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 magnitude of shear stress on the wall ($\tau_{wall}$) is
- A. $\frac{32\mu}{\rho u_m R}$
- B. $\frac{4\mu u_m}{R}$
- C. $\frac{\mu u_m}{R}$
- D. $-\frac{R^2}{4}\frac{d^2p}{dx^2}$