$7\mathrm{.}8$ Assuming that an acceptable error in the linear approximation for the velocity profile is $10\%,$ find the range of validity of Equation $(7\mathrm{.}6\mathrm{.}6).$ Use this result together with the criterion that $z\frac{D_{ij}}{v_{\text{m}\text{a}\text{x}}}{R}^2<mn>0</mn><mn>.</mn><mn>0</mn><mn>1</mn>$ to determine the smallest relative concentration that can be at the exit of a tube of length $L$ in order for the assumption to be valid.