# 2.1: Definitions

- Page ID
- 29269

# 2.1.1 The Friction Velocity or Shear Velocity u*

The term * friction velocity *comes from the fact that

**√(**

**τ**

_{12}

**/ρ**

_{l}

**)**has the same unit as velocity and it has something to do with the friction force. The bottom shear stress

**τ**

_{12}

**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 \]