Could someone please help me with the following PDE problem?

The ends of a pipe of length L are attached to 2 reservoirs of concentrations u0 (left) and u1 (right). What is the steady state rate at which the chemical diffuses through the pipe?

I know that the steady does not depend on time i.e. du/dt = 0. However I do not know where to go from here. I know how to solve for the steady state solution, but the answer is rate = -D*pi*r^2[(u1-u0)/L]

Thanks in advance

Arlington