Output of compressors connected in series.

As a purely hypothetical situation, in series your output would be closer to 100cfm at 895 psi! (assuming scfm; if you're talking cfm at pressure, it will be greatly reduced)

The reason is that both compressors have the same compression ratio and the ratio from atmospheric pressure to 100 psi will be matched again to go from 100 psi to final output. Ignoring temperature effects, Boyle's Law gives you the tool to calculate this: P₁V₁=P₂V₂. So (working in absolute pressures) 14.7psi * 1 = 114.7psi * V₂ or V₂=0.128 for a compression ratio of 7.8:1. Now, for the second compressor, you have: 114.7 psi * 1 = P₂ * 0.128 or P₂=895 psi! (subtract 14.7 for gauge pressure).

These are ideal, hypothetical calculations, (especially the part about ignoring temperature) but you get the idea. In reality, the initial P₁ will be slightly less than 14.7 psi due to the vacuum created to fill the compressor cylinder, and again you would see a pressure drop between the two compressors. This would actually result in a slightly higher compression ratio.

So, if this is something more than just a hypothetical question, don't try it! At best, the relief valve on the second compressor will open and you'll just be wasting energy. At worst you'll be trying to generate nearly 9 times the rated pressure in the second machine; that could be bad...very, very, bad.

As I read your post, I'm driven to the conclusion that you are trying to mathematically prove that successful multi-stage compression is not safely possible. Nothing could be further from the truth. In simple 2-stage air compressors of the two cylinder design, the second stage cylinder is roughly half the displacement of the first. Remember, in the original post that the compressor outputs are neither restricted or blocked. Therefore, the output of the first compressor can do nothing but pump air at roughly 1 atm to the input of the second. While I won't get into a dissertation on this, I did find your post rather crafty.

Apologies for my poor communication. I was not trying to be crafty. I was applying the math to a purely hypothetical, ideal setup without any losses. In no way was I trying to show that two-stage compression is impossible.

You are correct, since the second compressor will consume scfm at the same rate as the first compressor delivers scfm, all work of the first compressor will be lost. If the first compressor could get ahead of the second and deliver a supply of 100 psi volume to the second, the effects would be impressive. Having never assembled this arrangement, I'm trying to imagine the effects of placing a large receiver between the two compressors and allowing it to come to pressure before starting the second compressor...

Thanks for your interest.

No the problem was posed for casual observers, who might be tempted to make assumptions without a great deal of thought, based every day experience, like connecting batteries in series, you get double the volts, or resistors in series you get double the ohms, so why not double the pressure when two compressors compressors connected in series.

For those who know the basics, there is a bit more to it than that - as has been demonstrated by the various replies - for which I am grateful.

But it is still interesting to consider what would happen when two identical compressors are connected in series. To arrive at an answer assumptions have to made about the operating conditions, which for an ordinary compressor the max output pressure would be governed by an off-loading device - so each compressor would try to run 'normal', sometimes assisting each other, or fighting each other, depending on demand.

On balance nothing seems to have been achieved by such an arrangement.

It depends upon the system characteristics more than the compressors.

• Is there a relief valve that lifts at 120psi or will 150psi burst it?
• What load is there upon the system that might drag down the output to, say 200cfm at say 50psi?

Who can say?

It may not be possible to connect the compressors in series.

PWSlack is correct. But if the discharge were kept at 100 psig, the two units in series could move 210 CFM. It's based on the Volumetric Effciency of the piston compressor. VE is a function of compression ratios, the more ratios, the lower the VE becomes. So a 7.5" double acting, 3.5 inch stroke cylinder running at 1400 rpm, with a 0 to 100 psig compression (114/14=8.14 ratios) and a base clearance of 12.5% (whew) will have a VE of 41%.

When you connect a second one just like it in series the two will come to an equalibrium with the first stage going from 0 to 9 psig. This 1.65 ratios now allows the VE to increase to 89%, more than twice the efficency in volume. Beacuse the pressure is higher and the ratios lower in the second unit, it can move the larger volume and it VE is about 63%.

The reality is that no system will maintain exactly <...210 CFM> at <...100 psig...> for any length of time, if at all, which is why the system characteristic matters. The <...compressors...> will operate where their characteristic curve(s) intersect with the downstream piping and reservoir system characteristic curve.

• The electrical analogy is that, while two identical real-world zinc-carbon batteries wired in series will produce twice the voltage at zero current, putting a load onto the terminals will cause the voltage across them to drop. By how much is a function of the resistance, capacitance and inductance of the circuit to which they are connected.

No not unless the last compressor in your series can produce air at the volume of 100cfm @ 200psi.

If the 100cfm @ 200psi is the design limit of your compressor then when the first compressor fills the second compressor cylinder with 100psi air the motor will not have the force to compress the already pressurized air.

Also the first compressor would have to provide increased cfm about twice as much. As the compressors are reducing the volume of the air as they pressurize it.

I ran the case at 200 psig from above and you get exactly 200 cfm. It's just the way it worked out for the chosen cylinders.

Thanks all.

Two things arise. Bearing in mind that we are using gauge pressures, and 'cfm' refers the volume of air at atmospheric pressure.

The total output flow, regardless of pressure, cannot be more than the first compressor can suck into it's cylinder - the displacement.

The output pressure of the second compressor will the the back pressure of the system - which will not get much above 'zero' if there is nothing to restrict the flow.

Assuming the flow is restricted enough, the output pressure of the second compressor will keep rising.

The output pressure of the first compressor will settle to a value that gives each machine the same pressure ratio - which equates to a pressure equal to the sq.rt of the total output pressure - (use 'absolute' pressure when doing the sums.)

If left to run, the pressure will build up to a point (unless relieved or unloaded) where the second compressor will burst, stall, or burn out.

Am I right - or am I wrong.

Manufacturers of 2-stage compressors will know this - albeit the example used here was based on two separate compressors the same size - freewheeling so to speak.

The ratio across each WILL NOT BE EQUAL. As the Discharge pressure on the second unit rises, the pressure bewtween the two units will rise. If high pressure and high discharge tempoeratures were not a problem, the system would decrease in volume until it stalled when VE=0%.

You are probably right about the pressure ratio, it could be equal in some circumstances, but probably not, due to the 'circumstances' being rare and if they do happen, then unlikely to persist.

I am thinking in terms of free-wheeling compressors with pistons running exactly in phase (or exactly anti-phase) when the pressure in each cylinder is going from zero to max every cycle. The pressure wave being similar to a 'blunt' saw-tooth wave.

The intermediate pressure between compressors could be all over place, because in practice the load on each motor will affect the speed and therefore the cfm output of each compressor. The intermediate pressure will also depend on the clearance volume of each cylinder and volume of the interconnecting pipework.

Nevertheless, in ignorance of the theory, if you took two compressors and piped them in series and switched them on - something would happen - I wonder what.

My friend, the only way you are going to know is to do it- this is how most great discoveries were made(&are being made!) Happy Xmas to all.

One of the things that might happen is that the system safety pressure relief valve would lift. If one is not fitted then please make sure all other CR4 readers are a long way away from this equipment before so doing, otherwise there's an awful lot of paperwork to fill in when the contraption goes BANG!.

<...Assuming the flow is restricted enough,...> expresses the piping system characteristic curve suggested above.

The simple and most direct answer to your question is NO.