An engineer conducted a hydro$-$mechanical analysis for an idealized water injection from a one$-$meter production zone located between $6\mathrm{.}5$ and $7\mathrm{.}5$ m$.$ In the analysis, the well pressure was kept at Pwell $=140$ kPa, the size of well was rc $=0\mathrm{.}1$ m$,$ the far$-$field boundary was set at r$\backslash$infty $=50$ m and the bottom end of the geometry was set at z $=30$ m$,$ where the pore pressure remained constant as the in$-$situ value.

Assuming this is a vertically one$-$dimensional condition near the well, what is the exit gradient, the hydraulic gradient at z $=0$ m$,$ at the steady$-$state?