A square tube is open to air at atmospheric pressure on the top and capped with a porous membrane

on the bottom. The tube cross section is $L=1cm$ by $L=1cm.$ The porous membrane contains

$100$ vertically oriented cylindrical pores of diameter $d=0\mathrm{.}1mm.$ Surface tension holds a column

of water $(=0\mathrm{.}072\frac{N}{m})$ from falling through the membrane. The contact angle of water with

the tube is $20.$ The contact angle of water with the membrane pore walls is $180($as shown$)$ just

before the water column spills through the membrane. The membrane is $0\mathrm{.}01mm$ thick, over which

there is negligible hydrostatic pressure difference.

a$)$ Estimate the vertical capillary force by the tube on the water column.

b$)$ Estimate the vertical capillary force by a single membrane pore on the water column.

c$)$ Estimate the maximum water column height that the system can hold up$.$