Upwelling in the liquid region surrounding the keyhole in penetration welding with a laser

In penetration welding with a laser, the pressure in the keyhole is in excess at atmospheric pressure. A pressure gradient related to this is produced in the liquid region surrounding it, with the result that there is a flow parallel to the axis of the laser. The velocity of this flow is found as a function of the material constants, and the volume flow rate calculated. From this it is possible to construct an estimate of the elevation or depression of the surface of the weld. the shape of the surface cross section is discussed, and some deductions made about the pressure distribution in the liquid metal.