Fizzicks (air pressure/volume)

[Cursitor Doom]

Gentlemen,

Say I'm running an air tool off my compressor via a 20m long airline with a 10mm internal diameter bore which connects, at the far end, to the tool via a 10mm ID coupling. Let's say this arrangement is *just* sufficient to run the tool at its full rated power. Now for whatever reason I change the coupling to one with say a 7mm ID instead, with everything else remaining unchanged. Will the tool's performance be negatively affected? Common sense would seem to suggest so at first sight, but is that actually the case?

[Bob Minchin]

Yes. You will have about 1/2 the cross sectional are of the pipe and to compound the problem a larger proportion of the air will be close to the walls of the pipe where the greatest friction will be experienced.

[newshound]

To a first approximation, you reduce the area by a factor of 2, so the flow rate by a factor of two, so the power by a factor of 2. I'd expect you to notice a significant drop in performance.

[Roger Hayter]

My vague recollection is that flow resistance goes up a lot faster than inversely to the square of the diameter. But I thought the OP was just changing the diameter of one coupling, and I don't think this will make much difference compared with the flow resistance of 20m of tubing.

[Cursitor Doom]

What I was getting at (or trying to) is the question of whether a restriction in the air line of a mere 30mm in length, say, in a much longer and wider air-line has the same debilitating effect on performance as if the whole length of the air-line was the same diameter as the 30mm long restriction? IOW, is an analogy with "a chain is only as strong as its weakest link" a valid one? Let me give another analogy from electronics to better illustrate the matter. Voltage regulator ICs in TO-220 package have very thin leads in relation to the current they're expected to be able to pass, but because these leads are only a few mm in length, currents of say 60A or more can be successfully accommodated, such accommodation being unrealistic in the extreme if these same leads were a couple of meters long. Sorry if this isn't very clear; got the neighbours' kids around here at the moment screaming and shouting making it hard to focus! :(

[Thomas Prufer]

No...

Yup. Length counts...

The analogy between flow and current, and voltage and pressure is valid, though the "resistors" in an ail line will be nonlinear.

Thomas Prufer

[John Rumm]

No. Flow resistance is a function of both diameter and length (and viscosity etc) - so a short length reduction to 7mm will not have anything like the effect that having the whole 20m at 7mm in place of the larger hose.

[Cursitor Doom]

Thanks John (and Thomas) for this confirmation. It's counterintuitive, but so are a lot of other things that turn out to be true! I was suspicious because I have an air tool here that states it should be connected to a 10mm ID hose via its 1/4" connector.

[Roger Hayter]

Any very slight advantage of having bigger connectors on tools requiring the airflow of a larger hose would be greatly outweighed by the inconvenience of having a different connector. There is very little loss of pressure using a standard connector. I suppose very big tools such as for breaking up roads might be an exception, but they seem to have bigger hoses than 10mm anyway.

[newshound]

I did say *to a first approximation* and the OP said he assumed performance was *only just* adequate with a 10 mm final orifice. You get a pressure drop (the exit loss) at the final orifice. Drop that orifice to half the area and the exit loss will increase, causing a reduction in flow and performance. Of course the device itself may have a similar internal restriction, in which case the coupling will make little difference. This is probably the basis of the suggestion about hose and coupling sizes.

[Cursitor Doom]

I know from personal experience when I'm using one of those giant 500ml 'syringes' to pump oil into a gearbox case that using a short flexi-tube into the 'box requires much less force than a longer tube does. But we cannot equate fluid mechanics to the laws relating to gases; one category is compressible, the other isn't!

[Roger Hayter]

Apart from the pedantic point that gases, as well as liquids, are fluids, I agree. But I think they are similar in that maximum flow (for a given pressure) goes up faster than the square of the diameter. I am unclear on the details.

[A_lurker]

As I recall (from 50 years ago) the flow rate varies inversely as the

4th power of the cross-sectional area, and directly as the length of the conduit. That's for _laminar_ flow in liquids though; I'd guess that the flow here may be turbulent, and we carefully avoided turbulent flow. I can believe that your gearbox oil would exhibit laminar flow though.

[newshound]

Compressibility effects only really kick in at high Mach number.

[Vir Campestris]

That's normally true, but we are dealing with a compressed air line here...

The fact that the length of line and diameter matter also imply a significant pressure change.

Andy

[Thomas Prufer]

Thought of a vivid electrical analogy: think thick copper cabling, short bit of thin wire (aka a fuse) in series.

Wouldn't work if it were all fuse wire, but does if done as usual.

Thomas Prufer

[A_lurker]

Tsk. ... _inversely_ as the length of the conduit. Must try harder.

[newshound]

Yes, so you need to use the density (and velocity of sound) in the fluid at pressure, but since the flow velocity will be *much* less than the speed of sound, you use the same equations for a gas or a liquid.

Agreed (though it *will* depend on the flow rate)

[Vir Campestris]

My fluid dynamics is all very much rule of thumb - and usually used thinking about boats, where compressibility _really_ doesn't come into it - but surely if the density varies (which it will with the pressure) this is going to make the temperature change too, with a corresponding effect on the viscosity?

So the constants in your equation will have to change along the line?

Andy

[newshound]

Compressibility is an important factor in aerodynamics. At low speeds, the compressibility of air is not significant in relation to aircraft design, but as the airflow nears and exceeds the speed of sound, a host of new aerodynamic effects become important in the design of aircraft. These effects, often several of them at a time, made it very difficult for World War II era aircraft to reach speeds much beyond 800 km/h (500 mph).

Taken from