The hydraulic pressure loss in a pipe is calculated here as follows, see White [2]:
\begin{equation} \Delta p = \frac{1}{2} f \rho u^2 \frac{L}{D} \label{eq:pressureloss} \end{equation}
in which $\Delta p$ is hydraulic pressure loss, $f$ is the friction factor, $\rho$ the density of a fluid and $u$ the veloci. Furthermore, $L$ and $D$ are the pipe length and diameter respectively. The friction factor $f$ in Eq. (\ref{eq:pressureloss}), according to Haaland [1], reads:
\begin{equation} \frac{1}{\sqrt{f}} = -1.8 log_{10}\left[\left(\frac{\varepsilon/D}{3.7}\right)+\frac{6.9}{Re}\right] \end{equation}
where $\varepsilon$ is the so-called roughness factor and $Re$ is the Reynolds number. This number reads:
\begin{equation} Re=\frac{\rho u D}{\mu} \end{equation}
in which $\mu$ is the molecular viscosity of the fluid.