# Mass flow rate of a fluid with non-uniform density

**Classical Mechanics**Level 4

A strange fluid completely fills the pipe of radius \(r = 1\text{ m}\) through which it flows with speed \(v = \frac{1}{2-\ln 3} \frac{\text{m}}{\text{s}}.\) If the density varies radially according to \(\rho(r) = \frac{1000}{\pi (1 + 2r)},\) what is the mass flow rate in \(\frac{\text{kg}}{\text{s}}?\)