As shown in the figure below, air flows in parallel to a freshly painted solid surface of width $10 \: m$, along the $z$-direction.
The equilibrium vapor concentration of the volatile component $A$ in the paint, at the air-paint interface, is $C_{A,i}$. The concentration $C_A$ decreases linearly from this value to zero along the $y$-direction over a distance $\delta$ of $0.1 \: m$ in the air phase. Over this distance, the average velocity of the air stream is $0.033 \: m s^{-1}$ and its velocity profile (in $m \: s^{-1}$) is given by $$v_z(y)=10y^2$$ where $y$ is in meter.
Let $C_{A, m}$ represent the flow averaged concentration. The ratio of $C_{A, m}$ to $C_{A, i}$, is __________ (round off to $2$ decimal places).