Pressure drop calculator

Pressure drop calculator of turbulent pipe flow

pipe length $m$ pipe diameter $m$ wall roughness $mm$ fluid velocity $m/s$ fluid density $kg/m^3$ fluid viscosity $Pas$


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.


[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