Section: Fluid Mechanics | Marks: 2
Linked Answer Q.27 & Q.28: Consider a fully developed laminar flow in a pipe of radius $R$ in which $r$ and $x$ represent the radial and axial co-ordinates respectively. The axial velocity distribution is $u(r) = \left(\frac{-R^2}{4\mu}\frac{dp}{dx}\right)\left(1 - \frac{r^2}{R^2}\right)$ and the average axial velocity is $u_m = \left(\frac{-R^2}{8\mu}\frac{dp}{dx}\right)$. The local friction factor $C_f = \frac{\tau_{wall}}{0.5\rho u_m^2}$, with $\gamma = -\frac{dp}{dx}$ is given by
- A. $\frac{16\mu^2}{\rho R^3 \gamma}$
- B. $\frac{24\mu^2}{\rho R^3 \gamma}$
- C. $-\frac{R^2}{2\rho u_m^2}\frac{d^2p}{dx^2}$
- D. $\frac{64\mu^2}{\rho R^3 \gamma}$