  Osmotically driven flow across a semi-permeable membrane under a constant
static pressure difference is revisited with referring to the previous reports
for reverse osmosis. A few mathematical techniques for obtaining the
approximate solution, such as that for inverse problems used in the field of
heat transfer, are presented with an emphasis on the nonlinear boundary
condition and the time-dependent solvent flow-rate. It is concluded that the
layer is spontaneously formed by osmosis rapidly in the time scaled by $\sim
{\rm O}\bigl(\sqrt{t}\bigr)$, and that the layer thickness grows with no upper
limit in an infinite time interval. Based on the obtained solution, we will
also discuss the thermodynamical output work in an irreversible process which
is extracted from the system as an osmotic engine.
