A solution of \(13.5 \%\) by weight of polyisoprene has the following power-law parameters: \(\Lambda=5000 \mathrm{~Pa} \cdot \mathrm{s}^{n}\) and \(n=0.2\).

Consider the flow of such a solution in a pipe of internal diameter \(1 \mathrm{~cm}\) and length \(100 \mathrm{~cm}\). Calculate and plot the volumetric flow rate as a function of the imposed pressure difference across the pipe.

If the pipe diameter is doubled, how does the volumetric flow change?