as
Fanning type friction is calculated as:
Turbulent Friction
Calculates the turbulent friction for smooth or rough walls.
 Abuaf Friction Relation
 The Abuaf friction relation should generally be used for smooth walled tubes.
(8) In Flow Simulator, you have the option to use the Abuaf friction relation together with wall roughness. The following adjustment equation is used:
(9)  SwameeJain Approximation of the ColebrookWhite Equation (Moody Diagram)

(10) The Darcy and Fanning type frictions are calculated as:(11)  Userspecified Friction Factor

(12)
Roughness
ε=5.863∗R_{a,}  R_{a}=Average Absolute Roughness 
ε=3.100∗R_{rms,}  R_{rms}=Root Mean Square Roughness 
ε=0.978∗R_{zd,}  R_{zd}=Peak to Valley Roughness 
NonCircular Shapes in Flow Simulator Tubes
The friction factor and heat transfer coefficient (HTC) correlations were developed for circular pipes. The traditional method to use these correlations on noncircular shapes is to calculate a hydraulic diameter based on the shape area and perimeter.
The errors associated with this method can be +/40% for laminar flow but less for turbulent flow, +/15% (see White, ref 3).
A more accurate option is to adjust the hydraulic diameter with a friction factor ratio (see White, ref 3). The effective hydraulic diameter can then be used in the friction factor and HTC correlations.
The following table summarizes the relationship between the Dh based on 4*A/P and the effective hydraulic diameter.
Shape  Effective Dh Equation  Aspect Ratio (AR) 

Circle  $\frac{{Dh}_{eff}}{Dh}=1$  AR=1 
Rectangle

$\frac{{Dh}_{eff}}{Dh}=\frac{2}{3}+\frac{11}{24}*AR*(2AR)$  AR=b/a 
Ellipse  $\frac{{Dh}_{eff}}{Dh}=1.2109*{(1AR)}^{2}$  AR based on area and perimeter of the ellipse. 
Isosceles Triangle  $\frac{{Dh}_{eff}}{Dh}=\frac{64}{48+11.442*AR6.0026*{AR}^{2}}$  AR based on area and perimeter of the triangle.

Annulus

$\frac{{Dh}_{eff}}{Dh}=\frac{1+{AR}^{2}+\frac{\left(1{AR}^{2}\right)}{\mathrm{l}\mathrm{n}\left(AR\right)}}{{\left(1AR\right)}^{2}}$  AR=b/a 
Freeform (Arbitrary Shape) 
$\frac{{Dh}_{eff}}{Dh}=\frac{\sqrt{AR}*\left(1+AR\right)*\left(1\left(\frac{192}{{\pi}^{5}}\right)*AR*\mathrm{tanh}\left(\frac{\pi}{2*AR}\right)\right)}{.75*\frac{Dh}{\sqrt{Area}}}$  AR based on area and perimeter of freeform shape using a
rectangle equation. $AR=\frac{(P\sqrt{\left({P}^{2}16*A\right)})}{(P+\sqrt{\left({P}^{2}16*A\right)})}$ 
See Blevins (ref 15) and Muzychka et al. (ref 50) for additional information.
If the compressible tube, advanced orifice, and incompressible tube have a cross sectional shape that is not circular, the equations in this table are used for the effective hydraulic diameter equation.