# 2.1.1 The Friction Velocity or Shear Velocity u*

The term friction velocity comes from the fact that √(τ12lhas the same unit as velocity and it has something to do with the friction force. The bottom shear stress τ12 is often represented by friction velocity u*, defined by:

$\ \mathrm{u}_{*}=\sqrt{\frac{\tau_{12}}{\rho_{\mathrm{l}}}}=\sqrt{\frac{\lambda_{\mathrm{l}}}{\mathrm{8}}} \cdot \mathrm{v}_{\mathrm{l}_{\mathrm{s}}}$

## 2.1.2 The Thickness of the Viscous Sub Layer $$\ \mathrm{\delta}_{\mathrm{v}}$$

Very close to the pipe wall the flow is laminar in the so called viscous sub layer. The thickness of the viscous sub layer is:

$\ \delta_{\mathrm{v}}=11.6 \cdot \frac{v_{1}}{\mathrm{u}_{*}} \\ \delta_{\mathrm{v}}^{+}=\frac{\delta_{\mathrm{v}} \cdot \mathrm{u}_{*}}{v_{\mathrm{l}}}=11.6$