The Reynolds Number is Calculated As

Question

The Reynolds number is calculated as A) 8$\eta$l / $\pi$r⁴ B) QV/$\Delta$P C) $\Delta$V / $\Delta$P D) 2 a v $\rho$ /$\eta$ E) $\pi$r⁴ / 8$\eta$l

Accepted Answer

The Reynolds number is a dimensionless quantity used in fluid mechanics to predict flow patterns in different fluid flow situations. It is calculated as $Re = \frac{\rho v L}{\mu}$ or $\frac{v L}{\nu}$, where $\rho$ is the density of the fluid, $v$ is the velocity of the fluid with respect to the object, $L$ is a characteristic linear dimension, $\mu$ is the dynamic viscosity of the fluid, and $\nu$ is the kinematic viscosity of the fluid ($\nu = \frac{\mu}{\rho}$). Option D, $2 a v \rho /\eta$, closely resembles the formula for Reynolds number, considering $2a$ could represent a characteristic dimension (like diameter), $v$ is the velocity, $\rho$ is the density, and $\eta$ is the dynamic viscosity ($\mu$ in the standard formula).