Answer: flow = 1600 ml/min
Hi!
This problem si solved using Poiseuille law, which predicts the flow φ of a viscous fluid through a tube:
[tex]\phi = \frac{\pi r^4}{8\eta} \frac{\Delta P}{L}[/tex]
[tex]L = length\\r = radius\\\Delta P = \text{pressure gradient}\\\eta = viscosity[/tex]
We can calculate the ratio of initial (1) and final (2) flow. As we keep the same length, and viscosity, and pressure gradient the ratio is:
[tex]\frac{\phi_2}{\phi_1} = (\frac{r_2}{r_1} )^4 [/tex]
[tex]r_2 = 2r_1[/tex] (100% increase in radius)
[tex]\phi_2 = \phi_1 (\frac{r2}{r1}^4) = 100\frac{ml}{min} 2^4[/tex] = 1600 ml/min
