This is a complex idea, and making it realistic is difficult, but I will try my best to help you.
Speed and size
We can identify two apparent issues : speed and size.
For speed, contrary to what the other response said, nerve signals are more than 10 times slower than the speed of sound for water, with a max speed of 120 m/s for nerve signals vs 1500 m/s for the speed of sound of water. Signals are thus able to propagate much faster in a fluidic system based on water. Speed is thus a non-issue.
About size, capillaries are extremely small, down to a few micrometers, but axons aren't much bigger, being a bit more than one micrometer in diameter. The size of capillaries is actually limited by the diameter of red blood cells, meaning it could be smaller in your case. We could thus get a similar density to human brain, maybe a little less dense
Signal representation
The ducts need to carry information. There are several ways to represent information with this kind of system : either the information is represented by the flow, the pressure, or the volume of liquid. This is similar to current (flow), voltage (pressure) or charge (volume) in electrical systems. I will personally use the pressure, because it is easier to apply a weight to (reducing a duct size will increase it resistance to flow), which is critical for neuron-like behavior.
Pseudo-neuron
Now, we need to have a neuron-like element that can perform computations the same way real neurons do. To make a long story short, there are many inputs that comes from previous neurons, and the strength of the connection varies depending on many factors. The input accumulates in the neuron as the membrane potential and, once a threshold is reached, there is a discharge that is propagated through the axon to the next neurons. The membrane potential decreases with time through leaking, and this is an important aspect of biological neurons. The image below illustrate the process :
Image source : self
To simulate this behavior, we could imagine a special structure, be it a cell or multiple cells, that acts as a kind of reservoir and accumulate the fluid inside it. Once the volume of the element reaches a certain point, a contraction is triggered, the input ducts closes during the contraction, and the output one opens. The signal is propagated to the next unit, and information is computed like that. All these pseudo-neurons could float in the fluid, allowing them to leak or pump from it. Obviously, this liquid must have the same pressure everywhere. Below a functional diagram of the imaginary pseudo-neuron :
Image source : self
The tubes must be padded by some kind of fat or soft material. This is because the signal, effectively a sound impulsion, would propagate through rigid material and interfere with everything else.
Energy and nutrient source
This is taken care by the fluid itself, which could carry the oxygen and nutrients needed for the cells to function.
Tradeoffs and issues
This brain would be a bit less dense that mammal brains, and sensitive to chocs and sounds. But it could be significantly faster, allowing for better reflexes. If you use a very low viscosity fluid instead of water, like hexane for example, it would be possible to have a higher density, but the nutrient wouldn't dissolve as well, and being filled with a flammable substance isn't always great.
The main issue isn't actually speed or size, it is the sensitivity to choc, sound, acceleration and anything that involve pressure changes. It would impact the brain, and this is a massive issue. Even simply standing up could cause problems.
Conclusion
It is possible, but very unlikely to evolve. But if you accept twisting a bit the reality, you could make it work.