# Hydraulic resistor as a constriction in a pipe

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etotheipi
Earlier I was trying to explain to one of my siblings why current is constant in a series connection (invoking that if it weren't we would have an accumulation of charge, etc.), however to give a more intuitive picture I tried to describe the hydraulic model of electric circuits, representing a resistor as a constriction in a pipe. The analogues of potential and current were fluid pressure and flow rate respectively.

However, on the spot I couldn't come up with a satisfactory explanation for the pressure (i.e. voltage) drop. If it is to behave like it's electrical analogue, we would expect a permanent drop in fluid pressure between both ends of the constriction. Yet as far as I am aware, if the cross-sectional areas of the pipe are equal before and after the constriction (and if we ignore changes in height), by Bernoulli's principle the pressures before and after the constriction should also be equal!

I reasoned that "turbulence effects" would result in the pressure drop, however this on its own doesn't lend itself particularly nicely to a neat calculation of the size of the pressure drop. I was wondering if I am on the right track here?

Dale
Mentor
2020 Award
This is one reason why the hydraulic analogy is so pointless to me. Fluid mechanics is much more complicated than circuits. I don’t like analogies that are more complicated than the thing they are explaining.

The derivation of Bernoulli’s principle assumes no losses due to friction, turbulence, or heat.

berkeman and etotheipi
jbriggs444
Homework Helper
I hesitate to promote the hydraulic analogy, but viscosity with laminar flow gives a nice predictable pressure drop according to Poiseuille's law.

[Of course, Poiseuille's law itself has no electrical analogue. To my knowledge, charge flow is not viscous]

etotheipi
yes there are pressure losses called variously shock, form, or unrecoverable losses. there are tables of values for standard fittings (elbows, tees, etc.) and valves. valve manufacturers will give this info in the form of Cv values.

anorlunda
Staff Emeritus
Both @jbriggs444 and @gmax137 helped to prove @Dale 's point. Analogies are supposed to be simpler. If they aren't simpler, they make very poor teaching tools.

Dale