# Resistive divider hydraulics analogy, is this true?

The formulas for hydraulics and electricity are generally the same (theoretically), or for any type of flow. Air, water, hydraulic fluid, electrons... As shown on this website, a "hydraulic resistor" has a pressure drop across it equal to the supplied pressure from the pump. If two "hydraulic resistors" are connected in series, and they both have the same resistance to flow, will the pressure drop across each be half of the pressure from the pump? Solar Mike gave an answer that was very adamant that this is wrong. I am only interested in objectivity and what is right, but would be good to have some kind of proof provided as well. Otherwise anyone can claim something to be right, even when it is not. I will now eleborate on what I still think seems to be the case:

In Poiseuille's Law, if the resistance R doubles, the flow rate is cut in half. The resistance doubles if the radius decreases by 15%. Adding resistors in series, adds the resistances. To denote the resistance of each resistor, we can use R. The flow rate across the first resistor, is dependent on 2R. The pressure required to get the same flow across the second resistor, is half. If all pressure is converted to flow rate, and falls to zero at the end, it seems like this would cause a 50% pressure drop across the first resistor. This is also shown in another example I saw online, http://hyperphysics.phy-astr.gsu.edu/hbase/electric/watcir2.html, as mentioned in comment to Solar Mike.

With laminar flow (and some other assumptions like fully developed flow, everything at equilibrium, newtonian fluids, and uniform viscosity throughout the system), then Poiseuille's law applies and systems where the significant pressure drops come from straight tube geometry can be analyzed like electrical networks.

(pressure, flow) becomes analogous to (voltage, current).

"Resistance" then means pressure_drop / flow, for a straight segment with uniform diameter. That "R" is proportional to the tube's Length/Diameter^4.

• OK thanks. So there is 50% pressure drop? To understand the boundaries you describe, with water, in the boundaries of most standard hydraulic circuits, does the resistive divider analogy still apply? Occassionally it seems to upset some people, I just wonder if that is because it is wrong in some way, or they are passive aggressive about something else. I think the analogy is brilliant to understand electrical circuits, why I do not see why it is so controversial.
– Luke
Nov 7, 2021 at 15:02
• Re: your discussion with Solar Mike, I'd read the diagram a little differently than how I think(?) he did. The "0 kPa" suggests to me that the pressures marked on the tube restrictions are measured relative to the surface of the reservoir. So the pressure drops are around (300-150) and (150-0), ie around 150 each. With the L/D^4 scaling, the effects of all the other tubing become negligible, also depending on length, of course. Nov 7, 2021 at 15:47
• The voltage divider analogy, as well as stuff like Thevenin/Norton theorems can be used. If you can convince yourself that the equivalent of Ohm's law, and Kirchoff voltage and current laws, apply to a fluid network, that should lead to an informal proof I think. You can even have analogies to capacitance (elasticity and bulk modulus) and inductance (momentum of fluid), but it gets complicated. Both effects can be observed sometimes. Even with a "resistive" setup, all this analysis vs real world is often only a rough approximation though, because of other effects. Always good to measure. Nov 7, 2021 at 15:53
• It wasn't that I wanted to discuss, just that I wonder if hydraulics have same behaviour as electrical circuits. And, it seems to me like they do, so that's why I asked him about his answer, and was told that I can "assume what I want but I am wrong". The image I use was just an example, I only wonder if there is the same resistive divider effect, and it seems like there is. It is easier to grasp it with water than electrons, initially, because of scale and what eyes can see.
– Luke
Nov 7, 2021 at 16:46