# Do non-linear passive pneumatic throttles exist?

On of the more simple throttles is a channel, which is described by the Hagen-Poiseuille equation: $$\Delta P = \frac{8\mu L Q}{\pi r^4}$$ This equation, when rearranged, tells us that the Flowrate $Q$ is linearly dependent on $\Delta P$. Do passive non-linear pneumatic devices exist, which are not linearly dependent on $\Delta P$?

For example, is there a pneumatic equivalent to the Thermistor - which has a non-constant $R(U)$-dependency, and as such a nonlinear Flow vs Voltage curve?

• Well, above the Reynolds number, you'll go nonlinear, but probably not in a useful way. More to the point: can you post the problem you're trying to solve, rather than asking how to design the solution you've posited? Jun 17, 2016 at 12:20
• @CarlWitthoft In the application of interest, I want an approximate constant flowrate for a certain pressure range (e.g. 1-5 bar) through a device. I know there are devices that can accomplish that, but there are other constraints which wont allow me to use them. I think my question is a little too broad, I will rephrase it to be more specific.
– JHK
Jun 18, 2016 at 9:17
• When you rephrase the question, also include the solutions that won't work for you
– mart
Jun 21, 2016 at 7:04
• Give this link a look, might answer your question. If not, rephrase the question to look something like in this link: (engineering.stackexchange.com/questions/10733/…) Feb 16, 2017 at 14:21
• Well, a typical pressure regulator is entirely mechanical and produces constant output pressure for allowed range of input pressures; with constant output gas consumption you obtain constant flow.
– SF.
May 18, 2017 at 14:28

So you want a valve that, once set for a particular flow rate, gives the same flow rate for a variety of differential pressures? If so, I think the only thing you're going to get to do that is a constant flow valve. They're analog, but not exactly passive.

In the 'pass' direction it's very much linear per Hagen-Poiseuille equation. In the reverse direction for tiny $$\Delta P$$ it's linear, but as the pressure increases, the flow increase is vanishingly low. I'm not sure what the exact relation is in the inverse direction, but it's way far from linear - and the device is entirely passive, no moving parts whatsoever.

certainly. the most common example is the pressure/flow regulator in a drip irrigation system. It uses a thick rubber disc with a little hole through its center. Pressurized water hits the disc and flows through the hole in it towards the drip heads. But that pressure also deforms the rubber disc in such a way as to squeeze down the hole's diameter, choking off the flow through it. With cleverness, you can design the rubber disc so as to automatically furnish, say, a constant 5 gallons per hour over a range of water system pressures varying from 20 to 80 PSI- a very neat trick, eh?