Friction velocity

(Difference between revisions)

Latest revision as of 23:46, 7 December 2024

Dimensional analysis shows that at a wall a charateristic velocity, called the friction velocity, $u_*$ , can be defined in the following way:

$u_* \equiv \sqrt{\frac{\tau_w}{\rho}}$

Where $\tau_w$ is the wall shear stress and $\rho$ is the fluid density at the wall.

The friction velocity can also be computed from the Darcy friction factor:

$u_{\star} = U \cdot \sqrt{\frac{f}{8}}$

Where $U$ is the average velocity and $f$ is the Darcy friction factor.

@@ Line 1: / Line 1: @@
-Dimensional analysis shows that at a wall a charateristic velocity, called the ''friction velocity'', <math>u_*</math> can be defined in the following way:
+Dimensional analysis shows that at a wall a charateristic velocity, called the ''friction velocity'', <math>u_*</math>, can be defined in the following way:
 :<math>u_* \equiv \sqrt{\frac{\tau_w}{\rho}}</math>
-Where <math>\tau_w</math> is the wall shear stress and <math>\rho</math> is the fluid density at the wall.
+Where <math>\tau_w</math> is the [[Wall shear stress|wall shear stress]] and <math>\rho</math> is the fluid density at the wall.
+The friction velocity can also be computed from the [https://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation Darcy friction factor]:
+:<math>u_{\star} = U \cdot \sqrt{\frac{f}{8}}</math>
+Where <math>U</math> is the average velocity and <math>f</math> is the Darcy friction factor.