Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2014 / Paper 1 / A3 / Solution

Use $[\eta ]=M{L}^{-1}{T}^{-1}$ and $[dp/dx]=M{L}^{-2}{T}^{-2}$. Equating mass, length and time exponents giveshenceDimensional analysis leaves $k$ undetermined. If positive $Q$ denotes flow along increasing $x$, the signed pressure derivative is negative and its minus sign belongs in the proportionality constant; alternatively use the pressure-drop magnitude.