In this paper, we first construct a model for transient free surface flows that takes into account the air entrainment by a sytem of 4 partial differential equations. We derive it by taking averaged values of gas and fluid velocities on the cross surface flow in the Euler equations (incompressible for the fluid and compressible for the gas). Then, we propose a mathematical kinetic interpretation of this system to finally construct a well-balanced kinetic scheme having the properties of conserving the still water steady state and possesing an energy. Finally, numerical tests on closed uniforms water pipes are performed and discussed.