When turn on a faucet, water fall down to a flat tub. Then a flat area surrounded by a circular boundary is formed and the boundary is just like a wall that separate the water outside and the relative dry area inside. can anyone explain it to me using fluid mechancs knowledge? It may also be a type-change example,i.e. elliptic & Hyperbolic type equations apply to each zone.

That circular wall of water is known as a "bore" and is described in many standard hydro texts.