Is it possible for the stream of liquid water to reach supersonic speeds?
A weak answer would be to move yourself at supersonic speeds. However, you might ask if liquid water could reach speeds greater than the speed of sound in water. The speed of sound in water (I think) is the maximum speed at which force can travel through the medium. Without applying pressure “everywhere” (i.e. like in a graviational field), you’d have to take into account the “speed” at which the pressure gradient reaches various points in the fluid. However, at high velocities, turbulent flow would form, greatly reducing the required pressure gradient. However, a pressure gradient would still exist even in turbulent flow, so I don’t think it would be possible to maintain a stream of water at supersonic speeds. Obviously the speed of sound in air could be reached. taking compressibility into account, I get the impression that you’d have to slow down liquid somewhere to get it to speed up someplace else, using compression forces to move the fluid faster.
