  Direct and noninvasive measurement of the pressure distribution in test
sections of a micro-channel is a challenging, if not an impossible, task. Here,
we present an analytical method for extracting the pressure distribution in a
deformable micro-channel under flow. Our method is based on a measurement of
the channel deflection profile as a function of applied \emph{hydrostatic}
pressure; this initial measurement generates "constitutive curves" for the
deformable channel. The deflection profile under flow is then matched to the
constitutive curves, providing the \emph{hydrodynamic} pressure distribution.
The method is validated by measurements on planar micro-fluidic channels
against analytic and numerical models. The accuracy here is independent of the
nature of the wall deformations and is not degraded even in the limit of large
deflections, $\zeta_{\rm{max}}/2h_{0}= {\cal{O}}(1)$, with $\zeta_{\rm{max}}$
and $2h_0$ being the maximum deflection and the unperturbed height of the
channel, respectively. We discuss possible applications of the method in
characterizing micro-flows, including those in biological systems.
