I vaguely remember reading about a pneumatic (?) transistor that operated with air flow and no moving parts, but I can't find that anywhere. I don't mean the Tesla valve.
There was a whole field called fluidics that focused on performing operations analogous to those performed with electricity. This[0] gives a good overview of how fluidics worked. One the most commonly used elements of fluidics was the fluidic amplifier. This worked by using sideways flow of lower pressure to redirect a more powerful jet of fluid between two ports. Fluidic amplifiers could be made with frequency responses in the KHz range, so they have been used to amplify sound[1].
There was some brief interest in fluidics because it was cheap, more reliable than electronics of the time, and could function in extreme environments. So it found use in industrial automation and aircraft systems. This document[2] from NASA shows some applications it found at the time. Univac even built a completely fluidic 4 bit digital computer[3].
Fluidics is still around today, but used for very niche applications. One of the most absurd uses I've heard of was getting around rules prohibiting active aerodynamics in Formula 1. In 2010, the McLaren devised a system where the driver could cover a hole on part of the car, causing flow to be redirected to a fluidic amplifier that redirected flow over the rear spoilers causing them stall, allowing drag to be reduced on the straight aways. IIRC the entire purpose of the system was to get around rules which prohibited doing this with moving parts.
