Question

For a turbulent boundary layer (under zero pressure gradient), the velocity profile is described by the one-fifth power law. What is the ratio of displacement thickness to boundary layer thickness?

• A. 1/7
• B. 1/6
• C. 1/5
• D. 1/4

Answer 1

The correct option is B 1/6

$\frac{u}{u_{\infty }}={\left(\frac{y}{\delta }\right)}^{1/5}{\delta }^{\ast }={\int }_0^{\delta }[1-{\left(\frac{u}{u_{\infty }}\right)}^{1/5}]dy={\int }_0^{\delta }[1-{\left(\frac{y}{\delta }\right)}^{1/5}]dy=\delta -\frac{5\delta }{6}=\frac{\delta }{6}\frac{{\delta }^{\ast }}{\delta }=\frac{1}{6}$