Viscosity and Poiseuille Flow (4B) Practice Test

A student uses a syringe pump to generate steady laminar flow of a Newtonian fluid through a capillary. For a given trial, $\Delta P$, $r$, and $\eta$ are held constant while the student compares two capillary lengths: $L_1 = 4\ \text{cm}$ and $L_2 = 12\ \text{cm}$. Which statement is consistent with Poiseuille flow for the ratio of flow rates $Q_1/Q_2$?

In a microfluidics experiment, a Newtonian buffer is driven through a straight cylindrical glass capillary of length $L = 10\ \text{cm}$ and radius $r = 0.50\ \text{mm}$ under a constant pressure drop $\Delta P = 2.0\ \text{kPa}$. The flow is verified to be laminar and fully developed. The same capillary is then used with a second buffer at the same temperature, identical except its dynamic viscosity is doubled (from $\eta$ to $2\eta$). Based on Poiseuille flow, what change in volumetric flow rate $Q$ is expected under the same $\Delta P$, $L$, and $r$?