[UPSC CSE 2024] Mechanics of Continuous media (Q265, 10M)

Explain the Poiseuille's equation for the rate of flow of a liquid through a capillary tube. From this, show that if two capillary tubes of radii r_1 and r_2 having lengths l_1 and l_2, respectively, are connected in series, the rate of flow of the liquid is given by Q = \frac{\pi P}{8 \eta} \left( \frac{l_1}{r_1^4} + \frac{l_2}{r_2^4} \right)^{-1} where P is the pressure across the arrangement and \eta is the coefficient of viscosity of the liquid.