Actually, two questions:
- The existence of the sound:
The most common source of the flowing liquid sound is air bubbles popping. Surface waves (both over the open surface and inside the bubbles forming in the jet in less than spherical form) also create some sound.
Both of these phenomena are connected to the surface tension of the liquid/air interface and the viscosity of the liquid.
If you use hot oil (dangerous!) which is less viscous and has less surface tension, you can hear generally the same sound. You can as well hear that hot water (less viscosity and surface tension) makes different sound and a soapy water (less surface tension only, a lot of bubbles simply refuse to pop) is different, too.
- The sound pitch.
It is generally not a single pitch, but an open tube resonance. The noise of the popping bubbles just gets multiplied by the "tube" response. And, human ears are good at assigning a single pitch to a rather complex spectrum having equally separated maximums.