Power Law Velocity Profile

In many engineering calculations it is usual to employ a power law velocity profile given as

$$\frac {\overline{u}}{U} =\left( \frac {y}{R}\right )^{\frac{1}{n}}= \left ( 1 - \frac{r}{R} \right)^{\frac{1}{n}}$$ (7.35)

The exponent "n" is a function of Reynolds Number. However, n=7seems to be applicable to a wide range of pipe flows and is the one commonly used. It is referred to as "One seventh power law". The power law cannot be used to calculate the wall shear stress as it gives an infinite velocity gradient at the wall.

For a power law it can be shown that the ratio of average velocity to the centreline velocity is given by,

$$\frac {\overline{V}}{U} =\frac {2n^2} {(n+1)(2n+1)}$$ (7.36)

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney