**PipeFlow_turbulent**

Procedure PipeFlow_turbulent (Re, Pr, LoverD, RelRough: Nusselt, f) returns the average Nusselt number and friction factor for a circular tube characterized by Reynolds and Prandtl numbers, length/diameter, and relative roughness. The Reynold's number is expected to be > 2300.

**Inputs:**

Re - Reynolds number based on properties evaluated at the bulk average temperature

Pr - Prandtl number of the fluid evaluated at the bulk average temperature

LoverD - ratio of tube length to diameter.

RelRough - the ratio of the dispersions on the wall of the tube to the tube diameter (must be between 0 and 0.05)

**Outputs:**

Nusselt - average Nusselt number

f - apparent friction factor [-]

**Notes**

The friction factor for a smooth tube is determined using the Li, Seem, and Li (2011) correlation.

The friction factor for a rough tube is determined using the Offor and Alabi (2016) correlation.

The effect of developing flow is accounted for by multiplying the fully developed value of the friction factor by (1+C/(LoverD)^m) where

C = 1 and m = 0.7.

If LoverD is less than 1, it is set to 1 since correlations for smaller values of LoverD are not available.

The Gnielinski correlation (1976) as reported in Section 5.2.4 of Nellis and Klein is used for turbulent flow with Pr>0.5. The correlation by Notter and Sleicher is used to for turbulent flow with Pr<0.1. These two values are interpolated for 0.1<Pr<0.5. .

The Chilton-Colburn analogy based on the Churchill friction factor is used for rough tubes.

The effect of developing flow is accounted for by multiplying the fully developed value of the Nusselt number by (1+C/(LoverD)^m) where

C = 1 and m = 0.7.