##
Pressure loss calculation

###
Short mathematical formulation

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.

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References

[1] Haaland, S.E.
*
Simple and Explicit Formulas for the Friction Factor in Turbulent Flow
*
Journal of Fluids Engineering 105,
**
1983
**
pp. 89–90

[2] White, F. M.
*
Fluid Mechanics
*
WCB McGraw-Hill,
**
1999
**