# 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 $$\frac{\text{kg}}{\text{s}}?$$

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