GATE 2021 CH – Question 32

Consider a steady flow of an incompressible, Newtonian fluid through a smooth circular pipe. Let $\alpha_{laminar}$ and $\alpha_{turbulent}$ denote the kinetic energy correction factors for laminar and turbulent flow through the pipe, respectively. For turbulent flow, $\alpha_{turbulent}=\left(\frac{V_0}{\bar V}\right)^3\frac{2n^2}{(3+n)(3+2n)}$. Here, $\bar V$ is the average velocity, $V_0$ is the centerline velocity, and $n$ is a parameter. The ratio is given by $\bar V/V_0=\frac{2n^2}{(n+1)(2n+1)}$. For $n=7$, the value of $\alpha_{turbulent}/\alpha_{laminar}$ is _____ (round off to 2 decimal places).