 Pipe Calculations
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Calculation of Friction Losses in Pipes
Friction losses in various pipes are calculated based on the fluid temperature.
Currently, only water and HCl are included as fluids in the calculations.
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 formula used is the Colebrook – White equation 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}
The friction loss occurring along the pipe is found from 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].
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