A liquid of viscosity \(0.456 \mathrm{~Pa} \cdot \mathrm{s}\) and mass density \(882 \mathrm{~kg} / \mathrm{m}^{3}\) flows through a pipe at a volume flow rate of \(2.00 \mathrm{~m}^{3} / \mathrm{s}\). You need to increase this rate to \(8.50 \mathrm{~m}^{3} / \mathrm{s}\) by adding to the liquid a substance that will change its viscosity but not appreciably affect its mass density.

(a) If nothing else (including the pressure difference) changes, what new viscosity value do you need in order to achieve the desired volume flow rate? What is the mass flow rate, in kilograms per second,

(b) before you change the viscosity and

(c) after you make the change?