# Hydraulic analogy and pressure in pipes

In the latest days I've been quite obsessed with understanding how electricity work through the hydraulic analogy.
I still have some problems regarding how "voltage drop" works, and how pressure drops after a restricted pipe ( it should make sense).
I've drew a little sketch to better expose my doubts: I imagined 2 vessels connected by a pipe. Since water should try to reach the same height in both vessels, I thought it could make a good example.
The highest vessel is continuosly alimented with new water, but the height is costant since water in excess naturally flows down by the sides.
Instead the water pouring out of the shortest vessel is collected, so that I can measure how much water flows through the pipe in a given time.
Since the height of the 2 vessels is constant, the difference in potential is also constant at the ends (we will waste some water since I'm not using a pump, so I'm sorry).
I'm curious to understand how to calculate the different pressure at the points A,B and C, given the heights of the vessels (H1 and h2) and the size of the pipe and of the restricted pipe (D1 and d2), to see if it does match the analogy with voltage, resistance and intensity?
If some other things are needed in order to calculate the different pressures, take them for granted.

## 1 Answer

The way I interpret your drawing, there are only two places with significant flow restriction--the constrictions between A/B and between B/C. Everywhere else, the flow can be assumed to be unrestricted. The pressure drops from A to B, and again from B to C.

As you probably know, this is an analogy for a circuit consisting of a battery and two resistors in series. The pressure is analogous to the electric potential (voltage), the flow rate of the water to the current.

The pressure at A is determined by gravity, the density of the water, and the height of the left-hand vessel. Same for the pressure at C with respect to the right-hand vessel. If the two restrictions are identical, the pressure at B is midway between that at A and C.

The details of how the details of the geometry of the restrictions determine the resistance to flow are complicated and not relevant to electricity.