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Engineering LibreTexts

2.1: Definitions

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  • 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:

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