The pure water flowrate $(F)$ through a disc shaped membrane $($diameter $7\mathrm{.}5cm)$ has been

measured as a function of applied pressure $(P=P_{\text{f}\text{e}\text{e}\text{d}}-P_{\text{p}\text{e}\text{r}\text{m}\text{e}\text{a}\text{t}\text{e}}).$ The following are the

experimental data:

$(1)$ Determine the water permeance $(P_{m,w})$ graphically;

$(2)$ If the active membrane layer thickness is $2m$ and the support resistance is negligible,

calculate the membrane's water permeability $(P_{b,w})$ and plot $P_{b,w}$ as a function of $P$;

$(3)$ What is the relationship between the $P_{b,w}$ and $P_{m,w}$ that you observe from the above

analyses?