Friction Loss Calculation in Piping Systems

Explanation :
Reynolds Number (Formula \ref{Re}), \begin{equation}\label{Re} Re=\frac{vD}{\nu}=\frac{\rho vD}{\mu} \end{equation} \(Re\) is the Reynolds Number,
\(v\) is the velocity [m/s],
\(D\) is the inner diameter [m],
\(\nu\) is the kinematic viscosity [m²/s]
\(\rho\) is the density [kg/m³],
\(\mu\) is the dynamic viscosity [Pa.s]

Laminar flow in pipes \(Re<2500\) (Formula \ref{lam}), \begin{equation}\label{lam} f=\frac{64}{Re} \end{equation} The Colebrook–White equation is used for turbulent flow (Re> 4000).(Formula \ref{eu_Colebrook}) \begin{equation}\label{eu_Colebrook} \frac{1}{\sqrt{f }}=-2\log \left ( \frac{2.51}{Re\sqrt{f}}+\frac{\varepsilon /D}{3.71} \right ) \end{equation}
Friction loss along the pipe is calculated using the Darcy–Weisbach equation.
\begin{equation}\label{darcy} \displaystyle{h_{f}=f\displaystyle\frac{L}{D}\displaystyle\frac{v^{2}}{2g}} \qquad \text { mWG or }\qquad \displaystyle{\Delta P=f\displaystyle\frac{L}{D}\displaystyle\frac{\rho v^{2}}{2} }\quad \text { Pa} \end{equation} Here,
\( f\) is the dimensionless unit friction coefficient,
\( Re\) is the dimensionless reynolt number,
\(\varepsilon\) is the Roughness[m],
\(L\) is the pipe length[m],
\(\rho\) is the density [kg/m³].