A barge is in a rectangular lock on a freshwater river. The lock has length $65\mathrm{.}0$ m long and $20\mathrm{.}0$ m wide, and the steel doors on each end are closed. With the barge floating in the lock, a $3\mathrm{.}00106$ N load of scrap metal is put onto the barge. The metal has density $7400$ kg$/$m$3.$ When the load of scrap metal, initially on the bank, is placed onto the barge, what vertical distance does the water in the lock rise?

Express your answer with the appropriate units.